1
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Haseli G, Sheikh R, Ghoushchi SJ, Hajiaghaei-Keshteli M, Moslem S, Deveci M, Kadry S. An extension of the best-worst method based on the spherical fuzzy sets for multi-criteria decision-making. GRANULAR COMPUTING 2024; 9:40. [PMID: 38585422 PMCID: PMC10996092 DOI: 10.1007/s41066-024-00462-w] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 01/09/2024] [Accepted: 02/03/2024] [Indexed: 04/09/2024]
Abstract
The ambiguous information in multi-criteria decision-making (MCDM) and the vagueness of decision-makers for qualitative judgments necessitate accurate tools to overcome uncertainties and generate reliable solutions. As one of the latest and most powerful MCDM methods for obtaining criteria weight, the best-worst method (BWM) has been developed. Compared to other MCDM methods, such as the analytic hierarchy process, the BWM requires fewer pairwise comparisons and produces more consistent results. Consequently, the main objective of this study is to develop an extension of BWM using spherical fuzzy sets (SFS) to address MCDM problems under uncertain conditions. Hesitancy, non-membership, and membership degrees are three-dimensional functions included in the SFS. The presence of three defined degrees allows decision-makers to express their judgments more accurately. An optimization model based on nonlinear constraints is used to determine optimal spherical fuzzy weight coefficients (SF-BWM). Additionally, a consistency ratio is proposed for the SF-BWM to assess the reliability of the proposed method in comparison to other versions of BWM. SF-BWM is examined using two numerical decision-making problems. The results show that the proposed method based on the SF-BWM provided the criteria weights with the same priority as the BWM and fuzzy BWM. However, there are differences in the criteria weight values based on the SF-BWM that indicate the accuracy and reliability of the obtained results. The main advantage of using SF-BWM is providing a better consistency ratio. Based on the comparative analysis, the consistency ratio obtained for SF-BWM is threefold better than the BWM and fuzzy BWM methods, which leads to more accurate results than BWM and fuzzy BWM.
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Affiliation(s)
- Gholamreza Haseli
- Tecnologico de Monterrey, School of Engineering and Sciences, Monterrey, Mexico
- School of Architecture Planning and Environmental Policy, University College Dublin, Belfield, Dublin, D04 V1W8 Ireland
| | - Reza Sheikh
- Faculty of Industrial Engineering and Management, Shahrood University of Technology, Shahrood, Iran
| | | | | | - Sarbast Moslem
- School of Architecture Planning and Environmental Policy, University College Dublin, Belfield, Dublin, D04 V1W8 Ireland
| | - Muhammet Deveci
- Department of Industrial Engineering, Turkish Naval Academy, National Defence University, 34942 Tuzla, Istanbul, Turkey
- The Bartlett School of Sustainable Construction, University College London, 1-19 Torrington Place, London, WC1E 7HB UK
- Department of Electronical and Computer Engineering, Lebanese American University, Byblos, Lebanon
| | - Seifedine Kadry
- Department of Applied Data Science, Noroff University College, Kristiansand, Norway
- Artificial Intelligence Research Center (AIRC), Ajman University, 346 Ajman, United Arab Emirates
- MEU Research Unit, Middle East University, Amman, 11831 Jordan
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2
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Ajay D, Selvachandran G, Aldring J, Thong PH, Son LH, Cuong BC. Einstein exponential operation laws of spherical fuzzy sets and aggregation operators in decision making. MULTIMEDIA TOOLS AND APPLICATIONS 2023:1-24. [PMID: 37362734 PMCID: PMC10090759 DOI: 10.1007/s11042-023-14532-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/24/2021] [Revised: 05/21/2021] [Accepted: 01/31/2023] [Indexed: 06/28/2023]
Abstract
The spherical fuzzy set (SFS) model is one of the newly developed extensions of fuzzy sets (FS) for the purpose of dealing with uncertainty or vagueness in decision making. The aim of this paper is to define new exponential and Einstein exponential operational laws for spherical fuzzy sets and their corresponding aggregation operators. We introduce the operational laws for exponential and Einstein exponential SFSs in which the base values are crisp numbers and the exponents (weights) are spherical fuzzy numbers. Some of the properties and characteristics of the proposed operations are then discussed. Based on these operational laws, some new aggregation operators for the SFS model, namely Spherical Fuzzy Weighted Exponential Averaging (SFWEA) and Spherical Fuzzy Einstein Weighted Exponential Averaging (SFEWEA) operators are introduced. Finally, a decision-making algorithm based on these newly introduced aggregation operators is proposed and applied to a multi-criteria decision making (MCDM) problem related to ranking different types of psychotherapy.
