Li and Chen (Cognit Comput. 2018; 10:496–505) proposed the concept of D-intuitionistic hesitant fuzzy set as well a method for comparing two sets. have by introducing degree belief decision maker regarding opinion an expert in existing definition intuitionistic set. In future, other researchers may use Chen’s their research work. However, after deep study, it is observed that fails to different...

We define an extended fuzzy equivalence relation, discuss some basic properties of extended fuzzy equivalence relations, find the extended fuzzy equivalence relation generated by a fuzzy relation in a set, and give some lattice theoretic properties of extended fuzzy equivalence relations.

To investigate implicative filters of hoops furthermore, we apply n-fold theory to (?, ?)-hesitant fuzzy and introduce the notion (?,?)-hesitant filters, obtain some conditions for a filter be filter. We also study preimage image filters.

A sophisticated three-way decision model utilizing a multi-granularity probabilistic hesitant fuzzy rough set is introduced to mitigate the issue of information loss arising from sets when characterizing information. Initially, properties are examined, subsequently proposing distance measure and function tailored these sets. Following this, multi-attribute group decision-making incorporating es...

Correlation is an important index in decision-making. In weighted extended hesitant fuzzy sets (WEHFSs) environment, researchers have only defined a class of correlation coefficients between WEHFSs with values the unit interval [ 0 , 1 ] . This not ideal because it does extend classical coefficient case sets. fact, negative − are ignored, and such neglectfulness leads to unreasonable results ot...

The main purpose of this paper is to suggest an approach of multi-criteria decision-making that combines a hesitant fuzzy linguistic term set (HFLTS) with an outranking method involving systematic comparisons of the assessment values of alternatives for each criterion. A HFLTS is more suitable than the traditional fuzzy linguistic set for describing decision-makers’ preferences when they prefer...