A property on convex fuzzy sets

Yang, Xin; Yang, Feng

doi:10.1016/s0165-0114(01)00075-6

Cited by 26 publications

(3 citation statements)

References 8 publications

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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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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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“…In an earlier paper [11], we formulated several fuzzy nonlinear programming problems based on the concept of concavity and quasiconcavity. Different types of concavity and generalized concavity of fuzzy sets were studied by several authors, including Ammar and Metz [1], Ramik and Vlach [7], Sarkar [9], Syau and coworkers [3,10,12], and Yang [14][15][16], aiming at applications to fuzzy nonlinear programming. For a more detailed treatment, the reader should consult the recent book by Ramik and Vlach [8].…”

Section: Introductionmentioning

confidence: 99%