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Affiliation(s)
- D. Ajay
- Department of Mathematics, Sacred Heart College, Tamilnadu, India
| | - Ganeshsree Selvachandran
- Institute of Actuarial Science and Data Analytics, UCSI University, Jalan Menara Gading, 56000 Cheras, Kuala Lumpur Malaysia
- Symbiosis Institute of Technology Symbiosis International University, Pune, 412115 India
| | - J. Aldring
- Department of Mathematics, Sacred Heart College, Tamilnadu, India
- Panimalar Engineering College, Department of Mathematics, Chennai, 600 123 Tamil Nadu India
| | - Pham Huy Thong
- VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam
| | - Le Hoang Son
- VNU Information Technology Institute, Vietnam National University, Hanoi, Vietnam
| | - Bui Cong Cuong
- Institute of Mathematics, Vietnam Academy of Science and Technology, Hanoi, Vietnam
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3
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Alamoodi AH, Zaidan BB, Albahri OS, Garfan S, Ahmaro IYY, Mohammed RT, Zaidan AA, Ismail AR, Albahri AS, Momani F, Al-Samarraay MS, Jasim AN, R.Q.Malik. Systematic review of MCDM approach applied to the medical case studies of COVID-19: trends, bibliographic analysis, challenges, motivations, recommendations, and future directions. COMPLEX INTELL SYST 2023; 9:1-27. [PMID: 36777815 PMCID: PMC9895977 DOI: 10.1007/s40747-023-00972-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/27/2022] [Accepted: 01/01/2023] [Indexed: 02/05/2023]
Abstract
When COVID-19 spread in China in December 2019, thousands of studies have focused on this pandemic. Each presents a unique perspective that reflects the pandemic's main scientific disciplines. For example, social scientists are concerned with reducing the psychological impact on the human mental state especially during lockdown periods. Computer scientists focus on establishing fast and accurate computerized tools to assist in diagnosing, preventing, and recovering from the disease. Medical scientists and doctors, or the frontliners, are the main heroes who received, treated, and worked with the millions of cases at the expense of their own health. Some of them have continued to work even at the expense of their lives. All these studies enforce the multidisciplinary work where scientists from different academic disciplines (social, environmental, technological, etc.) join forces to produce research for beneficial outcomes during the crisis. One of the many branches is computer science along with its various technologies, including artificial intelligence, Internet of Things, big data, decision support systems (DSS), and many more. Among the most notable DSS utilization is those related to multicriterion decision making (MCDM), which is applied in various applications and across many contexts, including business, social, technological and medical. Owing to its importance in developing proper decision regimens and prevention strategies with precise judgment, it is deemed a noteworthy topic of extensive exploration, especially in the context of COVID-19-related medical applications. The present study is a comprehensive review of COVID-19-related medical case studies with MCDM using a systematic review protocol. PRISMA methodology is utilized to obtain a final set of (n = 35) articles from four major scientific databases (ScienceDirect, IEEE Xplore, Scopus, and Web of Science). The final set of articles is categorized into taxonomy comprising five groups: (1) diagnosis (n = 6), (2) safety (n = 11), (3) hospital (n = 8), (4) treatment (n = 4), and (5) review (n = 3). A bibliographic analysis is also presented on the basis of annual scientific production, country scientific production, co-occurrence, and co-authorship. A comprehensive discussion is also presented to discuss the main challenges, motivations, and recommendations in using MCDM research in COVID-19-related medial case studies. Lastly, we identify critical research gaps with their corresponding solutions and detailed methodologies to serve as a guide for future directions. In conclusion, MCDM can be utilized in the medical field effectively to optimize the resources and make the best choices particularly during pandemics and natural disasters.
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Affiliation(s)
- A. H. Alamoodi
- Faculty of Computing and Meta-Technology (FKMT), Universiti Pendidikan Sultan Idris (UPSI), Perak, Malaysia
| | - B. B. Zaidan
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, Douliu, Yunlin 64002 Taiwan, ROC
| | - O. S. Albahri
- Computer Techniques Engineering Department, Mazaya University College, Nasiriyah, Iraq
| | - Salem Garfan
- Department of Computing, Faculty of Arts, Computing and Creative Industry, Universiti Pendidikan Sultan Idris, Tanjung Malim, Malaysia
| | - Ibraheem Y. Y. Ahmaro
- Computer Science Department, College of Information Technology, Hebron University, Hebron, Palestine
| | - R. T. Mohammed
- Department of Computing Science, Komar University of Science and Technology (KUST), Sulaymaniyah, Iraq
| | - A. A. Zaidan
- SP Jain School of Global Management, Sydney, Australia
| | - Amelia Ritahani Ismail
- Department of Computer Science, Kulliyyah of Information and Communication Technology, International Islamic University Malaysia, Kuala Lumpur, Malaysia
| | - A. S. Albahri
- Iraqi Commission for Computers and Informatics (ICCI), Baghdad, Iraq
| | - Fayiz Momani
- E-Business and Commerce Department, Faculty of Administrative and Financial Sciences, University of Petra, Amman, 961343 Jordan
| | - Mohammed S. Al-Samarraay
- Department of Computing, Faculty of Arts, Computing and Creative Industry, Universiti Pendidikan Sultan Idris, Tanjung Malim, Malaysia
| | | | - R.Q.Malik
- Medical Intrumentation Techniques Engineering Department, Al-Mustaqbal University College, Babylon, Iraq
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Almulhim T, Barahona I. An extended picture fuzzy multicriteria group decision analysis with different weights: A case study of COVID-19 vaccine allocation. SOCIO-ECONOMIC PLANNING SCIENCES 2023; 85:101435. [PMID: 36187871 PMCID: PMC9508697 DOI: 10.1016/j.seps.2022.101435] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/17/2022] [Revised: 05/19/2022] [Accepted: 09/12/2022] [Indexed: 06/16/2023]
Abstract
The high contagion rates of COVID-19 and the limited amounts of vaccines forced public health authorities to develop vaccinations strategies for minimizing mortality, avoiding the collapse of health care infrastructure, and reducing their negative impacts to societies and economies. We propose a Multi Criteria Group Decision Making for prioritizing a set of COVID-19 vaccination alternatives, under a picture fuzzy environment, where the weights for Decisions Experts (DE) and criteria are unknown. A panel of six DEs assess six criteria for prioritizing four groups for vaccination. The weights for DE and criteria are handled in the form of fuzzy sets. Three types of weights are calculated: subjective, objective, and mixture weights. According to our results, three out of the six criteria hold 60% of the strategic importance: 1) allocation and distribution, 2) COVID-19 strains and 3) capabilities and infrastructures. However, persons with comorbidities became the group with the highest priority, followed by essential workers, women, and adults older than 40 years. Governments, decision makers, and policy makers can find rigorous scientific evidence for articulating effective vaccinations campaigns from this work, and contribute to minimize undesired outputs, such as high mortality rates or collapse of hospitals.
