Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making
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Intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices and their application in decision-making Serdar Enginoglu ˇ 1
· Burak Arslan1
Received: 22 March 2020 / Revised: 22 August 2020 / Accepted: 5 September 2020 © SBMAC - Sociedade Brasileira de Matemática Aplicada e Computacional 2020
Abstract This study aims to propose the concept of intuitionistic fuzzy parameterized intuitionistic fuzzy soft matrices (ifpifs-matrices) and to present several of its basic properties. Therefore, it would be possible to improve the problem-modelling capabilities of the available intuitionistic fuzzy parameterized intuitionistic fuzzy soft sets in the occurrence of a large number of data. Moreover, by using ifpifs-matrices, we suggest a new soft decision-making method, denoted by EA20, and apply it to a multi-criteria group decision-making (MCGDM) problem. We then compare the ranking performance of EA20 for five noise-removal filters with those of ten state-of-the-art soft decision-making methods. The results show that EA20 successfully models performance-based value assignment problems. Finally, we discuss ifpifs-matrices and EA20 for further research. Keywords Intuitionistic fuzzy sets · Soft sets · Soft matrices · ifpifs-matrices · Multi-criteria group decision-making Mathematics Subject Classification 03F55 · 90B50
1 Introduction Recently, many mathematical tools have been developed to overcome problems involving uncertainties. Fuzzy sets Zadeh (1965) and soft sets Molodtsov (1999) are among the known mathematical tools, and so far many theoretical and applied studies have been conducted on these concepts Atmaca (2017, 2019); Bera et al. (2017); Ça˘gman et al. (2010, 2011b); Ça˘gman and Deli (2010b, 2012b); Ça˘gman et al. (2011b); Çıtak and Ça˘gman (2017); ElShafei and Al-Shami (2020); Engino˘glu et al. (2019, 2015); Engino˘glu and Memi¸s (2018a); Karaaslan (2019); Maji et al. (2001a, 2003); Petchimuthu et al. (2020); Riaz and Hashmi
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Serdar Enginoˇglu [email protected] Burak Arslan [email protected]
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Department of Mathematics, Faculty of Arts and Sciences, Çanakkale Onsekiz Mart University, Çanakkale, Turkey 0123456789().: V,-vol
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S. Engino ˇ glu, B. Arslan
(2017, 2018, 2019); Riaz et al. (2018); Riaz et al. (2020a, b); Senel ¸ (2016, 2018a, b); Sezgin et al. (2019a, b); Sulukan et al. (2019). However, fuzzy sets, soft sets, or their hybrid versions cannot simply model some problems containing uncertainty. For example, if six of the data produced by the detector x, which sends ten signals a second, are positive and four are negative, then this case is expressed with the fuzzy value μ(x) = 0.6. Since intuitionistic fuzzy sets are a generalization of fuzzy sets, intuitionistic fuzzy sets can model this problem with intuitionistic fuzzy value μ(x) = 0.6 and ν(x) = 0.4. However, if six of the data collected from the same detector are positive, three are negative, and one is corrupt, then this case cannot be expressed with fuzzy values but with an intuitionistic fuzzy v
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