Bidirectional project method for dual hesitant Pythagorean fuzzy multiple attribute decision‐making and their application to performance assessment of new rural construction

Abstract

The dual hesitant Pythagorean fuzzy set (DHPFS) consists of two parts, that is, the membership hesitancy function and the nonmembership hesitancy function, supporting a more exemplary and flexible access to assign values for each element in the domain. It is very suitable to handle the situation that there are various possible values in membership and nonmembership degrees to depict the true circumstance. The bidirectional project method of DHPFS calculates method considered not only the bidirectional projection magnitudes and the distance but also includes angle between objects evaluated. Therefore, this paper proposes a bidirectional project method of DHPFS to handle the multiple attribute decision-making (MADM) problem under the dual hesitant Pythagorean fuzzy environment. Through the measure between each alternative decision matrix and the positive and negative ideal alternative matrix, the ranking order all alternatives can be used to select the best alternative. Furthermore, a model for MADM has been given. Finally, a numerical example for performance assessment of new rural construction has been given to demonstrate the application of bidirectional project method of DHPFS, and we used the dual hesitant Pythagorean weighted Bonferroni mean to compare its reasonable and effectiveness. K E Y W O R D Sbidirectional project method, dual hesitant Pythagorean fuzzy set, multiple attribute decision-making, new rural construction, performance assessment 1 | INTRODUCTION Atanassov 1,2 introduced the concept of intuitionistic fuzzy set (IFS) characterized by a membership function and a nonmembership function, which is a generalization of the concept of fuzzy set, 3 whose basic component is only a membership function. For the IFS, the sum of the membership and nonmembership degrees of each ordered pair is less than or equal to 1. Xu 4 developed the intuitionistic fuzzy weighted averaging (IFWA) operator, the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator, and the intuitionistic fuzzy hybrid aggregation (IFHA) operator. Xu 5 developed some geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator and gave an application of the IFHG operator to multiple attribute group decision-making with intuitionistic fuzzy information. Zhao and Wei 6 proposed some intuitionistic fuzzy Einstein hybrid aggregation operators for multiple attribute decision-making (MADM). Li et al 7 gave some methods for multiple attribute group decision-making based on intuitionistic fuzzy Dombi Hamy mean operators. The IFS and their extensions have received more and more attention since its appearance. A new extension of IFS, namely, the Pythagorean fuzzy set (PFS), 31,32 has been developed. The PFS is also characterized by the membership and nonmembership degrees. The difference between PFS and IFS is that the square sum of the membership and nonmembership de...

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