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Affiliation(s)
- Tarifa Almulhim
- Department of Quantitative Methods, School of Business, King Faisal University, 31982, Al-Ahsa, Saudi Arabia
| | - Igor Barahona
- Department of Information Systems & Operations Management, Business School, King Fahad University of Petroleum and Minerals (KFUPM), Dhahran, Saudi Arabia
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Evolving deep convolutional neutral network by hybrid sine-cosine and extreme learning machine for real-time COVID19 diagnosis from X-ray images. Soft comput 2023; 27:3307-3326. [PMID: 33994846 PMCID: PMC8107782 DOI: 10.1007/s00500-021-05839-6] [Citation(s) in RCA: 27] [Impact Index Per Article: 27.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Accepted: 04/20/2021] [Indexed: 11/05/2022]
Abstract
The COVID19 pandemic globally and significantly has affected the life and health of many communities. The early detection of infected patients is effective in fighting COVID19. Using radiology (X-Ray) images is, perhaps, the fastest way to diagnose the patients. Thereby, deep Convolutional Neural Networks (CNNs) can be considered as applicable tools to diagnose COVID19 positive cases. Due to the complicated architecture of a deep CNN, its real-time training and testing become a challenging problem. This paper proposes using the Extreme Learning Machine (ELM) instead of the last fully connected layer to address this deficiency. However, the parameters' stochastic tuning of ELM's supervised section causes the final model unreliability. Therefore, to cope with this problem and maintain network reliability, the sine-cosine algorithm was utilized to tune the ELM's parameters. The designed network is then benchmarked on the COVID-Xray-5k dataset, and the results are verified by a comparative study with canonical deep CNN, ELM optimized by cuckoo search, ELM optimized by genetic algorithm, and ELM optimized by whale optimization algorithm. The proposed approach outperforms comparative benchmarks with a final accuracy of 98.83% on the COVID-Xray-5k dataset, leading to a relative error reduction of 2.33% compared to a canonical deep CNN. Even more critical, the designed network's training time is only 0.9421 ms and the overall detection test time for 3100 images is 2.721 s.
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Menekse A, Akdag HC. A novel interval-valued spherical fuzzy CODAS: Reopening readiness evaluation of academic units in the era of COVID-19. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-220468] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
Combinative distance-based assessment (CODAS) is a multi-criteria decision-making (MCDM) method that is based on the Euclidean and Hamming distances of alternatives from the average scores of attributes. Spherical fuzzy sets, as the recent extensions of ordinary fuzzy sets, were developed based on Pythagorean and neutrosophic sets and enable decision-makers to express their membership, non-membership, and hesitancy degrees independently and in a larger domain than most other fuzzy extensions. This paper proposes a new interval-valued spherical fuzzy CODAS method and provides extra space for catching the vagueness in the nature of the problem. The feasibility and practicality of the proposed model are illustrated with an application for evaluating the reopening readiness of academic units for campus education in the era of COVID-19. Three decision-makers from a higher education institution evaluate four academic units with respect to five strategic criteria and prioritize them according to their readiness levels for the campus type of education. Sensitivity and comparative analyses, theoretical and practical contributions, limitations, and future research avenues are also presented in the study.
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Affiliation(s)
| | - Hatice Camgoz Akdag
- Department of Management Engineering, Istanbul Technical University, Istanbul, Turkey
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7
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Rahman K, Khan H, Abdullah S. Mathematical calculation of COVID-19 disease in Pakistan by emergency response modeling based on complex Pythagorean fuzzy information. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2022. [DOI: 10.3233/jifs-212160] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Abstract
The new emerged infectious disease that is known the coronavirus disease (COVID-19), which is a high contagious viral infection that started in December 2019 in China city Wuhan and spread very fast to the rest of the world. This infection caused millions of infected cases globally and still poses an alarming situation for human lives. Pakistan in Asian countries is considered the third country with higher number of cases of coronavirus with more than 649824. Recently, some mathematical models have been constructed for better understanding the coronavirus infection. Mostly, these models are based on classical integer-order derivative using real numbers which cannot capture the fading memory. So at the current position it is a challenge for the world to understand and control the spreading of COVID-19. Therefore, the aim of our paper is to develop some novel techniques, namely complex Pythagorean fuzzy weighted averaging (abbreviated as CPFWA) operator, complex Pythagorean fuzzy ordered weighted averaging (abbreviated as CPFOWA) operator, complex Pythagorean fuzzy hybrid averaging (abbreviated as CPFHA) operator, induced complex Pythagorean fuzzy ordered weighted averaging (abbreviated as I-CPFOWA) operator and induced complex Pythagorean fuzzy hybrid averaging (abbreviated as I-CPFHA) operator to analysis the spreading of COVID-19. At the end of the paper, an illustrative the emergency situation of COVID-19 is given for demonstrating the effectiveness of the suggested approach along with a sensitivity analysis, showing the feasibility and reliability of its results.
