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...

With respect to multiple attribute decision making (MADM) problems in which the attribute values take the form of hesitant fuzzy elements, the traditional grey relational projection (GRP) method is extended to solve multiple attribute decision making problems under hesitant fuzzy environment. Based on the hesitant fuzzy decision matrix provided by decision makers, all feasible alternatives are ...

The soft set theory is a newly mathematical tool to deal with uncertain problems. However, the classical soft sets are not appropriate to deal with imprecise and fuzzy parameters. In this paper, we introduce the average function and propose the interval-valued intuitionistic hesitant fuzzy soft sets (IVIHFSSs) which are a combination of the interval-valued intuitionistic hesitant fuzzy sets and...

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...

In hesitant fuzzy sets (HFSs), which are generalized from fuzzy sets, the membership degree of an element to a set, for which decision-makers hesitate while considering several values before expressing their preferences concerning weights and data, can be assigned one or more possible precise values between zero and one. If two or more decision-makers assign an equivalent value, that value is o...

The main goal of this publication is to show that the basic constructions in theories fuzzy sets, soft hesitant sets or intuitionistic have a common background, based on theory monads categories. It proven ad hoc defined concepts individual theories, such as power set structures these relations approximation operators by are only special examples applications monad This makes it possible, one h...

Hesitant fuzzy sets (HFSs), which were generalized from fuzzy sets, constrain the membership degree of an element to be a set of possible values between zero and one; furthermore if two or more decision-makers select the same value, it is only counted once. However, a situation where the evaluation value is repeated several times differs from one where the value appears only once. Multiset hesi...

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...