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Parameter Reductions of Bipolar Fuzzy Soft Sets with Their Decision-Making Algorithms

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Department of Mathematics, University of the Punjab, New Campus, Lahore 54590, Pakistan
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Department of Mathematics, College of Science, Jazan University, New Campus, P.O. Box 2097, Jazan 45142, Saudi Arabia
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BORDA Research Unit and IME, Universidad de Salamanca, 37008 Salamanca, Spain
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Author to whom correspondence should be addressed.
Symmetry 2019, 11(8), 949; https://doi.org/10.3390/sym11080949
Received: 12 June 2019 / Revised: 11 July 2019 / Accepted: 12 July 2019 / Published: 25 July 2019
Parameter reduction is a very important technique in many fields, including pattern recognition. Many reduction techniques have been reported for fuzzy soft sets to solve decision-making problems. However, there is almost no attention to the parameter reduction of bipolar fuzzy soft sets, which take advantage of the fact that membership and non-membership degrees play a symmetric role. This methodology is of great importance in many decision-making situations. In this paper, we provide a novel theoretical approach to solve decision-making problems based on bipolar fuzzy soft sets and study four types of parameter reductions of such sets. Parameter reduction algorithms are developed and illustrated through examples. The experimental results prove that our proposed parameter reduction techniques delete the irrelevant parameters while keeping definite decision-making choices unchanged. Moreover, the reduction algorithms are compared regarding the degree of ease of computing reduction, applicability, exact degree of reduction, applied situation, and multi-use of parameter reduction. Finally, a real application is developed to describe the validity of our proposed reduction algorithms. View Full-Text
Keywords: bipolar fuzzy soft set; soft set; parameter reduction; algorithm; decision-making bipolar fuzzy soft set; soft set; parameter reduction; algorithm; decision-making
MDPI and ACS Style

Ali, G.; Akram, M.; Koam, A.N.A.; Alcantud, J.C.R. Parameter Reductions of Bipolar Fuzzy Soft Sets with Their Decision-Making Algorithms. Symmetry 2019, 11, 949. https://doi.org/10.3390/sym11080949

AMA Style

Ali G, Akram M, Koam ANA, Alcantud JCR. Parameter Reductions of Bipolar Fuzzy Soft Sets with Their Decision-Making Algorithms. Symmetry. 2019; 11(8):949. https://doi.org/10.3390/sym11080949

Chicago/Turabian Style

Ali, Ghous, Muhammad Akram, Ali N. A. Koam, and José Carlos R. Alcantud. 2019. "Parameter Reductions of Bipolar Fuzzy Soft Sets with Their Decision-Making Algorithms" Symmetry 11, no. 8: 949. https://doi.org/10.3390/sym11080949

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