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.
This article addresses the issue of selecting Financial Strategies in MultiNational companies (F.S.M.). The F.S.M. typically has to consider multiple factors involving multiple stakeholders and, hence, can be handled by applying an appropriate Multi-Criteria Group Decision-Making (M.C.G.D.M.) approach. To address this issue, we develop an M.C.G.D.M. framework to tackle the F.S.M. problem. To handle inherent uncertainty in business decisions as reflected by linguistic reasoning, we embark on constructing a Linguistic Pythagorean Fuzzy (L.P.F.) M.C.G.D.M. framework that is capable of tackling both uncertain decision information and linguistic variables. The proposed approach extends the combinative distancebased assessment (C.O.D.A.S.) method into the L.P.F. environment, and processes decision input expressed as Pythagorean fuzzy sets (P.F.S.) and pure linguistic variables (rather than converting linguistic information into fuzzy numbers). The developed L.P.F.-C.O.D.A.S. technique aggregates the L.P.F. information and is applied to the F.S.M. problem with uncertain linguistic information. A comparative analysis is carried out to compare the results obtained from the proposed L.P.F.-C.O.D.A.S. approach with those from other extensions of C.O.D.A.S. Furthermore, a sensitivity analysis is conducted to check the impact of changes in a distance threshold parameter on the ranking results.
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