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Affiliation(s)
- K. Rahman
- Department of Mathematics, Shaheed Benazir Bhutto University Sheringal, Pakistan
| | - H. Khan
- Department of Mathematics, Shaheed Benazir Bhutto University Sheringal, Pakistan
| | - S. Abdullah
- Department of Mathematics, Abdul Wali Khan University Mardan, Pakistan
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8
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An Improved EDAS Method for the Multi-Attribute Decision Making Based on the Dynamic Expectation Level of Decision Makers. Symmetry (Basel) 2022. [DOI: 10.3390/sym14050979] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Abstract
The improved evaluation based on the distance from average solution (EDAS) of the interval-valued intuitionistic trapezoidal fuzzy set is proposed. At first, we propose a new distance between interval-valued intuitionistic trapezoidal fuzzy numbers according to their interval endpoints and centroid point, and its properties are also discussed. Furthermore, we apply the proposed distance measure to calculate the expectation level of the emergency plan, and the optimal dynamic expectation level of the emergency plan is obtained by solving the programming model. Then, we improve the EDAS method based on the dynamic expectation level of the decision makers and apply it to calculate the optimal emergency plan. Finally, a numerical example about flood disaster rescue is given to verify the feasibility and effectiveness of the proposed method, which is also compared with the existing methods.
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Radulescu CZ, Radulescu M, Boncea R. A Multi-Criteria Decision Support and Application to the Evaluation of the Fourth Wave of COVID-19 Pandemic. ENTROPY (BASEL, SWITZERLAND) 2022; 24:642. [PMID: 35626527 PMCID: PMC9141305 DOI: 10.3390/e24050642] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/17/2022] [Revised: 04/28/2022] [Accepted: 04/30/2022] [Indexed: 12/10/2022]
Abstract
The COVID-19 pandemic caused important health and societal damage across the world in 2020-2022. Its study represents a tremendous challenge for the scientific community. The correct evaluation and analysis of the situation can lead to the elaboration of the most efficient strategies and policies to control and mitigate its propagation. The paper proposes a Multi-Criteria Decision Support (MCDS) based on the combination of three methods: the Group Analytic Hierarchy Process (GAHP), which is a subjective group weighting method; Extended Entropy Weighting Method (EEWM), which is an objective weighting method; and the COmplex PRoportional ASsessment (COPRAS), which is a multi-criteria method. The COPRAS uses the combined weights calculated by the GAHP and EEWM. The sum normalization (SN) is considered for COPRAS and EEWM. An extended entropy is proposed in EEWM. The MCDS is implemented for the development of a complex COVID-19 indicator called COVIND, which includes several countries' COVID-19 indicators, over a fourth COVID-19 wave, for a group of European countries. Based on these indicators, a ranking of the countries is obtained. An analysis of the obtained rankings is realized by the variation of two parameters: a parameter that describes the combination of weights obtained with EEWM and GAHP and the parameter of extended entropy function. A correlation analysis between the new indicator and the general country indicators is performed. The MCDS provides policy makers with a decision support able to synthesize the available information on the fourth wave of the COVID-19 pandemic.
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Affiliation(s)
- Constanta Zoie Radulescu
- National Institute for Research and Development in Informatics, 8-10, Mareşal Averescu, 011455 Bucharest, Romania; (C.Z.R.); (R.B.)
| | - Marius Radulescu
- “Gheorghe Mihoc-Caius Iacob” Institute of Mathematical Statistics and Applied Mathematics of the Romanian Academy, Calea 13 Septembrie, No. 13, 050711 Bucharest, Romania
| | - Radu Boncea
- National Institute for Research and Development in Informatics, 8-10, Mareşal Averescu, 011455 Bucharest, Romania; (C.Z.R.); (R.B.)
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Alsalem MA, Alamoodi AH, Albahri OS, Dawood KA, Mohammed RT, Alnoor A, Zaidan AA, Albahri AS, Zaidan BB, Jumaah FM, Al-Obaidi JR. Multi-criteria decision-making for coronavirus disease 2019 applications: a theoretical analysis review. Artif Intell Rev 2022; 55:4979-5062. [PMID: 35103030 PMCID: PMC8791811 DOI: 10.1007/s10462-021-10124-x] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
The influence of the ongoing COVID-19 pandemic that is being felt in all spheres of our lives and has a remarkable effect on global health care delivery occurs amongst the ongoing global health crisis of patients and the required services. From the time of the first detection of infection amongst the public, researchers investigated various applications in the fight against the COVID-19 outbreak and outlined the crucial roles of different research areas in this unprecedented battle. In the context of existing studies in the literature surrounding COVID-19, related to medical treatment decisions, the dimensions of context addressed in previous multidisciplinary studies reveal the lack of appropriate decision mechanisms during the COVID-19 outbreak. Multiple criteria decision making (MCDM) has been applied widely in our daily lives in various ways with numerous successful stories to help analyse complex decisions and provide an accurate decision process. The rise of MCDM in combating COVID-19 from a theoretical perspective view needs further investigation to meet the important characteristic points that match integrating MCDM and COVID-19. To this end, a comprehensive review and an analysis of these multidisciplinary fields, carried out by different MCDM theories concerning COVID19 in complex case studies, are provided. Research directions on exploring the potentials of MCDM and enhancing its capabilities and power through two directions (i.e. development and evaluation) in COVID-19 are thoroughly discussed. In addition, Bibliometrics has been analysed, visualization and interpretation based on the evaluation and development category using R-tool involves; annual scientific production, country scientific production, Wordcloud, factor analysis in bibliographic, and country collaboration map. Furthermore, 8 characteristic points that go through the analysis based on new tables of information are highlighted and discussed to cover several important facts and percentages associated with standardising the evaluation criteria, MCDM theory in ranking alternatives and weighting criteria, operators used with the MCDM methods, normalisation types for the data used, MCDM theory contexts, selected experts ways, validation scheme for effective MCDM theory and the challenges of MCDM theory used in COVID-19 studies. Accordingly, a recommended MCDM theory solution is presented through three distinct phases as a future direction in COVID19 studies. Key phases of this methodology include the Fuzzy Delphi method for unifying criteria and establishing importance level, Fuzzy weighted Zero Inconsistency for weighting to mitigate the shortcomings of the previous weighting techniques and the MCDM approach by the name Fuzzy Decision by Opinion Score method for prioritising alternatives and providing a unique ranking solution. This study will provide MCDM researchers and the wider community an overview of the current status of MCDM evaluation and development methods and motivate researchers in harnessing MCDM potentials in tackling an accurate decision for different fields against COVID-19.
