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Quek SG, Garg H, Selvachandran G, Palanikumar M, Arulmozhi K, Smarandache F. VIKOR and TOPSIS framework with a truthful-distance measure for the ( t, s)-regulated interval-valued neutrosophic soft set. Soft comput 2023:1-27. [PMID: 37362303 PMCID: PMC10201540 DOI: 10.1007/s00500-023-08338-y] [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] [Accepted: 04/26/2023] [Indexed: 06/28/2023]
Abstract
This article introduces the structure of the ( t , s ) -regulated interval-valued neutrosophic soft set (abbr. ( t , s ) -INSS). The structure of ( t , s ) -INSS is shown to be capable of handling the sheer heterogeneity and complexity of real-life situations, i.e. multiple inputs with various natures (hence neutrosophic), uncertainties over the input strength (hence interval-valued), the existence of different opinions (hence soft), and the perception at different strictness levels (hence ( t , s ) -regulated). Besides, a novel distance measure for the ( t , s ) -INSS model is proposed, which is truthful to the nature of each of the three membership (truth, indeterminacy, falsity) values present in a neutrosophic system. Finally, a Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) and a Viekriterijumsko Kompromisno Rangiranje (VIKOR) algorithm that works on the ( t , s ) -INSS are introduced. The design of the proposed algorithms consists of TOPSIS and VIKOR frameworks that deploy a novel distance measure truthful to its intuitive meaning. The conventional method of TOPSIS and VIKOR will be generalized for the structure of ( t , s ) -INSS. The parameters t and s in the ( t , s ) -INSS model take the role of strictness in accepting a collection of data subject to the amount of mutually contradicting information present in that collection of data. The proposed algorithm will then be subjected to rigorous testing to justify its consistency with human intuition, using numerous examples which are specifically made to tally with the various human intuitions. Both the proposed algorithms are shown to be consistent with human intuitions through all the tests that were conducted. In comparison, all other works in the previous literature failed to comply with all the tests for consistency with human intuition. The ( t , s ) -INSS model is designed to be a conclusive generalization of Pythagorean fuzzy sets, interval neutrosophic sets, and fuzzy soft sets. This combines the advantages of all the three previously established structures, as well as having user-customizable parameters t and s , thereby enabling the ( t , s ) -INSS model to handle data of an unprecedentedly heterogeneous nature. The distance measure is a significant improvement over the current disputable distance measures, which handles the three types of membership values in a neutrosophic system as independent components, as if from a Euclidean vector. Lastly, the proposed algorithms were applied to data relevant to the ongoing COVID-19 pandemic which proves indispensable for the practical implementation of artificial intelligence.
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Affiliation(s)
- Shio Gai Quek
- Institute of Actuarial Science and Data Analytics, UCSI University, Jalan Menara Gading, 56000 Cheras, Kuala Lumpur, Malaysia
| | - Harish Garg
- Department of Mathematics, Thapar Institute of Engineering and Technology (Deemed University), Patiala, Punjab 147004 India
- Department of Mathematics, Graphic Era Deemed to be University, Dehra Dun, Uttarakhand 248002 India
- Applied Science Research Center, Applied Science Private University, Amman, 11931 Jordan
- College of Technical Engineering, The Islamic University, Najaf, Iraq
| | - 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
| | - M. Palanikumar
- Department of Mathematics, Saveetha School of Engineering, SIMATS, Chennai, 602105 India
| | - K. Arulmozhi
- Department of Mathematics, Bharath Institute of Higher Education and Research (Deemed University), Chennai, 600073 India
| | - Florentin Smarandache
- Department of Mathematics, University of New Mexico, 705 Gurley Avenue, Gallup, NM 87301 USA
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Prioritization of thermal energy techniques by employing picture fuzzy soft power average and geometric aggregation operators. Sci Rep 2023; 13:1707. [PMID: 36717612 PMCID: PMC9887075 DOI: 10.1038/s41598-023-27387-9] [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: 10/19/2022] [Accepted: 01/02/2023] [Indexed: 02/01/2023] Open
Abstract
Energy storage is a way of storing energy to reduce imbalances between demand and energy production. The ability to store electricity and use it later is one of the keys to reaching large quantities of renewable energy on the grid. There are several methods to store energy such as mechanical, electrical, chemical, electrochemical, and thermal energy. Regarding their operation, storage, and cost, the choice of these energy storage techniques appears to be interesting. This issue becomes very serious when there involves uncertainty. To consider this kind of uncertain information, a picture fuzzy soft set is found to be a more appropriate parameterization tool to deal with imprecise data. Based on the advanced structure of picture fuzzy soft set, here in this article, firstly, we have developed the notions of basic operational laws for picture fuzzy soft numbers. Then based on these developed operational laws, we have established the notions of picture fuzzy soft power average [Formula: see text], weighted picture fuzzy soft power average [Formula: see text] and ordered weighted picture fuzzy soft power average [Formula: see text] aggregation operators. Moreover, we have introduced the notions for picture fuzzy soft power geometric [Formula: see text], weighted picture fuzzy soft power geometric [Formula: see text] and ordered weighted picture fuzzy soft power geometric [Formula: see text] aggregation operators. Furthermore, we have established the application of picture fuzzy soft power aggregation operators for the selection of thermal energy storage techniques. For this, we have developed a decision-making approach along with an explanatory example to show the effective use of the developed theory. Furthermore, a comparative analysis of the introduced work shows the advancement of developed notions.
