SR-Fuzzy Sets and Their Weighted Aggregated Operators in Application to Decision-Making

Tareq M. Al-shami · Hariwan Zikri Ibrahim · A. A. Azzam · A. I. El-Maghrabi

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Multi-Criteria Decision Making Fuzzy and Soft Set Theory Fuzzy Systems and Optimization

Abstract

An intuitionistic fuzzy set is one of the efficient generalizations of a fuzzy set for dealing with vagueness/uncertainties in information. Under this environment, in this manuscript, we familiarize a new type of extensions of fuzzy sets called square-root fuzzy sets (briefly, SR-Fuzzy sets) and contrast SR-Fuzzy sets with intuitionistic fuzzy sets and Pythagorean fuzzy sets. We discover the essential set of operations for the SR-Fuzzy sets along with their several properties. In addition, we define a score function for the ranking of SR-Fuzzy sets. To study multiattribute decision-making problems, we introduce four new weighted aggregated operators, namely, SR-Fuzzy weighted average (SR-FWA) operator, SR-Fuzzy weighted geometric (SR-FWG) operator, SR-Fuzzy weighted power average (SR-FWPA) operator, and SR-Fuzzy weighted power geometric (SR-FWPG) operator over SR-Fuzzy sets. We apply these operators to select the top-rank university and show how we can choose the best option by comparing the aggregate outputs through score values.

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References

1965Fuzzy sets 1986Intuitionistic fuzzy sets 1999Soft set theory—First results 2013Pythagorean Membership Grades in Multicriteria Decision Making 2013Pythagorean fuzzy subsets 2007Intuitionistic Fuzzy Aggregation Operators 2006Some geometric aggregation operators based on intuitionistic fuzzy sets 2013Pythagorean Membership Grades, Complex Numbers, and Decision Making

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