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Affiliation(s)
- M. A. Alsalem
- Department of Computing, Faculty of Arts, Computing and Creative Industry (FSKIK), Universiti Pendidikan Sultan Idris, Tanjung Malim, Malaysia
| | - A. H. Alamoodi
- Department of Computing, Faculty of Arts, Computing and Creative Industry (FSKIK), Universiti Pendidikan Sultan Idris, Tanjung Malim, Malaysia
| | - O. S. Albahri
- Department of Computing, Faculty of Arts, Computing and Creative Industry (FSKIK), Universiti Pendidikan Sultan Idris, Tanjung Malim, Malaysia
| | - K. A. Dawood
- Department of Computing Science, Komar University of Science and Technology (KUST), Sulaymaniyah, Iraq
| | - R. T. Mohammed
- Department of Computing Science, Komar University of Science and Technology (KUST), Sulaymaniyah, Iraq
| | - Alhamzah Alnoor
- School of Management, Universiti Sains Malaysia, Pulau Pinang, Malaysia
| | - A. A. Zaidan
- Faculty of Engineering & IT, British, University in Dubia, Dubai, United Arab Emirates
| | - A. S. Albahri
- Informatics Institute for Postgraduate Studies (IIPS), Iraqi Commission for Computers and Informatics (ICCI), Baghdad, Iraq
| | - B. B. Zaidan
- Future Technology Research Center, National Yunlin University of Science and Technology, 123 University Road, Section 3, 64002 Douliou, Yunlin Taiwan
| | - F. M. Jumaah
- Department of Advanced Applications and Embedded Systems, Intel Corporation, Plot 6, Bayan Lepas Technoplex, 11900 Pulau Pinang, Malaysia
- Computer Engineering and Software Engineering Department, Polytechnique Montréal, Montréal, Canada
| | - Jameel R. Al-Obaidi
- Department of Biology, Faculty of Science and Mathematics, Universiti Pendidikan Sultan Idris, 35900 Perak, Tanjong Malim Malaysia
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11
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Ashraf S, Rehman N, Abdullah S, Batool B, Lin M, Aslam M. Decision support model for the patient admission scheduling problem based on picture fuzzy aggregation information and TOPSIS methodology. MATHEMATICAL BIOSCIENCES AND ENGINEERING : MBE 2022; 19:3147-3176. [PMID: 35240825 DOI: 10.3934/mbe.2022146] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
Health care systems around the world do not have sufficient medical services to immediately offer elective (e.g., scheduled or non-emergency) services to all patients. The goal of patient admission scheduling (PAS) as a complicated decision making issue is to allocate a group of patients to a limited number of resources such as rooms, time slots, and beds based on a set of preset restrictions such as illness severity, waiting time, and disease categories. This is a crucial issue with multi-criteria group decision making (MCGDM). In order to address this issue, we first conduct an assessment of the admission process and gather four (4) aspects that influence patient admission and design a set of criteria. Even while many of these indicators may be accurately captured by the picture fuzzy set, we use an advanced MCGDM approach that incorporates generalized aggregation to analyze patients' hospitalization. Finally, numerical real-world applications of PAS are offered to illustrate the validity of the suggested technique. The advantages of the proposed approaches are also examined by comparing them to various existing decision methods. The proposed technique has been proved to assist hospitals in managing patient admissions in a flexible manner.
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Affiliation(s)
- Shahzaib Ashraf
- Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, Khyber Pakhtunkhwa, Pakistan
| | - Noor Rehman
- Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, Khyber Pakhtunkhwa, Pakistan
| | - Saleem Abdullah
- Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Khyber Pakhtunkhwa, Pakistan
| | - Bushra Batool
- Department of Mathematics, University of Sargodha, Sargodha, Pakistan
| | - Mingwei Lin
- College of Computer and Cyber Security, Fujian Normal University, Fuzhou, China
| | - Muhammad Aslam
- Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia
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12
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Lotfi R, Kheiri K, Sadeghi A, Babaee Tirkolaee E. An extended robust mathematical model to project the course of COVID-19 epidemic in Iran. ANNALS OF OPERATIONS RESEARCH 2022:1-25. [PMID: 35013634 PMCID: PMC8732964 DOI: 10.1007/s10479-021-04490-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Accepted: 12/07/2021] [Indexed: 05/08/2023]
Abstract
This research develops a regression-based Robust Optimization (RO) approach to efficiently predict the number of patients with confirmed infection caused by the recent Coronavirus Disease (COVID-19). The main idea is to study the dynamics of the COVID-19 outbreak at the first stage and then provide efficient insights to estimate the necessary resources accordingly. The convex RO with Mean Absolute Deviation (MAD) objective function is utilized to project the course of COVID-19 epidemic in Iran. To validate the performance of the suggested model, a real-case study is investigated and compared to several well-known forecasting models including Simple Moving Average, Exponential Moving Average, Weighted Moving Average and Exponential Smoothing with Trend Adjustment models. Furthermore, the effect of parameter uncertainties is examined using a set of sensitivity analyses. The results demonstrate that by increasing the degree (coefficient) of regression up to 8, MAD value decreases to 1378.12, and consequently, the corresponding equation becomes more accurate. On the other hand, from the 8th degree onwards, MAD value follows an upward trend. Furthermore, by increasing the level of regression uncertainty, MAD value follows a downward trend to reach 1309.28 and the estimation accuracy of the model increases accordingly. Finally, our proposed model achieves the least MAD and the greatest correlation coefficient against the other models.