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A framework for choosing an appropriate fuzzy set extension in modeling. APPL INTELL 2022. [DOI: 10.1007/s10489-022-04244-2] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
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4
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Inspection of the Production Lot Using Two Successive Occasions Sampling Under Neutrosophy. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-022-00071-y] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractThe efficiency of the measuring tools and operators is a significant part of lot sentencing decisions. These tools have to pass some pre-specified quality levels to avoid problems during the quality assessment scenarios. These measurements have a serious risk to be encountered with any extent of ambiguity, doubt, or indeterminacy due to any of the factors like variation among the operating regimes, warming effects in the hot climatic conditions, the operators’ casual attitude, and so on. These factors as the most significant sources of extraneous variations can deeply affect the efficacy of lot sentencing decisions. Hence, the decision when based on the measurement through the operating tools and these tools have to pass which have fulfilled some adequate standards only then lot sentencing may avoid or save from the rejection of a good lot. The authors have put their focus on dealing with the factors that arise by measuring variability among the measured or determined values despite having the normal population distribution. In this study, the auxiliary information is used to estimate the variable of interest over the two successive occasions under the neutrosophic interval numbers and proved helpful to overcome this issue. The presented approach has discussed that in blurred, doubted, uncertain and undetermined datasets partially or completely, the efficacy of the decision for the whole lot cannot be decided on the single point crisped value. But the range of values around such a single crisp point in the form of neutrosophic theory is proved far better. In this context, the neutrosophic interval number successive sampling-based sampling plan is proposed which is the major contribution to the existing literature. It is explained in terms of operating characteristic function and the plan parameters are determined through the neutrosophic non-linear optimization approach. The comparative analysis is presented with the existing sampling plans and found efficient. Moreover, a real-life industrial dataset is used as an application of the concept.
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Hermite–Hadamard Type Inequalities for Interval-Valued Preinvex Functions via Fractional Integral Operators. INT J COMPUT INT SYS 2022. [DOI: 10.1007/s44196-021-00061-6] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022] Open
Abstract
AbstractIn this article, the notion of interval-valued preinvex functions involving the Riemann–Liouville fractional integral is described.
By applying this, some new refinements of the Hermite–Hadamard inequality for the fractional integral operator are presented. Some novel special cases of the presented results are discussed as well. Also, some examples are presented to validate our results. The established outcomes of our article may open another direction for different types of integral inequalities for fractional interval-valued functions, fuzzy interval-valued functions, and their associated optimization problems.
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Aslam M, Sherwani RAK, Saleem M. Vague data analysis using neutrosophic Jarque-Bera test. PLoS One 2021; 16:e0260689. [PMID: 34855840 PMCID: PMC8638977 DOI: 10.1371/journal.pone.0260689] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 11/16/2021] [Indexed: 11/28/2022] Open
Abstract
In decision-making problems, the researchers’ application of parametric tests is the first choice due to their wide applicability, reliability, and validity. The common parametric tests require the validation of the normality assumption even for large sample sizes in some cases. Jarque-Bera test is among one of the methods available in the literature used to serve the purpose. One of the Jarque-Bera test restrictions is the computational limitations available only for the data in exact form. The operational procedure of the test is helpless for the interval-valued data. The interval-valued data generally occurs in situations under fuzzy logic or indeterminate state of the outcome variable and is often called neutrosophic form. The present research modifies the existing statistic of the Jarque-Bera test for the interval-valued data. The modified design and operational procedure of the newly proposed Jarque-Bera test will be useful to assess the normality of a data set under the neutrosophic environment. The proposed neutrosophic Jarque-Bera test is applied and compared with its existing form with the help of a numerical example of real gold mines data generated under the fuzzy environment. The study’s findings suggested that the proposed test is effective, informative, and suitable to be applied in indeterminacy compared to the existing Jarque–Bera test.
