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

ABSTRACT

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.