Averaging aggregation functions for preferences expressed as Pythagorean membership grades and fuzzy orthopairs

Rather than denoting fuzzy membership with a single value, orthopairs such as Atanassov\u27s intuitionistic membership and non-membership pairs allow the incorporation of uncertainty, as well as positive and negative aspects when providing evaluations in fuzzy decision making problems. Such representations, along with interval-valued fuzzy values and the recently introduced Pythagorean membership grades, present particular challenges when it comes to defining orders and constructing aggregation functions that behave consistently when summarizing evaluations over multiple criteria or experts. In this paper we consider the aggregation of pairwise preferences denoted by membership and non-membership pairs. We look at how mappings from the space of Atanassov orthopairs to more general classes of fuzzy orthopairs can be used to help define averaging aggregation functions in these new settings. In particular, we focus on how the notion of \u27averaging\u27 should be treated in the case of Yager\u27s Pythagorean membership grades and how to ensure that such functions produce outputs consistent with the case of ordinary fuzzy membership degrees

Pythagorean fuzzy combinative distance-based assessment with pure linguistic information and its application to financial strategies of multi-national companies

This article addresses the issue of selecting Financial Strategies in Multi-National 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

Pythagorean fuzzy Muirhead mean operators in multiple attribute decision making for evaluating of emerging technology commercialization

In today’s world, with the advancement of technology, several emerging technologies are coming. Faced with massive emerging technologies which are the component of the technology pool, how to identify the commercial potential of emerging technologies in theory and practice is an important problem. The scientific approach to the selection of these emerging technologies is one of the main objectives of the research. In this paper, we extend Muirhead mean (MM) operator and dual MM (DMM) operator to process the Pythagorean fuzzy numbers (PFNs) and then to solve the multiple attribute decision making (MADM) problems. Firstly, we develop some Pythagorean fuzzy Muirhead mean operators by extending MM and DMM operators to Pythagorean fuzzy information. Then, we prove some properties and discuss some special cases with respect to the parameter vector. Moreover, we present some new methods to deal with MADM problems with the PFNs based on the proposed MM and DMM operators. Finally, we verify the validity and reliability of our methods by using an application example for potential evaluation of emerging technology commercialization, and analyze the advantages of our methods by comparing with other existing method