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Affiliation(s)
- Muhammad Aslam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, Saudi Arabia
- * E-mail:
| | | | - Muhammad Saleem
- Department of Industrial Engineering, Faculty of Engineering-Rabigh, King Abdulaziz University, Jeddah, Saudi Arabia
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Khan MJ, Ali MI, Kumam P, Kumam W, Aslam M, Alcantud JCR. Improved generalized dissimilarity measure‐based VIKOR method for Pythagorean fuzzy sets. INT J INTELL SYST 2021. [DOI: 10.1002/int.22757] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023]
Affiliation(s)
- Muhammad Jabir Khan
- KMUTT Fixed Point Research Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT), Thung Khru Bangkok Thailand
| | | | - Poom Kumam
- KMUTT Fixed Point Research Laboratory, Science Laboratory Building, Department of Mathematics, Faculty of Science King Mongkut's University of Technology Thonburi (KMUTT), Thung Khru Bangkok Thailand
- Center of Excellence in Theoretical and Computational Science (TaCS‐CoE), SCL 802 Fixed Point Laboratory, Science Laboratory Building King Mongkut's University of Technology Thonburi (KMUTT), Thung Khru Bangkok Thailand
- Department of Medical Research, China Medical University Hospital China Medical University Taichung Taiwan
| | - Wiyada Kumam
- Applied Mathematics for Science and Engineering Research Unit (AMSERU), Program in Applied Statistics, Department of Mathematics and Computer Science, Faculty of Science and Technology Rajamangala University of Technology Thanyaburi (RMUTT) Thanyaburi Pathum Thani Thailand
| | - Muhammad Aslam
- Department of Mathematics, College of Sciences King Khalid University Abha Saudi Arabia
| | - Jose Carlos R. Alcantud
- BORDA Research Unit and Multidisciplinary Institute of Enterprise (IME) University of Salamanca Salamanca Spain
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A New X-bar Control Chart for Multiple Dependent State Sampling Using Neutrosophic Exponentially Weighted Moving Average Statistics with Application to Monitoring Road Accidents and Road Injuries. INT J COMPUT INT SYS 2021. [DOI: 10.1007/s44196-021-00033-w] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022] Open
Abstract
AbstractIn this article, an efficient mean chart for symmetric data have been presented for multiple dependent state (MDS) sampling using neutrosophic exponentially weighted moving average (NEWMA) statistics. The existing neutrosophic exponentially weighted moving average charts are not capable of seizure the unusual changes threatened to the manufacturing processes. The control chart coefficients have been estimated using the symmetry property of the Gaussian distribution for the uncertain environment. The neutrosophic Monte Carlo simulation methodology has been developed to check the efficiency and performance of the proposed chart by calculating the neutrosophic average run lengths and neutrosophic standard deviations. The proposed chart has been compared with the counterpart charts for confirmation of the proposed technique and found to be a robust chart.
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9
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Akram M, Shahzadi G, Butt MA, Karaaslan F. A hybrid decision making method based on q-rung orthopair fuzzy soft information. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-202336] [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
Soft set (SfS) theory is a basic tool to handle vague information with parameterized study during the process as compared to fuzzy as well as q-rung orthopair fuzzy theory. This research article is devoted to establish some general aggregation operators (AOs), based on Yager’s norm operations, to cumulate the q-rung orthopair fuzzy soft data in decision making environments. In this article, the valuable properties of q-rung orthopair fuzzy soft set (q - ROFSfS) are merged with the Yager operator to propose four new operators, namely, q-rung orthopair fuzzy soft Yager weighted average (q - ROFSfYWA), q-rung orthopair fuzzy soft Yager ordered weighted average (q - ROFSfYOWA), q-rung orthopair fuzzy soft Yager weighted geometric (q - ROFSfYWG) and q-rung orthopair fuzzy soft Yager ordered weighted geometric (q - ROFSfYOWG) operators. The dominant properties of proposed operators are elaborated. To emphasize the importance of proposed operators, a multi-attribute group decision making (MAGDM) strategy is presented along with an application in medical diagnosis. The comparative study shows superiorities of the proposed operators and limitations of the existing operators. The comparison with Pythagorean fuzzy TOPSIS (PF-TOSIS) method shows that PF-TOPSIS method cannot deal with data involving parametric study but developed operators have the ability to deal with decision making problems using parameterized information.
