Novel score functions of generalized orthopair fuzzy membership grades with application to multiple attribute decision making

The notion of generalized orthopair fuzzy sets, as a natural extension of both intuitionistic fuzzy sets and Pythagorean fuzzy sets, provides a more flexible framework for expressing and processing uncertain information. In intelligent decision making based on generalized orthopair fuzzy sets, it is a pivotal issue to compare or rank q-rung orthopair membership grades. In this work, we investigate the ranking issue of q-rung orthopair membership grades from a geometric point of view. We propose the regular Minkowski distance of q-rung orthopair membership grades which strengthens or extends some useful distance measures in the literature. By virtue of the regular Minkowski distance, we define a generic class of novel score functions called the Minkowski score function of q-rung orthopair membership grades. This new type of score functions not only extends the existing notions such as the expectation score function, but also overcomes the difficulty that Hamming (or Euclidean) distance-based score functions cannot distinguish those intuitionistic fuzzy values with identical expectation score (or ideal positive degree). We examine several critical properties of the Minkowski score function of q-rung orthopair membership grades. By taking advantage of the q-rung orthopair fuzzy weighted averaging (or geometric) operator and the Minkowski score function, a flexible approach is developed to support multiple attribute decision making with generalized orthopair fuzzy soft information. Finally, a benchmark problem is used for comparison with several existing methods to verify the cogency and feasibility of the proposed method.