A Multicriteria Picture Fuzzy Decisionmaking Model for Green Supplier Selection based on Fractional Programming Due to the increasing complexity in green supplier selection, there would be some important issues for expressing inherent uncertainty or imprecision of decision makersxe2x80x99 cognitive information in decision making process. As an extension of intuitionistic fuzzy sets (IFSs) and neutrosophic sets (NSs), picture fuzzy sets (PFSs) can better model and represent the hesitancy and uncertainty of decision makersxe2x80x99 preference information. In this study, an attempt has been made to present a multicriteria picture fuzzy decisionmaking model for green supplier selection based on fractional programming. In this approach, the ratings of alternatives and weights of criteria are represented by PFSs and IFSs, respectively. Based on the available information, some pairs of fractional programming models are derived from the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and the proposed biparametric picture fuzzy distance measure to determine the relative closeness coefficient intervals of green suppliers, which are aggregated for the criteria to generate the ranking order of all green suppliers by computing their optimal degrees of membership based on the ranking method of interval numbers. Finally, an example is conducted to validate the effectiveness of the proposed multicriteria decision making (MCMD) method.

Negation of Pythagorean Fuzzy Number Based on a New Uncertainty Measure Applied in a Service Supplier Selection System The Pythagorean fuzzy number (PFN) consists of membership and nonmembership as an extension of the intuitionistic fuzzy number. PFN has a larger ambiguity, and it has a stronger ability to express uncertainty. In the multicriteria decisionmaking (MCDM) problem, it is also very difficult to measure the ambiguity degree of a set of PFN. A new entropy of PFN is proposed based on a technique for order of preference by similarity to ideal solution (Topsis) method of revised relative closeness index in this paper. To verify the new entropy with a good performance in uncertainty measure, a new Pythagorean fuzzy number negation approach is proposed. We develop the PFN negation and find the correlation of the uncertainty measure. Existing methods can only evaluate the ambiguity of a single PFN. The newly proposed method is suitable to systematically evaluate the uncertainty of PFN in Topsis. Nowadays, there are no uniform criteria for measuring service quality. It brings challenges to the future development of airlines. Therefore, grasping the future market trends leads to winning with advanced and highquality services. Afterward, the applicability in the service supplier selection system with the new entropy is discussed to evaluate the service quality and measure uncertainty. Finally, the new PFN entropy is verified with a good ability in the last MCDM numerical example.