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...

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...

In the first paper in this series we presented a typical set of galactic rotation curves associated with the conformal invariant fourth order theory of gravity which has recently been advanced by Mannheim and Kazanas as a candidate alternative to the standard second order Einstein theory. Reasonable agreement with data was obtained for four representative galaxies without the need for any non-l...

Traditional idea generation techniques based on customer input usually collect information on new product needs from a random or typical set of customers. The “lead user process” takes a different approach. It collects information about both needs and solutions from users at the leading edges of the target market, as well as from users in other markets that face similar problems in a more extre...

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...