Multiple attribute group decision making based on 2-dimension linguistic intuitionistic fuzzy aggregation operators
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METHODOLOGIES AND APPLICATION
Multiple attribute group decision making based on 2-dimension linguistic intuitionistic fuzzy aggregation operators Rajkumar Verma1,2
•
Jose´ M. Merigo´1,2
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract The 2-dimension linguistic variables (2-DLVs) add a subjective evaluation on the reliability of the evaluation results provided by decision makers, so 2-DLVs are very useful tools for describing uncertain or fuzzy information. This work extends the idea of 2-DLVs by introducing 2-dimension linguistic intuitionistic fuzzy variables (2-DLIFVs) in which 1 class and 2 class information describe in the form of linguistic intuitionistic fuzzy numbers. The paper defines some operational laws, score, and accuracy functions for 2-DLIFVs. Further, we develop some arithmetic and geometric aggregation operators for aggregating 2-DLIF information and prove a number of valuable properties associated with them. Using the proposed aggregation operators, an approach for multiple attribute group decision making with 2-DLIF information is formulated. Finally, an illustrated example is given to verify and prove the validity of the developed method. The computed results are also compared with the existing results. Keywords Multiple attribute decision making Linguistic intuitionistic fuzzy numbers Linguistic variables 2-dimension linguistic variables 2-dimension linguistic intuitionistic fuzzy variables
1 Introduction Multiple attribute decision making is one of the most widely used phenomena in our day-to-day life to select the best alternative(s) from a set of feasible alternatives based on the available information. Due to the complexities of real-world situations, it is tough for a decision maker to provide his/her preference information over attributes/alternatives in the form of crisp numbers. Fuzzy set (FS), proposed by Zadeh (1965), is a powerful tool for representing vague or uncertain information and has been
Communicated by V. Loia. & Rajkumar Verma [email protected]; [email protected] Jose´ M. Merigo´ [email protected] 1
Department of Management Control and Information Systems, University of Chile, Av. Diagonal Paraguay 257, Santiago 8330015, Chile
2
School of Information, Systems and Modelling, Faculty of Engineering and Information Technology, University of Technology Sydney, Sydney, Australia
received full attention from researchers and practitioners. Out of several generalizations of fuzzy set, the notion of intuitionistic fuzzy sets (IFSs) (Atanassov 1986) has been extensively studied and used in different application areas because of its efficient modeling capability to represent fuzzy information (Angelov 1997; De et al. 2001; Li 2005; Xu et al. 2008; Boran et al. 2009; Xia and Xu 2012). In the past three decades, a significant number of results on IFS theory have been developed, which include operational laws (Atanassov 1994, 2000; De et al. 2001; Verma and Sharma 2011, 2013c), entropy and diverge
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