Generalized intuitionistic fuzzy soft power aggregation operator based ont‐norm and their application in multicriteria decision‐making

Abstract

The aim of this paper is to develop some new power aggregation operators for intuitionistic fuzzy (IF) soft numbers. The aggregation operators are named as IF soft power averaging (IFSPA) operator, weighted IFSPA (WIFSPA) operator, ordered WIFSPA operator, IF soft power geometric (IFSPG) operator, and weighted and ordered weighted IFSPG aggregation operators. The salient features of these operators are discussed in detail. Further, these operators are extended to its generalized version and called generalized IFSPA or geometric aggregation operators. Then, we utilized these operators to develop an approach to solve the decision‐making problem under IF soft set environment and demonstrated with an illustrative example. A comparative analysis of existing approaches has been done for showing the validity of the proposed work.

Confidence levelsq‐rung orthopair fuzzy aggregation operators and its applications to MCDM problems

“…To cope with such situations, Zadeh introduced fuzzy sets and which was further extended by Atanassov by introducing the concept of intuitionistic fuzzy set (IFS), which is characterized in such a way that the sum of the support for membership and support against membership is less than or equal to one. Due to this characteristic, IFS theory is one of the successful and powerful tools to deal with imprecise, vague and ambiguous information, and receives attention to many practitioners to deal with real life situations. But, the aggregation of all the performances in dealing with real life problems is a very critical step to obtain decisions.…”

A Dempster‐Shafer theory and uninorm‐based framework of reasoning and multiattribute decision‐making for surveillance system

“…Therefore, it is necessary to construct or choose a flexible aggregation operator that can reflect individualities of different security managers in combining evidence from different sources in different surveillance environments. Some clues of such aggregation operators may be hidden in some recent work on aggregation operators in multicriterion decision‐making . Third, in a real‐time surveillance environment, if the suspects have more than one potential attack targets but the security resources are limited, the security manger needs to consider the suspect's simultaneously response to the security coverage, the suspect's uncertain preferences, and his plan according to the information from the surveillance system.…”

“…Recently there are a lot of studies to do so. For example, Garg and Arora develop some new power aggregation operators for intuitionistic fuzzy soft numbers and applied these operators into MADM problems. Garg identifies two new exponential operational laws about the interval‐valued Pythagorean fuzzy set, presents their corresponding aggregation operators and an MADM approach based on these operators.…”

Some results on information measures for complex intuitionistic fuzzy sets

“…After it, Atanassov 4 added a new function named as nonmembership function to the theory of FS and hence, introduced intuitionistic fuzzy set (IFS) theory to reflect the fact that sum of membership and nonmembership degrees is not always equal to 1 because there may be some degree of hesitation also. Under this theory, numerous scholars and authors have presented their theories and methodologies [5][6][7][8][9][10][11][12][13][14] for analyzing the problems of DM and applied them to the various different disciplines. Among these methodologies, information measures play a significant role in processing the imperfect and uncertain information.…”