Multiple attribute decision-making method for dealing with heterogeneous relationship among attributes and unknown attribute weight information under q-rung orthopair fuzzy environment

A Q-rung orthopair fuzzy set (q-ROFS) originally proposed by Yager (2017) is a new generalization of orthopair fuzzy sets, which has a larger representation space of acceptable membership grades and gives decision makers more flexibility to express their real preferences. In this paper, for multiple attribute decision-making problems with q-rung orthopair fuzzy information, we propose a new method for dealing with heterogeneous relationship among attributes and unknown attribute weight information. First, we present two novel q-rung orthopair fuzzy extended Bonferroni mean (q-ROFEBM) operator and its weighted form (q-ROFEWEBM). A comparative example is provided to illustrate the advantages of the new operators, that is, they can effectively model the heterogeneous relationship among attributes. We prove that some existing known intuitionistic fuzzy aggregation operators and Pythagorean fuzzy aggregation operators are special cases of the proposed q-ROFEBM and q-ROFEWEBM operators. Meanwhile, several desirable properties are also investigated. Then, a new knowledge-based entropy measure for q-ROFSs is also proposed to obtain the attribute weights. Based on the proposed q-ROFWEBM and the new entropy measure, a new method is developed to solve multiple attribute decision making problems with q-ROFSs. Finally, an illustrative example is given to demonstrate the application process of the proposed method, and a comparison analysis with other existing representative methods is also conducted to show its validity and superiority.