The extended VIKOR method for multi-attribute group decision making with triangular intuitionistic fuzzy numbers
TL;DR: This work investigates multiple attribute group decision-making problems in which the ratings of alternatives are expressed with TIFNs, and the weights of the attributes and DMs are completely unknown, and develops the triangular intuitionistic fuzzy weighted average (TIF-WA) operator.
Abstract: Triangular intuitionistic fuzzy numbers (TIFNs) are a special intuitionistic fuzzy set (IFS) on a real number set, which are very useful for decision makers (DMs) to depict their fuzzy preference information. In this work, we investigate multiple attribute group decision-making (MAGDM) problems in which the ratings of alternatives are expressed with TIFNs, and the weights of the attributes and DMs are completely unknown. Firstly, the crisp weighted possibility mean of TIFNs is defined, and the Hamming distance and Euclidean distance for TIFNs are defined based on Hausdorff distance. The triangular intuitionistic fuzzy weighted average (TIF-WA) operator is developed. Then, the weights of attributes are calculated by applying Shannon entropy measure and the weights of DMs are determined objectively combining the evidence theory with Bayes approximation. The individual decision matrixes for all DMs are aggregated into the group decision matrix by using the TIF-WA operator. Thereby, the classic Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method is extended for solving the MAGDM with TIFNs. Finally, the ranking order of alternative is given according to the closeness of alternative with respect to the ideal solution. The personnel selection example verifies the effectiveness of the proposed method.
Citations
More filters
TL;DR: This paper surveys the latest status of fuzzy multicriteria decision-making methods and classify these methods dividing into two parts: fuzzy multiattribute decision- Making (MADM) and fuzzy multiobjective decision- making (MODM).
Abstract: Multicriteria decision-making (MCDM) refers to making decisions in the presence of multiple and usually conflicting criteria. Fuzzy decision-making is used where vague and incomplete data exist for the solution. Fuzzy multicriteria decision-making is one of the most popular problems handled by the researchers in the literature. In this paper, we survey the latest status of fuzzy multicriteria decision-making methods and classify these methods dividing into two parts: fuzzy multiattribute decision-making (MADM) and fuzzy multiobjective decision-making (MODM). Most of the publications are on fuzzy MADM since there are a plenty of classical multiattribute decision-making methods in the literature. Tabular and graphical illustrations for each method are given.
376 citations
TL;DR: A quantitative evaluation model to measure the uncertainty of GSCM activities is developed and an approach based on Vlsekriterijumska Optimizacija I Kompromisno Resenje (VIKOR) method which is an extension of intuitionistic fuzzy environment aiming to solve the green multi-criteria decision making (GMCDM) problem is applied.
345 citations
Cites methods from "The extended VIKOR method for multi..."
...Compared with technique for ordering preference by similarity to ideal solution (TOPSIS), VIKOR not only consider group utility maximization and individual regret minimization, but also can fully reflect the DMs subjective preferences (Opricovic and Tzeng, 2004; Liu and Wu, 2012; Wan et al., 2013)....
[...]
TL;DR: A systematic review of the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method in several application areas such as sustainability and renewable energy is presented in this article.
Abstract: The main objective of this paper is to present a systematic review of the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) method in several application areas such as sustainability and renewable energy. This study reviewed a total of 176 papers, published in 2004 to 2015, from 83 high-ranking journals; most of which were related to Operational Research, Management Sciences, decision making, sustainability and renewable energy and were extracted from the “Web of Science and Scopus” databases. Papers were classified into 15 main application areas. Furthermore, papers were categorized based on the nationalities of authors, dates of publications, techniques and methods, type of studies, the names of the journals and studies purposes. The results of this study indicated that more papers on VIKOR technique were published in 2013 than in any other year. In addition, 13 papers were published about sustainability and renewable energy fields. Furthermore, VIKOR and fuzzy VIKOR methods, had the first rank in use. Additionally, the Journal of Expert Systems with Applications was the most significant journal in this study, with 27 publications on the topic. Finally, Taiwan had the first rank from 22 nationalities which used VIKOR technique.
242 citations
Cites methods from "The extended VIKOR method for multi..."
...[80], extended the VIKOR technique for solving multi-criteria group decision making problems with triangular intuitionistic fuzzy numbers (TIFNs)....
[...]