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Affiliation(s)
- Muhammad Akram
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - Gulfam Shahzadi
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - Muhammad Arif Butt
- Department of Mathematics, Punjab University College of Information Technology, University of the Punjab, Old Campus, Lahore, Pakistan
| | - Faruk Karaaslan
- Department of Mathematics, Faculty of Sciences, Çankırı Karatekin University, Çankırı, Turkey
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10
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Islam SR, Pal M. First Zagreb index on a fuzzy graph and its application. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-201293] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The Zagreb index (ZI) is a very important graph parameter and it is extensively used in molecular chemistry, spectral graph theory, network theory and several fields of mathematics and chemistry. In this article, the first ZI is studied for several fuzzy graphs like path, cycle, star, fuzzy subgraph, etc. and presented an ample number of results. Also, it is established that the complete fuzzy graph has maximal first ZI among n-vertex fuzzy graphs. Some bounds of first ZI are discussed for Cartesian product, composition, union and join of two fuzzy graphs. An algorithm has been designed to calculate the first ZI of a fuzzy graph. At the end of the article, a multi-criteria decision making (MCDM) method is provided using the first ZI of a fuzzy graph to find the best employee in a company. Also a comparison is provided among related indices on the result of application and shown that our method gives better results.
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Affiliation(s)
- Sk Rabiul Islam
- Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
| | - Madhumangal Pal
- Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, India
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11
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Chutia R, Gogoi MK, Firozja MA, Smarandache F. Ordering single‐valued neutrosophic numbers based on flexibility parameters and its reasonable properties. INT J INTELL SYST 2021. [DOI: 10.1002/int.22362] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023]
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12
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Jana C, Muhiuddin G, Pal M. Multi-criteria decision making approach based on SVTrN Dombi aggregation functions. Artif Intell Rev 2021. [DOI: 10.1007/s10462-020-09936-0] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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13
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Jana C, Pal M. Multi-criteria decision making process based on some single-valued neutrosophic Dombi power aggregation operators. Soft comput 2021. [DOI: 10.1007/s00500-020-05509-z] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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14
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Shahzadi G, Akram M. Group decision-making for the selection of an antivirus mask under fermatean fuzzy soft information. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-201760] [Citation(s) in RCA: 23] [Impact Index Per Article: 7.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
With the rapid increase of COVID-19, mostly people are facing antivirus mask shortages. It is necessary to select a good antivirus mask and make it useful for everyone. For maximize the efficacy of the antivirus masks, we propose a decision support algorithm based on the concept of Fermatean fuzzy soft set (FFSfS). The basic purpose of this article is to introduce the notion of FFSfS to deal with problems involving uncertainty and complexity corresponding to various parameters. Here, the valuable properties of FFSfS are merged with the Yager operator to propose four new operators, namely, Fermatean fuzzy soft Yager weighted average (FFSfYWA), Fermatean fuzzy soft Yager ordered weighted average (FFSfYOWA), Fermatean fuzzy soft Yager weighted geometric (FFSfYWG) and Fermatean fuzzy soft Yager ordered weighted geometric (FFSfYOWG) operators. The fundamental properties of proposed operators are discussed. For the importance of proposed operators, a multi-attribute group decision-making (MAGDM) strategy is presented along with an application for the selection of an antivirus mask over the COVID-19 pandemic. The comparison with existing operators shows that existing operators cannot deal with data involving parametric study but developed operators have the ability to deal decision-making problems using parameterized information.
