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Paulraj S, Tamilarasi G. Generalized ordered weighted harmonic averaging operator with trapezoidal neutrosophic numbers for solving MADM problems. JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2021; 13:4089-4102. [PMID: 34659583 PMCID: PMC8503884 DOI: 10.1007/s12652-021-03509-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 02/04/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
Harmonic mean is suitable for algebraic calculation and other mathematical treatments and also suitable for directly aggregated negative indicators. In many different situations, harmonic mean improves the flexibility. In this paper, we develop some new aggregation operators under neutrosophic environment and apply with multi attribute decision making (MADM) problems. First, we provide a Single valued trapezoidal neutrosophic Generalized ordered weighted harmonic averaging(SVTNGOWHA) operator which is the extension of single valued trapezoidal neutrosophic ordered weighted harmonic averaging (SVTNOWHA) operator. To fix the operators on the mount, we have tested these methods in few illustrative examples, and the results have been presented.
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Affiliation(s)
- S. Paulraj
- Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamil Nadu 600025 India
| | - G. Tamilarasi
- Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamil Nadu 600025 India
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Yang L, Li D, Tan R. Particle swarm optimization for the shortest path problem. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2021. [DOI: 10.3233/jifs-210233] [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
Solving the shortest path problem is very difficult in situations such as emergency rescue after a typhoon: road-damage caused by a typhoon causes the weight of the rescue path to be uncertain and impossible to represent using single, precise numbers. In such uncertain environments, neutrosophic numbers can express the edge distance more effectively: membership in a neutrosophic set has different degrees of truth, indeterminacy, and falsity. This paper proposes a shortest path solution method for interval-valued neutrosophic graphs using the particle swarm optimization algorithm. Furthermore, by comparing the proposed algorithm with the Dijkstra, Bellman, and ant colony algorithms, potential shortcomings and advantages of the proposed method are deeply explored, and its effectiveness is verified. Sensitivity analysis performed using a 2020 typhoon as a case study is presented, as well as an investigation on the efficiency of the algorithm under different parameter settings to determine the most reasonable settings. Particle swarm optimization is a promising method for dealing with neutrosophic graphs and thus with uncertain real-world situations.
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Affiliation(s)
- Lehua Yang
- College of Electronics and Information Science, Fujian Jiangxia University, Fuzhou Fujian, China
- Research Institute for Data Analysis and Intelligent Decision Making, Fuzhou Fujian, China
| | - Dongmei Li
- College of Foreign Languages, Fujian Jiangxia University, Fuzhou Fujian, China
| | - Ruipu Tan
- College of Electronics and Information Science, Fujian Jiangxia University, Fuzhou Fujian, China
- Research Institute for Data Analysis and Intelligent Decision Making, Fuzhou Fujian, China
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Zhou F, Chen TY. An extended Pythagorean fuzzy VIKOR method with risk preference and a novel generalized distance measure for multicriteria decision-making problems. Neural Comput Appl 2021. [DOI: 10.1007/s00521-021-05829-7] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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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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Wei G, He Y, Lei F, Wu J, Wei C, Guo Y. Green supplier selection with an uncertain probabilistic linguistic MABAC method. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-191584] [Citation(s) in RCA: 31] [Impact Index Per Article: 7.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In recent years, with the increased voice for protecting the environment by the people all over the world, the governments also have actively adopted more and more measures to further promote environmental conservation and sustainable development. Traditional procurement approaches have not well updated to the current needs of the society, especially for the retail industry which is in relation to the national economy due to numerous products and different suppliers being involved. Therefore, the need for green procurement is more important. The qualified green supplier selection is the core of green procurement, which is the utmost importance in the business competition throughout the supply chain in today’s strong business competition. Thus, in order to obtain the optimal green supplier, integration of Entropy weights and multi-attributive border approximation area comparison (MABAC) under uncertain probabilistic linguistic sets (UPLTSs) has offered a novel integrated model, in which information Entropy is utilized for calculating objective weights with UPLTSs to acquire the final ranking result of green supplier. Besides, so as to indicate the applicability of devised method, it is confirmed by a numerical case for green supplier selection. Some comparative studies are made with some existing methods. The proposed method can also serve for selecting suitable alternative successfully in other selection problems.
