Some distance measures for type 2 hesitant fuzzy sets and their applications to multi-criteria group decision-making problems

Dynamic nonlinear simplified neutrosophic sets for multiple-attribute group decision making

In this paper, the concept of a dynamic nonlinear simplified neutrosophic set (DNSNS) is proposed for describing the real-time changing expert preference information. Furthermore, the DNSNS aggregation model and decision algorithm are provided to solve the actual multiple-attribute group decision making (MAGDM) problems. The basic notions, the similarity measure, the entropy measure, and the index of distance of DNSNS are presented first. Secondly, the univariate time series of DNSNS are projected into dynamic nonlinear simplified neutrosophic curves in three-dimensional space. The areas of the surface enclosed by the curves represent the variance among the DNSNSs. Thus, the DNSNS aggregation model is established correctly without preprocessing the original data. Afterward, the aggregation algorithm extended from the plant growth simulation algorithm (PGSA) is proposed for calculating the optimal aggregation preference curve and constructing the collective matrix. Additionally, a novel corresponding decision algorithm based on TOPSIS and projection theory is proposed for obtaining the overall ranking of alternatives in the actual MAGDM problem. Finally, a typical example is presented to illustrate the feasibility and effectiveness of the proposed model and algorithm.

A new distance measure for pythagorean fuzzy sets based on earth mover’s distance and its applications

In uncertain information processing, new knowledge can be discovered by measuring the proximity between discovered and undiscovered knowledge. Pythagorean Fuzzy Sets (PFSs) is one of the important tools to describe the natural attributes of uncertain information. Therefore, how to appropriately measure the distance between PFSs is an important topic. The earth mover’s distance (EMD) is a real distance metric that can be used to describe the difference between two distribution laws. In this paper, a new distance measure for PFSs based on EMD is proposed. It is a new perspective to measure the distance between PFSs from the perspective of distribution law. First, a new distance measure namely DEMD is presented and proven to satisfy the distance measurement axiom. Second, an example is given to illustrate the advantages of DEMD compared with other distance measures. Third, the problem statements and solving algorithms of pattern recognition, medical diagnosis and multi-criteria decision making (MCDM) problems are given. Finally, by comparing the application of different methods in pattern recognition, medical diagnosis and MCDM, the effectiveness and practicability of DEMD and algorithms presented in this paper are demonstrated.