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Affiliation(s)
- Gulfam Shahzadi
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
| | - Muhammad Akram
- Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
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15
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Medical diagnostic process based on modified composite relation on pythagorean fuzzy multi-sets. GRANULAR COMPUTING 2021. [DOI: 10.1007/s41066-020-00248-w] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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16
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Peng X, Smarandache F. A decision-making framework for China’s rare earth industry security evaluation by neutrosophic soft CoCoSo method. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-200847] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
The rare earth industry is a crucial strategic industry that is related to the national economy and national security. In the context of economic globalization, international competition is becoming increasingly fierce, and the rare earth industry is facing a more severe survival and development environment than ever before. Although China is the greatest world’s rare earth country in rare earth reserves, production, consumption and export volume, it is not a rare earth power. The rare earth industry has no right to speak in the international market. The comparative advantage is weakening and the security of rare earth industry appears. Therefore, studying the rare earth industry security has important theoretical and practical significance. When measuring the China’s rare earth industry security, the primary problem involves tremendous uncertainty. Neutrosophic soft set (NSS), depicted by the parameterized form of truth membership, falsity membership and indeterminacy membership, is a more serviceable pattern for capturing uncertainty. In this paper, five dimensions of rare earth industry security are identified and then prioritized against twelve different criteria relevant to structure, organization, layout, policy and ecological aspects of industry security. Then, the objective weight is computed by CRITIC (Criteria Importance Through Inter-criteria Correlation) method while the integrated weight is determined by concurrently revealing subjective weight and objective weight. Later, neutrosophic soft decision making method based CoCoSo (Combined Compromise Solution) is explored for settling the issue of low discrimination. Lastly, the feasibility and validity of the developed algorithm is verified by the issue of China’s rare earth industry security evaluation.
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Affiliation(s)
- Xindong Peng
- School of Information Science and Engineering, Shaoguan University, Shaoguan, China
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17
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Aslam M, Al Shareef A, Khan K. Monitoring the temperature through moving average control under uncertainty environment. Sci Rep 2020; 10:12182. [PMID: 32699315 PMCID: PMC7376069 DOI: 10.1038/s41598-020-69192-8] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/13/2020] [Accepted: 06/19/2020] [Indexed: 12/01/2022] Open
Abstract
The existing moving average control charts can be only applied when all observations in the data are determined, precise, and certain. But, in practice, the data from the weather monitoring is not exact and express in the interval. In this situation, the available monitoring plans cannot be applied for the monitoring of weather data. A new moving average control chart for the normal distribution is offered under the neutrosophic statistics. The parameters of the offered chart are determined through simulation under neutrosophic statistics. The comparison study shows the superiority of the proposed chart over the moving average control chart under classical statistics. A real example from the weather is chosen to present the implementation of the chart. From the simulation study and real data, the proposed chart is found to be effective to be applied for temperature monitoring than the existing control chart.
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Affiliation(s)
- Muhammad Aslam
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia.
| | | | - Khushnoor Khan
- Department of Statistics, Faculty of Science, King Abdulaziz University, Jeddah, 21551, Saudi Arabia
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18
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Risky Multi-Attribute Decision-Making Method Based on the Interval Number of Normal Distribution. Symmetry (Basel) 2020. [DOI: 10.3390/sym12020264] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
Focusing on risky decision-making problems taking the interval number of normal distribution as the information environment, this paper proposes a decision-making method based on the interval number of normal distribution. Firstly, the normalized matrix based on the decision maker’s attitude is obtained through analysis and calculation. Secondly, according to the existing properties of standard normal distribution, the risk preference factors of the decision makers are considered to confirm the possibility degree of each scheme. The possibility degree is then used for establishing a possibility degree matrix and, consequently, sequencing of all schemes is conducted according to existing theories of possibility degree meaning and the value size of possibility degree. Finally, the feasibility and validity of this method is verified through calculation example analysis.
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19
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New Diagnosis Test under the Neutrosophic Statistics: An Application to Diabetic Patients. BIOMED RESEARCH INTERNATIONAL 2020; 2020:2086185. [PMID: 32420326 PMCID: PMC7204183 DOI: 10.1155/2020/2086185] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Subscribe] [Scholar Register] [Received: 05/24/2019] [Revised: 12/19/2019] [Accepted: 12/28/2019] [Indexed: 11/18/2022]
Abstract
The diagnosis tests (DT) under classical statistics are applied under the assumption that all observations in the data are determined. Therefore, these DT cannot be applied for the analysis of the data when some or all observations are not determined. The neutrosophic statistics (NS) which is the extension of classical statistics can be applied for the data having uncertain, unclear, and fuzzy observations. In this paper, we will present the DT, and gold-standard tests under NS are called neutrosophic diagnosis tests (NDT). Therefore, the proposed NDT is the generalization of the existing DT and can be applied under the uncertainty environment. We will present the NDT table and present a real example from the medical field. The use of the proposed method will be more effective and adequate to be used in medical science, biostatistics, decision, and classification analysis.