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Affiliation(s)
- Reza Lotfi
- Department of Industrial Engineering, Yazd University, Yazd, Iran
- Behineh Gostar Sanaye Arman, Tehran, Iran
| | - Kiana Kheiri
- Department of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
| | - Ali Sadeghi
- Department of Industrial Engineering, Yazd University, Yazd, Iran
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13
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Ozceylan E, Ozkan B, Kabak M, Dagdeviren M. A state-of-the-art survey on spherical fuzzy sets1. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-219186] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In addition to the well-known fuzzy sets, a novel type of fuzzy set called spherical fuzzy set (SFS) is recently introduced in the literature. SFS is the generalized structure over existing structures of fuzzy sets (intuitionistic fuzzy sets-IFS, Pythagorean fuzzy sets-PFS, and neutrosophic fuzzy sets-NFS) based on three dimensions (truth, falsehood, and indeterminacy) to provide a wider choice for decision-makers (DMs). Although the SFS has been introduced recently, the topic attracts the attention of academicians at a remarkable rate. This study is the expanded version of the authors’ earlier study by Ozceylan et al. [1]. A comprehensive literature review of recent and state-of-the-art papers is studied to draw a framework of the past and to shed light on future directions. Therefore, a systematic review methodology that contains bibliometric and descriptive analysis is followed in this study. 104 scientific papers including SFS in their titles, abstracts and keywords are reviewed. The papers are then analyzed and categorized based on titles, abstracts, and keywords to construct a useful foundation of past research. Finally, trends and gaps in the literature are identified to clarify and to suggest future research opportunities in the fuzzy logic area.
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Affiliation(s)
- Eren Ozceylan
- Industrial Engineering Department, Gaziantep University, Gaziantep, Turkey
| | - Baris Ozkan
- Industrial Engineering Department, Ondokuz Mayıs University, Samsun, Turkey
| | - Mehmet Kabak
- Industrial Engineering Department, Gazi University, Ankara, Turkey
| | - Metin Dagdeviren
- Industrial Engineering Department, Gazi University, Ankara, Turkey
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14
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Landfill Site Selection for Medical Waste Using an Integrated SWARA-WASPAS Framework Based on Spherical Fuzzy Set. SUSTAINABILITY 2021. [DOI: 10.3390/su132413950] [Citation(s) in RCA: 19] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
Abstract
Selecting suitable locations for the disposal of medical waste is a serious matter. This study aims to propose a novel approach to selecting the optimal landfill for medical waste using Multi-Criteria Decision-Making (MCDM) methods. For better considerations of the uncertainty in choosing the optimal landfill, the MCDM methods are extended by spherical fuzzy sets (SFS). The identified criteria affecting the selection of the optimal location for landfilling medical waste include three categories; environmental, economic, and social. Moreover, the weights of the 13 criteria were computed by Spherical Fuzzy Step-Wise Weight Assessment Ratio Analysis (SFSWARA). In the next step, the alternatives were analyzed and ranked using Spherical Fuzzy Weighted Aggregated Sum Product Assessment (SFWASPAS). Finally, in order to show the accuracy and validity of the results, the proposed approach was compared with the IF-SWARA-WASPAS method. Examination of the results showed that in the IF environment the ranking is not complete, and the results of the proposed method are more reliable. Furthermore, ten scenarios were created by changing the weight of the criteria, and the results were compared with the proposed method. The overall results were similar to the SF-SWARA-WASPAS method.
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15
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Gül S. Fermatean fuzzy set extensions of SAW, ARAS, and VIKOR with applications in COVID-19 testing laboratory selection problem. EXPERT SYSTEMS 2021; 38:e12769. [PMID: 34511690 PMCID: PMC8420344 DOI: 10.1111/exsy.12769] [Citation(s) in RCA: 10] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/08/2021] [Revised: 05/31/2021] [Accepted: 06/23/2021] [Indexed: 05/09/2023]
Abstract
The multiple attribute decision-making models are empowered with the support of fuzzy sets such as intuitionistic, q-rung orthopair, Pythagorean, and picture fuzzy sets, and also neutrosophic sets, etc. These concepts generate varying representation opportunities for the decision-maker's preferences and expertise. Pythagorean and Fermatean fuzzy sets are special cases of q-rung orthopair fuzzy set when q = 2 and q = 3, respectively. From a geometric perspective, the latter provides a broader representation domain than the former does. In this study, the emerging concept of Fermatean fuzzy set is studied in detail and three well-known multi-attribute evaluation methods, namely SAW, ARAS, and VIKOR are extended under Fermatean fuzzy environment. In this manner, the decision-makers will have more freedom in specifying their preferences, thoughts, and expertise, and the abovementioned decision approaches will be able to handle this new type of data. The applicability of the propositions is shown in determining the best Covid-19 testing laboratory which is an important topic of the ongoing global health crisis. To validate the proposed methods, a benchmark analysis covering the results of the existing Fermatean fuzzy set-based decision methods, namely TOPSIS, WPM, and Yager aggregation operators is presented.