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Affiliation(s)
- Guiwu Wei
- School of Business, Sichuan Normal University, Chengdu, P.R. China
| | - Yan He
- School of Mathematical Sciences, Sichuan Normal University, Chengdu, P.R. China
| | - Fan Lei
- School of Mathematical Sciences, Sichuan Normal University, Chengdu, P.R. China
| | - Jiang Wu
- School of Statistics, Southwestern University of Finance and Economics, Chengdu, P.R. China
| | - Cun Wei
- School of Statistics, Southwestern University of Finance and Economics, Chengdu, P.R. China
| | - Yanfeng Guo
- School of Finance, Southwestern University of Finance and Economics, Chengdu, China
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Wei G, He Y, Lei F, Wu J, Wei C. MABAC method for multiple attribute group decision making with probabilistic uncertain linguistic information. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2020. [DOI: 10.3233/jifs-191688] [Citation(s) in RCA: 20] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Abstract
In recent years, ecological problems have become increasingly serious which are forcing people to give up the past high investment, high consumption and high emission development to promote green growth, implement the green new deal and pay attention to green supply chain research and practice. Therefore, in order to attach great importance to the economic and environmental benefits, enterprises should implement green supply chain and “green” change which has become the trend and urgent. Thus, in order to obtain an optimal green supplier, integration of combined weights and multi-attributive border approximation area comparison (MABAC) under probabilistic uncertain linguistic sets (PULTSs) has offered a novel integrated model, in which information entropy is utilized for calculating objective weights with PULTSs to acquire the final ranking result of green supplier. Besides, so as to indicate the applicability of devised method, it is confirmed by a numerical case for green supplier selection. Some comparative studies are made with some existing methods. The proposed method can also serve for selecting suitable alternative successfully in other selection problems.
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Affiliation(s)
- Guiwu Wei
- School of Business, Sichuan Normal University, Chengdu, P.R. China
| | - Yan He
- School of Mathematical Sciences, Sichuan Normal University, Chengdu, P.R. China
| | - Fan Lei
- School of Mathematical Sciences, Sichuan Normal University, Chengdu, P.R. China
| | - Jiang Wu
- School of Statistics, Southwestern University of Finance and Economics, Chengdu, P.R. China
| | - Cun Wei
- School of Statistics, Southwestern University of Finance and Economics, Chengdu, P.R. China
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An Extended MABAC Method Based on Triangular Fuzzy Neutrosophic Numbers for Multiple-Criteria Group Decision Making Problems. AXIOMS 2020. [DOI: 10.3390/axioms9030104] [Citation(s) in RCA: 9] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
In this manuscript, we extend the traditional multi-attributive border approximation area comparison (MABAC) method for the multiple-criteria group decision-making (MCGDM) with triangular fuzzy neutrosophic numbers (TFNNs) to propose the TFNNs-MABAC method. In the proposed method, we utilize the TFNNs to express the values of criteria for each alternative in MCGDM problems. First, we briefly acquaint the basic concept of TFNNs and describe its corresponding some operation laws, the functions of score and accuracy, and the normalized hamming distance. We then review two aggregation operators of TFNNs. Afterward, we combine the traditional MABAC method with the triangular fuzzy neutrosophic evaluation and provide a sequence of calculation procedures of the TFNNs-MABAC method. After comparing it with some TFNNs aggregation operators and another method, the results showed that our extended MABAC method can not only effectively handle the conflicting attributes, but also practically deal with incomplete and indeterminate information in the MCGDM problem. Therefore, the extended MABAC method is more effective, conformable, and reasonable. Finally, an investment selection problem is demonstrated as a practice to verify the reasonability of our MABAC method.
