Fuzzy Entropy for Pythagorean Fuzzy Sets with Application to Multicriterion Decision Making

Abstract

The concept of Pythagorean fuzzy sets (PFSs) was initially developed by Yager in 2013, which provides a novel way to model uncertainty and vagueness with high precision and accuracy compared to intuitionistic fuzzy sets (IFSs). The concept was concretely designed to represent uncertainty and vagueness in mathematical way and to furnish a formalized tool for tackling imprecision to real problems. In the present paper, we have used both probabilistic and nonprobabilistic types to calculate fuzzy entropy of PFSs. Firstly, a probabilistic-type entropy measure for PFSs is proposed and then axiomatic definitions and properties are established. Secondly, we utilize a nonprobabilistic-type with distances to construct new entropy measures for PFSs. Then a min–max operation to calculate entropy measures for PFSs is suggested. Some examples are also used to demonstrate suitability and reliability of the proposed methods, especially for choosing the best one/ones in structured linguistic variables. Furthermore, a new method based on the chosen entropies is presented for Pythagorean fuzzy multicriterion decision making to compute criteria weights with ranking of alternatives. A comparison analysis with the most recent and relevant Pythagorean fuzzy entropy is conducted to reveal the advantages of our developed methods. Finally, this method is applied for ranking China-Pakistan Economic Corridor (CPEC) projects. These examples with applications demonstrate practical effectiveness of the proposed entropy measures.

Entropy-Based GLDS Method for Social Capital Selection of a PPP Project with q-Rung Orthopair Fuzzy Information

“…To denote the entropy of the Pythagorean fuzzy set (PFS), Xue et al [ 52 ] first developed the Pythagorean fuzzy entropy and the interval-valued Pythagorean fuzzy entropy based on the similarity measure and hesitance measure; then, a Pythagorean fuzzy entropy-based LINMAP method was proposed for a railway project investment problem. Yang and Hussain [ 53 ] also defined several Pythagorean fuzzy entropy for MADM. Thus, motivated by intuitionistic entropy and Pythagorean fuzzy entropy, in this study, the q-rung orthopair fuzzy entropy (q-ROFE) was defined as follows.…”

Analysis of Decision Support System Based on 2-Tuple Spherical Fuzzy Linguistic Aggregation Information

“…Unfortunately, the former does not take a good decision on better company feeds for more broiler chicken weight, giving a higher per kg price and generating more revenue from the flock. For the best company (alternative) selection for the feeds, we have four attributes (1) weight of the chicken, (2) price of the feeds, (3) quality of chicken, and (4) price of chicken, with the weighting vector Θ = (0.27, 0.24, 0.23, 0.26) T , which is obtained by using the method of [52]. Now to select the best feeds company, we collect the data from the different forms, and write in the form of 2-tuple spherical fuzzy numbers.…”

TOPSIS Method Based on Correlation Coefficient and Entropy Measure for Linguistic Pythagorean Fuzzy Sets and Its Application to Multiple Attribute Decision Making

“…In the initial stage of decision-making evolution, crisp numbers are usually used to rate the alternatives [10]. With the growing complexity of decision-making problems, human beings do not have the capability to express the vague and ambiguous information [11][12][13]. To model this kind of information, fuzzy set (FS) was initially put forward in [14].…”