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Affiliation(s)
- Sait Gül
- Faculty of Engineering and Natural Sciences, Management Engineering DepartmentBahçeşehir UniversityBeşiktaş, İstanbul34353Turkey
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16
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Ashraf S, Rehman N, Hussain A, AlSalman H, Gumaei AH. q-Rung Orthopair Fuzzy Rough Einstein Aggregation Information-Based EDAS Method: Applications in Robotic Agrifarming. COMPUTATIONAL INTELLIGENCE AND NEUROSCIENCE 2021; 2021:5520264. [PMID: 34751227 PMCID: PMC8572123 DOI: 10.1155/2021/5520264] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 07/31/2021] [Accepted: 09/27/2021] [Indexed: 11/17/2022]
Abstract
The main purpose of this manuscript is to present a novel idea on the q-rung orthopair fuzzy rough set (q-ROFRS) by the hybridized notion of q-ROFRSs and rough sets (RSs) and discuss its basic operations. Furthermore, by utilizing the developed concept, a list of q-ROFR Einstein weighted averaging and geometric aggregation operators are presented which are based on algebraic and Einstein norms. Similarly, some interesting characteristics of these operators are initiated. Moreover, the concept of the entropy and distance measures is presented to utilize the decision makers' unknown weights as well as attributes' weight information. The EDAS (evaluation based on distance from average solution) methodology plays a crucial role in decision-making challenges, especially when the problems of multicriteria group decision-making (MCGDM) include more competing criteria. The core of this study is to develop a decision-making algorithm based on the entropy measure, aggregation information, and EDAS methodology to handle the uncertainty in real-word decision-making problems (DMPs) under q-rung orthopair fuzzy rough information. To show the superiority and applicability of the developed technique, a numerical case study of a real-life DMP in agriculture farming is considered. Findings indicate that the suggested decision-making model is much more efficient and reliable to tackle uncertain information based on q-ROFR information.
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Affiliation(s)
- Shahzaib Ashraf
- Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, Khyber Pakhtunkhwa, Pakistan
| | - Noor Rehman
- Department of Mathematics and Statistics, Bacha Khan University, Charsadda 24420, Khyber Pakhtunkhwa, Pakistan
| | - Azmat Hussain
- Department of Mathematics and Statistics, International Islamic University, Isalambad, Pakistan
| | - Hussain AlSalman
- Department of Computer Science, College of Computer and Information Sciences, King Saud University, Riyadh 11543, Saudi Arabia
| | - Abdu H. Gumaei
- Computer Science Department, Faculty of Applied Sciences, Taiz University, Taiz 6803, Yemen
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17
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Ashraf S, Abdullah S, Chinram R. Emergency decision support modeling under generalized spherical fuzzy Einstein aggregation information. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021; 13:2091-2117. [PMID: 34603537 PMCID: PMC8475448 DOI: 10.1007/s12652-021-03493-2] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/29/2020] [Accepted: 09/06/2021] [Indexed: 06/13/2023]
Abstract
Dominant emergency action should be adopted in the case of an emergency situation. Emergency is interpreted as limited time and information, harmfulness and uncertainty, and decision-makers are often critically bound by uncertainty and risk. This framework implements an emergency decision-making approach to address the emergency situation of COVID-19 in a spherical fuzzy environment. As the spherical fuzzy set (SFS) is a generalized framework of fuzzy structure to handle more uncertainty and ambiguity in decision-making problems (DMPs). Keeping in view the features of the SFSs, the purpose of this paper is to present some robust generalized operating laws in accordance with the Einstein norms. In addition, list of propose aggregation operators using Einstein operational laws under spherical fuzzy environment are developed. Furthermore, we design the algorithm based on the proposed aggregation operators to tackle the uncertainty in emergency decision making problems. Finally, numerical case study of COVID-19 as an emergency decision making is presented to demonstrate the applicability and validity of the proposed technique. Besides, the comparison of the existing and the proposed technique is established to show the effectiveness and validity of the established technique.
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Affiliation(s)
- Shahzaib Ashraf
- Department of Mathematics and Statistics, Bacha Khan University, Charsadda, 24420 Khyber Pakhtunkhwa, Pakistan
| | - Saleem Abdullah
- Department of Mathematics, Abdul Wali Khan University, Mardan, 23200 Khyber Pakhtunkhwa, Pakistan
| | - Ronnason Chinram
- Department of Mathematics and Statistics, Faculty of Science, Prince of Songkla University, Hat Yai, Songkhla 90110 Thailand
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Khan A, Abosuliman SS, Ashraf S, Abdullah S. Hospital admission and care of COVID‐19 patients problem based on spherical hesitant fuzzy decision support system. INT J INTELL SYST 2021. [DOI: 10.1002/int.22455] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Aziz Khan
- Department of Mathematics Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa Pakistan
| | - Shougi S. Abosuliman
- Department of Supply Chain and Maritime Business, Faculty of Maritime Studies King Abdulaziz University Jeddah Saudi Arabia
| | - Shahzaib Ashraf
- Department of Mathematics and Statistics Bacha Khan University Charsadda, Khyber Pakhtunkhwa Pakistan
| | - Saleem Abdullah
- Department of Mathematics Abdul Wali Khan University Mardan, Khyber Pakhtunkhwa Pakistan
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Batool B, Abosuliman SS, Abdullah S, Ashraf S. EDAS method for decision support modeling under the Pythagorean probabilistic hesitant fuzzy aggregation information. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021; 13:5491-5504. [PMID: 33868508 PMCID: PMC8039808 DOI: 10.1007/s12652-021-03181-1] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/20/2020] [Accepted: 03/25/2021] [Indexed: 06/12/2023]
Abstract
The significance of emergency decision-making (EmDM) has been experienced recently due to the continuous occurrence of various emergency situations that have caused significant social and monetary misfortunes. EmDM assumes a manageable role when it is important to moderate property and live misfortunes and to reduce the negative effects on the social and natural turn of events. Genuine world EmDM issues are usually described as complex, time-consuming, lack of data, and the effect of mental practices that make it a challenging task for decision-makers. This article shows the need to manage the various types of vulnerabilities and to monitor practices to resolve these concerns. In clinical analysis, how to select an ideal drug from certain drugs with efficacy values for coronavirus disease has become a common problem these days. To address this issue, we are establishing a multi-attribute decision-making approach (MADMap) based on the EDAS method under Pythagorean probabilistic hesitant fuzzy information. In addition, an algorithm is developed to address the uncertainty in the selection of drugs in EmDM issues with regards to clinical analysis. The actual contextual analysis of the selection of the appropriate drug to treat coronavirus ailment is utilized to show the practicality of our proposed technique. Finally, with the help of a comparative analysis of the TOPSIS technique, we demonstrate the efficiency and applicability of the established methodology.
