Abstract
The information aggregation operator plays a key rule in the group decision making problems. The aim of this paper is to investigate the information aggregation operators method under the picture fuzzy environment with the help of Einstein norms operations. The picture fuzzy set is an extended version of the intuitionistic fuzzy set, which not only considers the degree of acceptance or rejection but also takes into the account of neutral degree during the analysis. Under these environments, some basic aggregation operators namely picture fuzzy Einstein weighted and Einstein ordered weighted operators are proposed in this paper. Some properties of these aggregation operators are discussed in detail. Further, a group decision making problem is illustrated and validated through a numerical example. A comparative analysis of the proposed and existing studies is performed to show the validity of the proposed operators.
Highlights
The core idea of the fuzzy set (FS) theory was first developed by Zadeh [55] in 1965
The aim of this paper is to investigate the information aggregation operators method under the picture fuzzy environment with the help of Einstein norms operations
In ‘‘Einstein operations of picture fuzzy sets’’ section, we proposed picture fuzzy Einstein operations
Summary
The core idea of the fuzzy set (FS) theory was first developed by Zadeh [55] in 1965 In this theory, Zadeh only discussed the positive membership degree of the function. Wei [49] introduced the basic idea of picture 2-tuple linguistic Bonferroni mean operation and their application to MADM problems. . .; nÞ and Einstein operations of picture fuzzy sets In this part of the paper, we have presented the Einstein operations and discussed some basic properties of the defined operations on the PFSs. Let the t-norm T, and t-conorm S, be Einstein product Te and Einstein sum Se, respectively; the generalized union and the intersection between two PFSs that is b and . By the Einstein operation law, we have a À b 2c 2e k:eðb Èe b2Þ 1⁄4 k:e a þb;d þ
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