Convexity and level sets for interval-valued fuzzy sets

Pedro Huidobro (), Pedro Alonso (), Vladimír Janiš () and Susana Montes ()
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Pedro Huidobro: University of Oviedo
Pedro Alonso: University of Oviedo
Vladimír Janiš: Matej Bel University
Susana Montes: University of Oviedo

Fuzzy Optimization and Decision Making, 2022, vol. 21, issue 4, No 3, 553-580

Abstract: Abstract Convexity is a deeply studied concept since it is very useful in many fields of mathematics, like optimization. When we deal with imprecision, the convexity is required as well and some important applications can be found fuzzy optimization, in particular convexity of fuzzy sets. In this paper we have extended the notion of convexity for interval-valued fuzzy sets in order to be able to cover some wider area of imprecision. We show some of its interesting properties, and study the preservation under the intersection and the cutworthy property. Finally, we applied convexity to decision-making problems.

Keywords: Interval-valued fuzzy set; Epistemic interpretation; Intersection; Level set; Convexity; Decision-making (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10700-021-09376-7

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