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Affiliation(s)
- Bushra Batool
- Department of Mathematics, University of Sargodha, Sargodha, Pakistan
| | - Shougi Suliman Abosuliman
- Department of Transportation and Port Management, Faculty of Maritime Studies, King Abdulaziz University, Jeddah, 21588 Saudi Arabia
| | - Saleem Abdullah
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Pakistan
| | - Shahzaib Ashraf
- Department of Mathematics and Statistics, Bacha Khan University, Charsadda, 24420 KP Pakistan
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20
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Khan A, Abosuliman SS, Abdullah S, Ayaz M. A Decision Support Model for Hotel Recommendation Based on the Online Consumer Reviews Using Logarithmic Spherical Hesitant Fuzzy Information. ENTROPY (BASEL, SWITZERLAND) 2021; 23:432. [PMID: 33917646 PMCID: PMC8067595 DOI: 10.3390/e23040432] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Revised: 03/22/2021] [Accepted: 03/23/2021] [Indexed: 11/17/2022]
Abstract
Spherical hesitant fuzzy sets have recently become more popular in various fields. It was proposed as a generalization of picture hesitant fuzzy sets and Pythagorean hesitant fuzzy sets in order to deal with uncertainty and fuzziness information. Technique of Aggregation is one of the beneficial tools to aggregate the information. It has many crucial application areas such as decision-making, data mining, medical diagnosis, and pattern recognition. Keeping in view the importance of logarithmic function and aggregation operators, we proposed a novel algorithm to tackle the multi-attribute decision-making (MADM) problems. First, novel logarithmic operational laws are developed based on the logarithmic, t-norm, and t-conorm functions. Using these operational laws, we developed a list of logarithmic spherical hesitant fuzzy weighted averaging/geometric aggregation operators to aggregate the spherical hesitant fuzzy information. Furthermore, we developed the spherical hesitant fuzzy entropy to determine the unknown attribute weight information. Finally, the design principles for the spherical hesitant fuzzy decision-making have been developed, and a practical case study of hotel recommendation based on the online consumer reviews has been taken to illustrate the validity and superiority of presented approach. Besides this, a validity test is conducted to reveal the advantages and effectiveness of developed approach. Results indicate that the proposed method is suitable and effective for the decision process to evaluate their best alternative.
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Affiliation(s)
- Aziz Khan
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan; (A.K.); (M.A.)
| | - Shougi S. Abosuliman
- Department of Transportation and Port Management, Faculty of Maritime Studies, King Abdulaziz University, Jeddah 21588, Saudi Arabia;
| | - Saleem Abdullah
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan; (A.K.); (M.A.)
| | - Muhammad Ayaz
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan 23200, Pakistan; (A.K.); (M.A.)
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21
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Almagrabi AO, Abdullah S, Shams M, Al-Otaibi YD, Ashraf S. A new approach to q-linear Diophantine fuzzy emergency decision support system for COVID19. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021; 13:1687-1713. [PMID: 33841585 PMCID: PMC8019990 DOI: 10.1007/s12652-021-03130-y] [Citation(s) in RCA: 11] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 07/27/2020] [Accepted: 03/09/2021] [Indexed: 06/12/2023]
Abstract
The emergency situation of COVID-19 is a very important problem for emergency decision support systems. Control of the spread of COVID-19 in emergency situations across the world is a challenge and therefore the aim of this study is to propose a q-linear Diophantine fuzzy decision-making model for the control and diagnose COVID19. Basically, the paper includes three main parts for the achievement of appropriate and accurate measures to address the situation of emergency decision-making. First, we propose a novel generalization of Pythagorean fuzzy set, q-rung orthopair fuzzy set and linear Diophantine fuzzy set, called q-linear Diophantine fuzzy set (q-LDFS) and also discussed their important properties. In addition, aggregation operators play an effective role in aggregating uncertainty in decision-making problems. Therefore, algebraic norms based on certain operating laws for q-LDFSs are established. In the second part of the paper, we propose series of averaging and geometric aggregation operators based on defined operating laws under q-LDFS. The final part of the paper consists of two ranking algorithms based on proposed aggregation operators to address the emergency situation of COVID-19 under q-linear Diophantine fuzzy information. In addition, the numerical case study of the novel carnivorous (COVID-19) situation is provided as an application for emergency decision-making based on the proposed algorithms. Results explore the effectiveness of our proposed methodologies and provide accurate emergency measures to address the global uncertainty of COVID-19.
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Affiliation(s)
- Alaa O. Almagrabi
- Department of Information Systems, Faculty of Computing and Information Technology, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
| | - Saleem Abdullah
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa Pakistan
| | - Maria Shams
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa Pakistan
| | - Yasser D. Al-Otaibi
- Department of Information Systems, Faculty of Computing and Information Technology in Rabigh, King Abdulaziz University, Jeddah, 21589 Saudi Arabia
| | - Shahzaib Ashraf
- Department of Mathematics, Abdul Wali Khan University Mardan, Mardan, Khyber Pakhtunkhwa Pakistan
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