Abstract
Pythagorean fuzzy sets are highly appealing in dealing with uncertainty as they allow for greater flexibility in regards to the membership and non-membership degrees by extending the set of possible values. In this paper, we propose a multi-criteria group decision-making approach based on the Pythagorean normal cloud. Some cloud aggregation operators are presented in this paper to facilitate the appraisal of the underlying utilities of the alternatives under consideration. The concept and properties of the Pythagorean normal cloud and its backward generation algorithm, aggregation operators and distance measurement are outlined. The proposed approach resembles the TOPSIS technique, which, indeed, considers the symmetry of the distances to the positive and negative ideal solutions. Furthermore, an example from e-commerce is presented to demonstrate and validate the proposed decision-making approach. Finally, the comparative analysis is implemented to check the robustness of the results when the aggregation rules are changed.
Highlights
Decision-making is an important issue in the domain of economics and society in general [1,2], ass human input and interaction are often the decisive elements of the decision-making
The proposed Pythagorean fuzzy numbers (PFNs) approach is compared to those based on the intuitionistic normal cloud (INC) and neutrosophic normal cloud (NNC) approach developed by Wang and Yang [26] and Zhang et al [41], respectively
The concept of the Pythagorean normal cloud was proposed in this study
Summary
Decision-making is an important issue in the domain of economics and society in general [1,2], ass human input and interaction are often the decisive elements of the decision-making. The information rendered by the decision-makers might be imprecise (in the case that no exact values are provided), incomplete (in the case that certain values are missing) and uncertain (in the case that the likelihood of observing different values can be specified) Under these circumstances, the theory of the fuzzy sets can be regarded as a possible means for handling the decision-making process and overcoming the limitations, which would have existed if conventional tools (e.g., crisp sets) had been applied. This implies that the underlying cognitive peculiarities of decision-makers can be accounted for Another example of the concepts for handling imprecise information is the hesitant fuzzy set proposed by Torra [13], which allows considering the hesitancy to provide certain ratings of the alternatives. The proposed approach relies on the backward cloud generator, aggregation operators and distance measures to deal with the proposed PNCs. Thereafter, the group decision-making procedure based on the PNCs is proposed. The paper concludes with an illustrative example where the proposed approach is tested by considering the case study of e-commerce
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