A new distance between rankings.

This paper analyzes the behavior of the well-known Spearman's footrule distance (-distance) to measure the distance between two rankings over the same set of objects. We show that -distance is not invariant to labeling, and therefore, it suffers from a serious drawback for its use in applications. To circumvent this problem, we propose a new distance between rankings which is invariant under indexing (i.

Making Group Decisions within the Framework of a Probabilistic Hesitant Fuzzy Linear Regression Model.

A fuzzy set extension known as the hesitant fuzzy set (HFS) has increased in popularity for decision making in recent years, especially when experts have had trouble evaluating several alternatives by employing a single value for assessment when working in a fuzzy environment. However, it has a significant problem in its uses, i.e.

The Group Decision-Making Using Pythagorean Fuzzy Entropy and the Complex Proportional Assessment.

The Pythagorean fuzzy sets conveniently capture unreliable, ambiguous, and uncertain information, especially in problems involving multiple and opposing criteria. Pythagorean fuzzy sets are one of the popular generalizations of the intuitionistic fuzzy sets. They are instrumental in expressing and managing hesitant under uncertain environments, so they have been involved extensively in a diversity of scientific fields.

New Pythagorean Entropy Measure with Application in Multi-Criteria Decision Analysis.

The purpose of this paper is to propose a new Pythagorean fuzzy entropy for Pythagorean fuzzy sets, which is a continuation of the Pythagorean fuzzy entropy of intuitionistic sets. The Pythagorean fuzzy set continues the intuitionistic fuzzy set with the additional advantage that it is well equipped to overcome its imperfections. Its entropy determines the quantity of information in the Pythagorean fuzzy set.