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...

The aim of this manuscript is to introduce the \((\alpha,\beta)\)-hesitant fuzzy set and apply it semigroups. In paper, as a generalization concept hesitant sets semigroup theory, subsemigroups semigroups introduced, related properties are discussed. Furthermore, we define study ideals on particular, investigate structure ideal generated by in semigroup. addition, also concepts semiprime semigr...

Abstract The paper aims to present an integrated approach solve the decision-making problem under probabilistic hesitant fuzzy information (PHFI) features, which is extension of set. considered PHFI not only allows multiple opinions, but also associates occurrence probability each opinion, increases reliability information. Motivated by these features PHFI, presented decision with partial known...

The present study considered a fuzzy natural color system (NCS) in which triangular pyramid membership functions are constructed on the NCS color triangle. This system can process a fuzzy input to an NCS system and output to a center of gravity of three weights associated with respective grades. Triangular membership functions are applied to the hue, and triangular pyramid membership functions ...

The intuitionistic hesitant fuzzy set (IHFS) is an enriched version of sets (HFSs) that can cover both (FSs) and (IFSs). By assigning membership non-membership grades as subsets [0, 1], the IHFS model handle situations more proficiently. Another related theory pair analysis (SPA), which considers certainties uncertainties a cohesive system represents them from three aspects: identity, discrepan...