In this study, a new technique for order preference by similarity to ideal solution (TOPSIS)‐based methodology is proposed to solve multicriteria group decision‐making problems within Pythagorean fuzzy environment, where the information about weights of both the decision makers (DMs) and criteria are completely unknown. Initially, generalized distance measure for Pythagorean fuzzy sets (PFSs) is defined and used to initiate a new Pythagorean fuzzy entropy measure for computing weights of the criteria. In the decision‐making process, at first, weights of DMs are computed using TOPSIS through the geometric distance model. Then, weights of the criteria are determined using the entropy weight model through the newly defined entropy measure for PFSs. Based on the evaluated criteria weights, TOPSIS is further applied to obtain the score value of alternatives corresponding to each decision matrix. Finally, the score values of the alternatives are aggregated with the calculated DMs’ weights to obtain the final ranking of the alternatives to avoid the loss of information, unlike other existing methods. Several numerical examples are considered, solved, and compared with the existing methods.
In this paper, a series of similarity measures based on point operators for Pythagorean fuzzy sets are proposed. Using the proposed similarity measures, two new aggregation operators, viz., Pythagorean fuzzy‐dependent averaging operator and Pythagorean fuzzy‐dependent geometric operator, are developed. The advantage of using these operators is that the influence of unfair arguments of aggregated results could be eliminated, since the associated weights are taken from the aggregated Pythagorean fuzzy arguments. Also, the proposed operators have the capability to adjust the degree of aggregated arguments with the controlling parameters. To establish the application potentiality of those operators, a methodology for solving multicriteria group decision‐making problems having Pythagorean fuzzy arguments is developed. A numerical example is provided to demonstrate the proficiency of the proposed method. The achieved results are compared with the results of other existing technique.
In multicriteria decision‐making (MCDM), the existing aggregation operators are mostly based on algebraic t‐conorm and
t‐norm. But, Archimedean
t‐conorms and
t‐norms are the generalized forms of
t‐conorms and
t‐norms which include algebraic, Einstein, Hamacher, Frank, and other types of
t‐conorms and
t‐norms. From that view point, in this paper the concepts of Archimedean
t‐conorm and
t‐norm are introduced to aggregate Pythagorean hesitant fuzzy information. Some new operational laws for Pythagorean hesitant fuzzy numbers based on Archimedean
t‐conorm and
t‐norm have been proposed. Using those operational laws, Archimedean
t‐conorm and
t‐norm‐based Pythagorean hesitant fuzzy weighted averaging operator and weighted geometric operator are developed. Some of their desirable properties have also been investigated. Afterwards, these operators are applied to solve MCDM problems in Pythagorean hesitant fuzzy environment. The developed Archimedean aggregation operators are also applicable in Pythagorean fuzzy contexts also. To demonstrate the validity, practicality, and effectiveness of the proposed method, a practical problem is considered, solved, and compared with other existing method.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.