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

In this paper, a new soft computing group decision method based on the concept of compromise ratio is introduced for determining decision makers (DMs)' weights through the group decision process under uncertainty. In this method, preferences and judgments of the DMs or experts are expressed by linguistic terms for rating the industrial alternatives among selected criteria as well as the relativ...

Decision making is a process common to human beings. The uncertainty and fuzziness of problems demand the use of the fuzzy linguistic approach to model qualitative aspects of problems related to decision. The recent proposal of hesitant fuzzy linguistic term sets supports the elicitation of comparative linguistic expressions in hesitant situations when experts hesitate among different linguisti...

The use of interval-valued hesitant fuzzy sets (IVHFS) can aid decision-makers in evaluating a variable using multiple interval numbers, making it valuable tool for addressing decision-making problems. However, fails to obtain information with greyness. grey set (GFS) improve this problem but studies on have lost the advantages IVHFS. In order accuracy and more reasonable results, is important ...

In the field of mechanical engineering, steam turbine fault diagnosis is a difficult task for mechanical engineers who are confronted with challenges in dealing with copious amounts of uncertain information. Different mechanical engineers may have their own opinions about the system fault knowledge base that differs slightly from other mechanical engineers. Thus, to solve the problems presented...

The weighted ordered weighted averaging(WOWA) operator introduced by Torra is an important aggregation technique, which includes the famous weighted averaging(WA) operator and the ordered weighted averaging(OWA) operator as special cases. In this paper, we introduce a new hesitant fuzzy decision making technique called the hesitant fuzzy weighted OWA(HFWOWA) operator. It is an extension of the ...

Since its original formulation, the theory of fuzzy sets has spawned a number of extensions where the role of membership values in the real unit interval $[0, 1]$ is handed over to more complex mathematical entities. Amongst the many existing extensions, two similar ones, the fuzzy multisets and the hesitant fuzzy sets, rely on collections of several distinct values to represent fuzzy membershi...

Fuzzy decision making is the collection of single or multicriteria techniques aiming at selecting the best alternative in case of imprecise, incomplete, and vague data. This chapter reviews the fuzzy decision making literature and summarizes the review results by tabular and graphical illustrations. The classification is based on the new extensions of fuzzy sets: Intuitionistic, hesitant, and t...