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20
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Neutrosophic Portfolios of Financial Assets. Minimizing the Risk of Neutrosophic Portfolios. MATHEMATICS 2019. [DOI: 10.3390/math7111046] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
This paper studies the problem of neutrosophic portfolios of financial assets as part of the modern portfolio theory. Neutrosophic portfolios comprise those categories of portfolios made up of financial assets for which the neutrosophic return, risk and covariance can be determined and which provide concomitant information regarding the probability of achieving the neutrosophic return, both at each financial asset and portfolio level and also information on the probability of manifestation of the neutrosophic risk. Neutrosophic portfolios are characterized by two fundamental performance indicators, namely: the neutrosophic portfolio return and the neutrosophic portfolio risk. Neutrosophic portfolio return is dependent on the weight of the financial assets in the total value of the portfolio but also on the specific neutrosophic return of each financial asset category that enters into the portfolio structure. The neutrosophic portfolio risk is dependent on the weight of the financial assets that enter the portfolio structure but also on the individual risk of each financial asset. Within this scientific paper was studied the minimum neutrosophic risk at the portfolio level, respectively, to establish what should be the weight that the financial assets must hold in the total value of the portfolio so that the risk is minimum. These financial assets weights, after calculations, were found to be dependent on the individual risk of each financial asset but also on the covariance between two financial assets that enter into the portfolio structure. The problem of the minimum risk that characterizes the neutrosophic portfolios is of interest for the financial market investors. Thus, the neutrosophic portfolios provide complete information about the probabilities of achieving the neutrosophic portfolio return but also of risk manifestation probability. In this context, the innovative character of the paper is determined by the use of the neutrosophic triangular fuzzy numbers and by the specific concepts of financial assets, in order to substantiating the decisions on the financial markets.
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21
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Jana C, Muhiuddin G, Pal M. Some Dombi aggregation of
Q
‐rung orthopair fuzzy numbers in multiple‐attribute decision making. INT J INTELL SYST 2019. [DOI: 10.1002/int.22191] [Citation(s) in RCA: 71] [Impact Index Per Article: 14.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Affiliation(s)
- Chiranjibe Jana
- Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar University Midnapore India
| | - G. Muhiuddin
- Department of MathematicsUniversity of Tabuk Tabuk Saudi Arabia
| | - Madhumangal Pal
- Department of Applied Mathematics with Oceanology and Computer ProgrammingVidyasagar University Midnapore India
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22
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23
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A Method of Determining Multi-Attribute Weights Based on Single-Valued Neutrosophic Numbers and Its Application in TODIM. Symmetry (Basel) 2019. [DOI: 10.3390/sym11040506] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022] Open
Abstract
In this paper, the TODIM method is used to solve the multi-attribute decision-making problem with unknown attribute weight in venture capital, and the decision information is given in the form of single-valued neutrosophic numbers. In order to consider the objectivity and subjectivity of decision-making problems reasonably, the optimal weight is obtained by combining subjective weights and objective weights. Subjective weights are given directly by decision makers. Objective weights are obtained by establishing a weight optimization model with known decision information, then this method will compare with entropy weight method. These simulation results also validate the effectiveness and reasonableness of this proposed method.
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Abstract
Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establish a bridge to connect a soft set and the union operations on sets, then applying it to B C K / B C I -algebras. Firstly, we introduce the notion of the ( α , β ) -Union-Soft ( ( α , β ) -US) set, with some supporting examples. Then, we discuss the soft B C K / B C I -algebras, which are called ( α , β ) -US algebras, ( α , β ) -US ideals, ( α , β ) -US closed ideals, and ( α , β ) -US commutative ideals. In particular, some related properties and relationships of the above algebraic structures are investigated. We also provide the condition of an ( α , β ) -US ideal to be an ( α , β ) -US closed ideal. Some conditions for a Union-Soft (US) ideal to be a US commutative ideal are given by means of ( α , β ) -unions. Moreover, several characterization theorems of (closed) US ideals and US commutative ideals are given in terms of ( α , β ) -unions. Finally, the extension property for an ( α , β ) -US commutative ideal is established.
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