A new type of generalized picture fuzzy soft set and its application in decision making

Author:

Lu Hanchuan12,Khalil Ahmed Mostafa3,Alharbi W.4,El-Gayar M. A.5

Affiliation:

1. School of Mathematical Sciences, Nanjing Normal University, Nanjing, China

2. School of Mathematics and Statistics, Guizhou University, Guiyang, Guizhou, China

3. Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt

4. Physics Department, Faculty of Science, University of Jeddah, Jeddah, Saudi Arabia

5. Department of Mathematics, Faculty of Science, Helwan University, Egypt

Abstract

 In this article, we propose a novel concept of the generalized picture fuzzy soft set by combining the picture fuzzy soft set and the fuzzy parameter set. For possible applications, we explain five kinds of operations (e.g., subset, equal, union, intersection, and complement) based on generalized picture fuzzy soft sets. Then, we establish several theoretical operations of generalized picture fuzzy soft sets. In addition, we present the new type by using the AND operation of the generalized picture fuzzy soft set for fuzzy decision-making and clarify its applicability with a numerical example. Finally, we give a comparison between the picture fuzzy soft set theory and the generalized picture fuzzy soft set theory. It is shown that our proposed (i.e., generalized picture fuzzy soft set theory) is viable and provide decision makers a more mathematical insight before making decisions on their options.

Publisher

IOS Press

Subject

Artificial Intelligence,General Engineering,Statistics and Probability

Reference41 articles.

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2. Intuitionistic fuzzy sets,;Atanassov;Fuzzy Sets and Systems,1986

3. Picture fuzzy sets;Cuong;Journal of Computer Science and Cybernetics,2014

4. Soft set theory-first results,;Molodtsov;Computers and Mathematics with Applications,1999

5. Soft set theory,;Maji;Computers and Mathematics with Applications,2003

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