A New Approach for Normal Parameter Reduction Using σ -Algebraic Soft Sets and Its Application in Multi-Attribute Decision Making

Abid Khan, Miin-Shen Yang, Mirajul Haq, Ashfaq Ahmad Shah and Muhammad Arif
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Abid Khan: School of Management Science and Engineering, Nanjing University of Information Science & Technology, Nanjing 210044, China
Miin-Shen Yang: Department of Applied Mathematics, Chung Yuan Christian University, Chung-Li, Taoyuan 32023, Taiwan
Mirajul Haq: Department of Mathematics, Abdul Wali Khan University, Mardan 23200, Pakistan
Ashfaq Ahmad Shah: Research Center for Environment and Society, Hohai University, Nanjing 210098, China
Muhammad Arif: Department of Computer Science, University of Management and Technology, Lahore 54770, Pakistan

Mathematics, 2022, vol. 10, issue 8, 1-17

Abstract: The soft set is one of the key mathematical tools for uncertainty description and has many applications in real-world decision-making problems. However, most of the time, these decision-making problems involve less important and redundant parameters, which make the decision making process more complex and challenging. Parameter reduction is a useful approach to eliminate such irrelevant and redundant parameters during soft set-based decision-making problems without changing their decision abilities. Among the various reduction methods of soft sets, normal parameter reduction (NPR) can reduce decision-making problems without changing the decision order of alternatives. This paper mainly develops a new algorithm for NPR using the concept of σ -algebraic soft sets. Before this, the same concept was used to introduce the idea of intersectional reduced soft sets (IRSSs). However, this study clarifies that the method of IRSSs does not maintain the decision order of alternatives. Thus, we need to develop a new approach that not only keeps the decision order invariant but also makes the reduction process more simple and convenient. For this reason, we propose a new algorithm for NPR using σ -algebraic soft sets that not only overcome the existing problems of IRSSs method but also reduce the computational complexity of the NPR process. We also compare our proposed algorithm with one of the existing algorithms of the NPR in terms of computational complexity. It is evident from the experimental results that the proposed algorithm has greatly reduced the computational complexity and workload in comparison with the existing algorithm. At the end of the paper, an application of the proposed algorithm is explored by a real-world decision-making problem.

Keywords: fuzzy sets; soft sets; ?-algebraic soft sets; normal parameter reduction; algorithm; multi-attribute decision making (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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