TL;DR: A novel hybrid MCDM model that combines fuzzy Decision Making Trial and Evaluation Laboratory Model (DEMATEL), fuzzy Analytical Network Process (ANP) and fuzzy Visekriterijumska Optimizacija i kompromisno Resenje (VIKOR) methods is developed and successfully performed in this paper for the City of Belgrade.
Abstract: City logistics (CL) tends to increase efficiency and mitigate the negative effects of logistics processes and activities and at the same time to support the sustainable development of urban areas. Accordingly, various measures and initiatives are applying and various conceptual solutions are defining. The effects vary depending on the characteristics of the city. This paper proposes a framework for the selection of the CL concept which would be most appropriate for different participants, stakeholders, and which would comply with attributes of the surroundings. CL participants have different, usually conflicting goals and interests, so it is necessary to define a large number of criteria for concepts evaluation. On the other hand, the importance of the criteria is dependent on the specific situation, i.e., a large number of factors describing the surroundings. In situations like this, selecting the best alternative is a complex multi-criteria decision-making (MCDM) problem consisting of conflicting and uncertain elements. A novel hybrid MCDM model that combines fuzzy Decision Making Trial and Evaluation Laboratory Model (DEMATEL), fuzzy Analytical Network Process (ANP) and fuzzy Visekriterijumska Optimizacija i kompromisno Resenje (VIKOR) methods is developed in this paper. The model provides support to decision makers (planners, city administration, logistics service providers, users, etc.) when selecting the CL concept, which is successfully performed in this paper for the City of Belgrade.
232 citations
TL;DR: In this paper, a methodology for solving multi-attribute decision making problems with SVN-numbers is presented, which is based on the concept of cut sets of SVNnumbers.
Abstract: The concept of a single valued neutrosophic number (SVN-number) is of importance for quantifying an ill-known quantity and the ranking of SVN-numbers is a very difficult problem in multi-attribute decision making problems. The aim of this paper is to present a methodology for solving multi-attribute decision making problems with SVN-numbers. Therefore, we firstly defined the concepts of cut sets of SVN-numbers and then applied to single valued trapezoidal neutrosophic numbers (SVTN-numbers) and triangular neutrosophic numbers (SVTrN-numbers). Then, we proposed the values and ambiguities of the truth-membership function, indeterminacy-membership function and falsity-membership function for a SVN-numbers and studied some desired properties. Also, we developed a ranking method by using the concept of values and ambiguities, and applied to multi-attribute decision making problems in which the ratings of alternatives on attributes are expressed with SVTN-numbers.
196 citations
References
More filters
TL;DR: Various properties are proved, which are connected to the operations and relations over sets, and with modal and topological operators, defined over the set of IFS's.
13,376 citations
TL;DR: A comparative analysis of the multiple criteria decision making methods VIKOR and TOPSIS is illustrated with a numerical example, showing their similarity and some differences.
3,563 citations
01 May 2002
TL;DR: The fundamental features of the ER approach are investigated and new schemes for weight normalization and basic probability assignments are proposed to enhance the process of aggregating attributes with uncertainty.
Abstract: In multiple attribute decision analysis (MADA), one often needs to deal with both numerical data and qualitative information with uncertainty. It is essential to properly represent and use uncertain information to conduct rational decision analysis. Based on a multilevel evaluation framework, an evidential reasoning (ER) approach has been developed for supporting such decision analysis, the kernel of which is an ER algorithm developed on the basis of the framework and the evidence combination rule of the Dempster-Shafer (D-S) theory. The approach has been applied to engineering design selection, organizational self-assessment, safety and risk assessment, and supplier assessment. In this paper, the fundamental features of the ER approach are investigated. New schemes for weight normalization and basic probability assignments are proposed. The original ER approach is further developed to enhance the process of aggregating attributes with uncertainty. Utility intervals are proposed to describe the impact of ignorance on decision analysis. Several properties of the new ER approach are explored, which lay the theoretical foundation of the ER approach. A numerical example of a motorcycle evaluation problem is examined using the ER approach. Computation steps and analysis results are provided in order to demonstrate its implementation process.
841 citations
TL;DR: A principled distance between two basic probability assignments (BPAs) (or two bodies of evidence) based on a quantification of the similarity between sets is introduced based on the evidential theory of Dempster–Shafer.
832 citations
TL;DR: A generalised and extended decision matrix is constructed and rule and utility based techniques are developed for transforming various types of information within the matrix for aggregating attributes via ER that are equivalent with regard to underlying utility and rational in terms of preserving the features of original assessments.
710 citations