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Deli I, Karaaslan F. Generalized trapezoidal hesitant fuzzy numbers and their applications to multi criteria decision-making problems. Soft comput 2020. [DOI: 10.1007/s00500-020-05201-2] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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Shortest Path Solution of Trapezoidal Fuzzy Neutrosophic Graph Based on Circle-Breaking Algorithm. Symmetry (Basel) 2020. [DOI: 10.3390/sym12081360] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The shortest path problem is a topic of increasing interest in various scientific fields. The damage to roads and bridges caused by disasters makes traffic routes that can be accurately expressed become indeterminate. A neutrosophic set is a collection of the truth membership, indeterminacy membership, and falsity membership of the constituent elements. It has a symmetric form and indeterminacy membership is their axis of symmetry. In uncertain environments, the neutrosophic number can more effectively express the edge distance. The objectives in this study are to solve the shortest path problem of the neutrosophic graph with an edge distance expressed using trapezoidal fuzzy neutrosophic numbers (TrFNN) and resolve the edge distance according to the score and exact functions based on the TrFNN. Accordingly, the use of a circle-breaking algorithm is proposed to solve the shortest path problem and estimate the shortest distance. The feasibility of this method is verified based on two examples, and the rationality and effectiveness of the approach are evaluated by comparing it with the Dijkstra and Bellman algorithms.
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A Further Study on Multiperiod Health Diagnostics Methodology under a Single-Valued Neutrosophic Set. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2020. [DOI: 10.1155/2020/6093545] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
Employing the concept and function of tangency with similarity measures and counterpart distances for reliable medical consultations has been extensively studied in the past decades and results in lots of isomorphic measures for application. We compared the majority of such isomorphic measures proposed by various researchers and classified them into (a) maximum norm and (b) one-norm categories. Moreover, we found that previous researchers used monotonic functions to transform an identity function and resulted in complicated expressions. In this study, we provide a theoretical foundation to explain the isomorphic nature of a newer measure proposed by the following research paper against its studied existing one in deriving the same pattern recognition results. Specifically, this study initially proposes two similarity measures using maximum norm, arithmetic mean, and aggregation operators and followed by a detailed discussion on their mathematical characteristics. Subsequently, a simplified version of such measures is presented for easy application. This study completely covers two previous methods to point out that the complex approaches used were unnecessary. The findings will help physicians, patients, and their family members to obtain a proper medical diagnosis during multiple examinations.
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Failure prioritization and control using the neutrosophic best and worst method. GRANULAR COMPUTING 2019. [DOI: 10.1007/s41066-019-00206-1] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Broumi S, Nagarajan D, Bakali A, Talea M, Smarandache F, Lathamaheswari M. The shortest path problem in interval valued trapezoidal and triangular neutrosophic environment. COMPLEX INTELL SYST 2019. [DOI: 10.1007/s40747-019-0092-5] [Citation(s) in RCA: 27] [Impact Index Per Article: 5.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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A novel defuzzification method of SV-trapezoidal neutrosophic numbers and multi-attribute decision making: a comparative analysis. Soft comput 2019. [DOI: 10.1007/s00500-019-03803-z] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
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Ju D, Ju Y, Wang A. Multiple attribute group decision making based on Maclaurin symmetric mean operator under single-valued neutrosophic interval 2-tuple linguistic environment. JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2018. [DOI: 10.3233/jifs-17496] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022]
Affiliation(s)
- Dawei Ju
- School of Management and Economics, Beijing Institute of Technology, Beijing, China
| | - Yanbing Ju
- School of Management and Economics, Beijing Institute of Technology, Beijing, China
| | - Aihua Wang
- Graduate School of Education, Peking University, Beijing, China
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Liang W, Zhao G, Hong C. Selecting the optimal mining method with extended multi-objective optimization by ratio analysis plus the full multiplicative form (MULTIMOORA) approach. Neural Comput Appl 2018. [DOI: 10.1007/s00521-018-3405-5] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Abdel-Basset M, Gunasekaran M, Mohamed M, Smarandache F. A novel method for solving the fully neutrosophic linear programming problems. Neural Comput Appl 2018. [DOI: 10.1007/s00521-018-3404-6] [Citation(s) in RCA: 36] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/17/2022]
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Novel single-valued neutrosophic decision-making approaches based on prospect theory and their applications in physician selection. Soft comput 2017. [DOI: 10.1007/s00500-017-2949-0] [Citation(s) in RCA: 28] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Liang RX, Wang JQ, Zhang HY. A multi-criteria decision-making method based on single-valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput Appl 2017. [DOI: 10.1007/s00521-017-2925-8] [Citation(s) in RCA: 46] [Impact Index Per Article: 6.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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Liang RX, Wang JQ, Li L. Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information. Neural Comput Appl 2016. [DOI: 10.1007/s00521-016-2672-2] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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