Generalized convexities related to aggregation operators of fuzzy sets

Díaz, Susana; Induráin, Esteban; Janiš, Vladimír; Llinares, Juan Vicente; Montes, Susana

doi:10.14736/kyb-2017-3-0383

Cited by 4 publications

(3 citation statements)

References 14 publications

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“…The need for managing imprecision in real-world problems has been a drawn-out exploration challenge that has originated several extensions of fuzzy sets. Thus, many authors studied different types of convexity of fuzzy sets and its extensions (see, for instance, Ammar and Metz 1992;Díaz et al 2017;Syau and Lee 2006;Zhang et al 2016).…”

Section: Introductionmentioning

confidence: 99%

Convexity and level sets for interval-valued fuzzy sets

Huidobro

Alonso

Janiš

et al. 2022

Fuzzy Optim Decis Making

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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.

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Section: Introductionmentioning

confidence: 99%

Convexity and level sets for interval-valued fuzzy sets

Huidobro

Alonso

Janiš

et al. 2022

Fuzzy Optim Decis Making

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“…On the other hand, convexity is a mathematical notion that can be a useful tool in many different problems and, in particular, in decision-making problems. Since Zadeh introduced convexity for fuzzy sets, several authors have been developing this theory (see, for instance, Ammar and Metz [1], Diaz et al [8], Ramik and Vlach [15], Syau and Lee [17] and Yang [19]). It has important applications in areas such as optimization [13].…”

Section: Introductionmentioning

confidence: 99%

Convexity of Interval-valued Fuzzy Sets Applied to Decision-Making Problems

Huidobro¹,

Alonso²,

Janiš³

et al. 2021

Atlantis Studies in Uncertainty Modelling

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“…Since most of practical problems include approximate information, fuzzy convexity has been studied in deep in the literature. Thus, several types of convexity of fuzzy sets were studied by different authors (see, for instance, Ammar and Metz [2], Diaz et al [8], Ramik and Vlach [25], Sarkar [29], Syau and Lee [31] and Yang [38]).…”

Section: Introductionmentioning

confidence: 99%

Convexity of hesitant fuzzy sets based on aggregation functions

et al. 2021

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Convexity is one of the most important geometric properties of sets and a useful concept in many fields of mathematics, like optimization. As there are also important applications making use of fuzzy optimization, it is obvious that the studies of convexity are also frequent. In this paper we have extended the notion of convexity for hesitant fuzzy sets in order to fulfill some necessary properties. Namely, we have found an appropriate definition of convexity for hesitant fuzzy sets on any ordered universe based on aggregation functions such that it is compatible with the intersection, that is, the intersection of two convex hesitant fuzzy sets is a convex hesitant fuzzy set and it fulfills the cut worthy property.

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Generalized convexities related to aggregation operators of fuzzy sets

Cited by 4 publications

References 14 publications

Convexity and level sets for interval-valued fuzzy sets

Convexity and level sets for interval-valued fuzzy sets

Convexity of Interval-valued Fuzzy Sets Applied to Decision-Making Problems

Convexity of hesitant fuzzy sets based on aggregation functions

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