Pythagorean fuzzy preference ranking organization method of enrichment evaluations

Abstract

Recently, a new extension of fuzzy sets, Pythagorean fuzzy sets (PFS), has attracted a lot of attention from scholars in various fields of research. Due to PFS’s powerfulness in modeling the imprecision of human perception in multicriteria decision‐making (MCDM) problems, this paper aims to extend the classical preference ranking organization method of enrichment evaluations (PROMETHEE) into the Pythagorean fuzzy environment. The proposed method takes not only the weights related to different criteria but also the preference relations as Pythagorean fuzzy numbers, therefore providing a broader range of choices for the decision‐maker to express their preferences. Five properties are put forward to regulate the designing of both intuitionistic and Pythagorean fuzzy PROMETHEE (PF‐PROMETHEE) preference functions. Furthermore two illustrative examples are given to demonstrate the detailed procedure of PF‐PROMETHEE, and comparisons are made to distinguish the differences among our proposed method, the classical PROMETHEE and intuitionistic PROMETHEE. The results show that PF‐PROMETHEE is effective, comprehensive, and applicable to a wide range of MCDM problems.

Pythagorean fuzzy likelihood function based on beta distributions and its based dominance ordering model in an uncertain multiple criteria decision support framework

“…Lin et al 37 improved the technique for order preference by similarity to ideal solutions (TOPSIS) by virtue of correlation coefficients and entropy measures for linguistic PF sets. Zhang et al 38 exploited generalized PF preference functions to promote an advanced preference ranking organization method for enrichment evaluations (PROMETHEE) involving PF information. Leveraging the advantages of PF theory, numerous investigations have focused on the exploitation of PF sets in managing the uncertainties associated with the decision‐maker's judgments and manipulating the MCDA problems under conditions of vagueness and impreciseness 4,6,14,23,24 …”

Multiple Criteria Group Decision Making Using a Parametric Linear Programming Technique for Multidimensional Analysis of Preference Under Uncertainty of Pythagorean Fuzziness

“…Step 8 Ranking of Alternatives: Solve for the optimal weightw j and the optimalZ k i i . Employ (28) to derive the optimal collective comprehensive closeness measure K k=1 CM k i of each a i for acquiring the ultimate priority ranking of alternatives and the best compromise solution.…”

“…Accordingly, PF sets have been widely popular in handling complex uncertainty involved in practical decision-making problems, and they have attracted numerous scholars' research interests in recent years. A series of methodologies have been developed to handle a variety of decision-making problems, such as PF techniques for order preference by similarity to ideal solutions (TOPSIS) [23], [25], [26], PF preference ranking organization methods for enrichment evaluations (PROMETHEE) [27], [28], cubic PF weighted averaging and weighted geometric operations [20], weighted distance based approximation with new score functions [29], and GDM approaches based on PF preference relations [14] and based on order relations for PF numbers [15]. Because PF sets provide a powerful and flexible tool in modeling real-world uncertainty, the extension of the LINMAP structure can create a more promising research subject and capture vagueness and incompleteness in human evaluations.…”

Fermatean fuzzy linguistic weighted averaging/geometric operators based on modified operational laws and their application in multiple attribute group decision-making

“…Further, if we consider the sum of the squares of both the degrees, i.e., 0.8 2 +0.5 2 , that gives 0.89 <1, hence this information can be represented in the form of PFS, not in IFS. In a short span, the PFS theory has become an efficient tool to solve various real-life problems [37][38][39][40][41][42][43][44][45][46].…”