Convexity of hesitant fuzzy sets

Article type: Research Article

Authors: Janiš, Vladimír^{a; *} | Montes, Susana^b | Renčová, Magdaléna^a

Affiliations: [a] Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovakia | [b] Department of Statistics and Operational Research, University of Oviedo, Spain

Correspondence: [*] Corresponding author. Vladimír Janiš, Department of Mathematics, Faculty of Natural Sciences, Matej Bel University, Slovakia. Tel.: +421 948 998 759; E-mail: vladimir.janis@umb.sk.

Abstract: We show that a definition of convexity based on the convexity of the score function does not guarantee preservation of convexity under intersections and provide a concept of convexity for hesitant fuzzy sets without this backdraw. We study the relationship between convex hesitant fuzzy sets and convex rough sets as their cuts.

Keywords: Fuzzy sets, hesitant fuzzy sets, convexity, rough sets

DOI: 10.3233/JIFS-162204

Journal: Journal of Intelligent & Fuzzy Systems, vol. 34, no. 4, pp. 2099-2012, 2018