Q-rung orthopair fuzzy decision-making method of multi-source information based on the compression mapping and inverse score function

Abstract

Intelligent computing is an independent algorithm system that imitates the laws and principles of nature's biological chain to design and solve practical problems in modern society, it can help people better handle some big data problems through artificial intelligence technology and different cognitive characteristics. Especially, when dealing with group decision problems, it is often considered as human behavior based on cognitive computing. The q-rung orthopair fuzzy set (q-ROFS) is not only a generalization of Pythagorean fuzzy set (PFS), but also can deal with the decision problem of multi-source information in a wider area. In this paper, we first give the detailed explanations of the relationship between the q-ROFS and q-rung orthopair fuzzy number (q-ROFN)by an example, and itis pointed out that there are some defects in the existing two ranking methods for the Pythagorean fuzzy numbers (PFNs) and intuitionistic fuzzy numbers (IFNs) through counterexamples, and then all q-ROFNs are mapped into the unit triangle of the first quadrant through q-compression mapping, and the concept of distance factor for q-ROFNs is proposed by Euclidean distance between each q-ROFN and the maximum element (1,0).Secondly, a novel inverse score function for q-ROFNs are put forward by the distance factor and hesitancy degree, and the monotonicity of the inverse score function are discussed. Finally, a new ranking criterion of q-ROFNs is given by the new score formula, and then the rationality of the ranking criterion is proved, and through the method of solving the conditional extreme value of multivariate function (Lagrange multiplier method), there is indeed an extreme value point (corresponding to the maximum q-ROFN) on υ=μ. Besides, a q-rung orthopair fuzzy decision-making method for multi-source information is given by the new ranking criterion and aggregation operations, and the comparison of examples shows that the inverse score function and decision-making method do have many advantages in the q-ROFN environment.