A note on “possibility multi-fuzzy soft set and its application in decision making”

Article type: Research Article

Authors: Khalil, Ahmed Mostafa^a | Hassan, Nasruddin^{b; *}

Affiliations: [a] Department of Mathematics, Faculty of Science, Al-Azhar University, Assiut, Egypt | [b] School of Mathematical Sciences, Faculty of Science and Technology, Universiti KebangsaanMalaysia, UKM Bangi Selangor DE, Malaysia

Correspondence: [*] Corresponding author. Nasruddin Hassan, School of Mathematical Sciences, Faculty of Science and Technology, Universiti Kebangsaan Malaysia, 43600 UKM Bangi Selangor DE, Malaysia. Tel.: +603 89213710; E-mail: [email protected].

Abstract: The aim of this paper is to correct the assertions (3) and (4) of Theorem 3.23 proposed by Zhang and Shu [Journal of Intelligent and Fuzzy Systems 27 (2014) 2115-2125]. A counterexample illustrates the flaw of the assertions. We introduce the notion of generalized possibility multi-fuzzy soft sets and use it to correct the flaw in those assertions. Finally we introduce two new definitions and five theorems to improve the work of Zhang and Shu, along with two examples.

Keywords: Generalized distributive law, multi-fuzzy set, multi-fuzzy soft set, possibility multi-fuzzy soft set

DOI: 10.3233/JIFS-16264

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 3, pp. 2309-2314, 2017