Abstract
The researcher has been facing problems while handling imprecise and vague information, i.e., the problems of networking, decision-making, etc. For encountering such complicated data, the notion of fuzzy sets (FS) has been considered an influential tool. The notion was extended to its generalizations by a number of researchers in different ways which helps to understand and assess even more complex issues. This article characterizes imprecision with four kinds of values of membership. In this work, we aim to define and examine cubic picture fuzzy sets and give an application on averaging aggregation operators. We first introduce the notion of a cubic picture fuzzy set, which is a pair of interval-valued picture fuzzy set and a picture fuzzy set by giving examples. Then, we define two kinds of ordering on these sets and also discuss some set-theoretical properties. Moreover, we introduce three kinds of averaging aggregation operators based on cubic picture fuzzy sets and, at the end, we illustrate the results with a decision-making problem by using one of the provided aggregation operators.
Highlights
In 1965, Zadeh generalized the classical set and perceived the idea of fuzzy sets [1] to deal with uncertainty. is idea allows creating some new dimensions in the field of research and has been applied in many fields such as decisionmaking, medical diagnosis, and pattern recognition [1,2,3,4,5,6]
Several extensions have been made by many researchers such as interval-valued fuzzy sets [7], intuitionistic fuzzy sets (IFSs) [8], cubic sets [9], and neutrosophic sets [10]
Inspiring from the above study, we propose the concept of cubic picture fuzzy sets, which is an extension of cubic sets, picture fuzzy sets, and interval-valued picture fuzzy sets
Summary
In 1965, Zadeh generalized the classical set and perceived the idea of fuzzy sets [1] to deal with uncertainty. is idea allows creating some new dimensions in the field of research and has been applied in many fields such as decisionmaking, medical diagnosis, and pattern recognition [1,2,3,4,5,6]. E limitation of fuzzy sets is that the nonmembership degree cannot be defined independently To overcome this limitation, several extensions have been made by many researchers such as interval-valued fuzzy sets [7], intuitionistic fuzzy sets (IFSs) [8], cubic sets [9], and neutrosophic sets [10]. The notion of fuzzy sets was further generalized by Coung et al and they proposed the concept of picture fuzzy sets [18, 19], and this idea gained more and more attention from the researchers.
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