Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making

The neutrosophic cubic set can contain much more information to express its interval neutrosophic numbers and single-valued neutrosophic numbers simultaneously in indeterminate environments. Hence, it is a usual tool for expressing much more information in complex decision-making problems. Unfortunately, there has been no research on similarity measures of neutrosophic cubic sets so far. Since the similarity measure is an important mathematical tool in decision-making problems, this paper proposes three cosine measures between neutrosophic cubic sets based on the included angle cosine of two vectors, distance, and cosine functions, and investigates their properties. Then, we develop a cosine measures-based multiple attribute decision-making method under a neutrosophic cubic environment in which, from the cosine measure between each alternative (each evaluated neutrosophic cubic set) and the ideal alternative (the ideal neutrosophic cubic set), the ranking order of alternatives and the best option can be obtained, corresponding to the cosine measure values in the decision-making process. Finally, an illustrative example about the selection problem of investment alternatives is provided to illustrate the application and feasibility of the developed decision-making method.

Exponential operations and aggregation operators of interval neutrosophic sets and their decision making methods

An interval neutrosophic set (INS) is a subclass of a neutrosophic set and a generalization of an interval-valued intuitionistic fuzzy set, and then the characteristics of INS are independently described by the interval numbers of its truth-membership, indeterminacy-membership, and falsity-membership degrees. However, the exponential parameters (weights) of all the existing exponential operational laws of INSs and the corresponding exponential aggregation operators are crisp values in interval neutrosophic decision making problems. As a supplement, this paper firstly introduces new exponential operational laws of INSs, where the bases are crisp values or interval numbers and the exponents are interval neutrosophic numbers (INNs), which are basic elements in INSs. Then, we propose an interval neutrosophic weighted exponential aggregation (INWEA) operator and a dual interval neutrosophic weighted exponential aggregation (DINWEA) operator based on these exponential operational laws and introduce comparative methods based on cosine measure functions for INNs and dual INNs. Further, we develop decision-making methods based on the INWEA and DINWEA operators. Finally, a practical example on the selecting problem of global suppliers is provided to illustrate the applicability and rationality of the proposed methods.

A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses

In medical science, disease diagnosis is one of the difficult tasks for medical experts who are confronted with challenges in dealing with a lot of uncertain medical information. And different medical experts might express their own thought about the medical knowledge base which slightly differs from other medical experts. Thus, to solve the problems of uncertain data analysis and group decision making in disease diagnoses, we propose a new rough set model called dual hesitant fuzzy multigranulation rough set over two universes by combining the dual hesitant fuzzy set and multigranulation rough set theories. In the framework of our study, both the definition and some basic properties of the proposed model are presented. Finally, we give a general approach which is applied to a decision making problem in disease diagnoses, and the effectiveness of the approach is demonstrated by a numerical example.

Multi-period medical diagnosis method using a single valued neutrosophic similarity measure based on tangent function

Because of the increased volume of information available to physicians from advanced medical technology, the obtained information of each symptom with respect to a disease may contain truth, falsity and indeterminacy information. Since a single-valued neutrosophic set (SVNS) consists of the three terms like the truth-membership, indeterminacy-membership and falsity-membership functions, it is very suitable for representing indeterminate and inconsistent information. Then, similarity measure plays an important role in pattern recognition and medical diagnosis. However, existing medical diagnosis methods can only handle the single period medical diagnosis problem, but cannot deal with the multi-period medical diagnosis problems with neutrosophic information. Hence, the purpose of this paper was to propose similarity measures between SVNSs based on tangent function and a multi-period medical diagnosis method based on the similarity measure and the weighted aggregation of multi-period information to solve multi-period medical diagnosis problems with single-valued neutrosophic information. Then, we compared the tangent similarity measures of SVNSs with existing similarity measures of SVNSs by a numerical example about pattern recognitions to indicate the effectiveness and rationality of the proposed similarity measures. In the multi-period medical diagnosis method, we can find a proper diagnosis for a patient by the proposed similarity measure between the symptoms and the considered diseases represented by SVNSs and the weighted aggregation of multi-period information. Then, a multi-period medical diagnosis example was presented to demonstrate the application of the proposed diagnosis method and to indicate the effectiveness of the proposed diagnosis method by the comparative analysis. The diagnosis results showed that the developed multi-period medical diagnosis method can help doctors make a proper diagnosis by the comprehensive information of multi-periods.

Operational efficiency evaluation of Urban and rural residents’ basic pension insurance system based on the triangular fuzzy neutrosophic GRA method

At present, the basic pension insurance system for urban and rural residents in China has played a positive role in guaranteeing the basic life of the elderly in urban and rural areas. At present, the basic pension insurance system for urban and rural residents is not perfect, and there is still a great lag in the formulation of cross-system and cross-regional policies. There are differences in treatment between groups, between regions and between urban and rural areas. The coverage is not comprehensive enough and there are still some people who are not included in the basic protection system, etc. People urgently need a social pension insurance system that can provide reliable and sustainable protection in their old age. The operational efficiency evaluation of urban and rural residents’ basic pension insurance systems is viewed as the multi-attribute decision-making (MADM). In this paper, the triangular fuzzy neutrosophic numbers grey relational analysis (TFNN-GRA) method is built based on the traditional grey relational analysis (GRA) and triangular fuzzy neutrosophic sets (TFNSs). Finally, a numerical example for operational efficiency evaluation of urban and rural residents’ basic pension insurance systems has been given and some comparisons are used to illustrate advantages of 2TLNN-GRA method.