Element-Weighted Neutrosophic Correlation Coefficient and Its Application in Improving CAMShift Tracker in RGBD Video

Neutrosophic set (NS) is a new branch of philosophy to deal with the origin, nature, and scope of neutralities. Many kinds of correlation coefficients and similarity measures have been proposed in neutrosophic domain. In this work, by considering that there may exist different contributions for the neutrosophic elements of T (Truth), I (Indeterminacy), and F (Falsity), a method of element-weighted neutrosophic correlation coefficient is proposed, and it is applied for improving the CAMShift tracker in RGBD (RGB-Depth) video. The concept of object seeds is proposed, and it is employed for extracting object region and calculating the depth back-projection. Each candidate seed is represented in the single-valued neutrosophic set (SVNS) domain via three membership functions, T, I, and F. Then the element-weighted neutrosophic correlation coefficient is applied for selecting robust object seeds by fusing three kinds of criteria. Moreover, the proposed correlation coefficient is applied for estimating a robust back-projection by fusing the information in both color and depth domains. Finally, for the scale adaption problem, two alternatives in the neutrosophic domain are proposed, and the corresponding correlation coefficient between the proposed alternative and the ideal one is employed for the identification of the scale. When considering challenging factors like fast motion, blur, illumination variation, deformation, and camera jitter, the experimental results revealed that the improved CAMShift tracker performs well.

The Cosine Measure of Single-Valued Neutrosophic Multisets for Multiple Attribute Decision-Making

Based on the multiplicity evaluation in some real situations, this paper firstly introduces a single-valued neutrosophic multiset (SVNM) as a subclass of neutrosophic multiset (NM) to express the multiplicity information and the operational relations of SVNMs. Then, a cosine measure between SVNMs and weighted cosine measure between SVNMs are presented to measure the cosine degree between SVNMs, and their properties are investigated. Based on the weighted cosine measure of SVNMs, a multiple attribute decision-making method under a SVNM environment is proposed, in which the evaluated values of alternatives are taken in the form of SVNMs. The ranking order of all alternatives and the best one can be determined by the weighted cosine measure between every alternative and the ideal alternative. Finally, an actual application on the selecting problem illustrates the effectiveness and application of the proposed method.

The cosine measure of refined-single valued neutrosophic sets and refined-interval neutrosophic sets for multiple attribute decision-making

This paper introduces a Refined-Interval Neutrosophic Set (R-INS) as an extension of a Refined-Single Valued Neutrosophic Set (R-SVNS) and puts forward the decision-making models based on the Cosine Measures of R-SVNSs and Refined-Interval Neutrosophic Sets (R-INSs). By the cosine measure between every alternative and the ideal alternative, all the alternatives can be ranked with the measure values, and the best one of all alternatives can be selected. The proposed methods for multiple attribute decision making (MADM) are more clear (more refined) and the refined evaluation results are credible, so the proposed decision-making models are very suitable for handling with the decision-making problems with refined neutrosophic information.

Simplified Neutrosophic Exponential Similarity Measures for the Initial Evaluation/Diagnosis of Benign Prostatic Hyperplasia Symptoms

When a physician carries out the clinical survey of a patient with benign prostatic hyperplasia (BPH) symptoms to reach the initial evaluation/diagnosis of BPH, the existing initial evaluation method of BPH based on the international prostate symptom score (I-PSS) usually uses the objective evaluation/diagnosis method with crisp values without considering fuzzy information. However, this common evaluation/diagnosis method may lead to the loss of a great deal of useful incomplete, uncertain, and inconsistent information in the clinical survey and initial evaluation process of the BPH symptoms for a patient, resulting in an unreasonable evaluation and diagnosis distortion of the BPH symptoms. To overcome this drawback, this paper aims to propose new exponential similarity measures (ESMs) between simplified neutrosophic sets (SNSs), including single-valued neutrosophic ESMs and interval neutrosophic ESMs, and their initial evaluation/diagnosis method of the BPH symptoms with simplified neutrosophic information. Finally, two evaluation/diagnosis examples of the BPH symptoms are provided to demonstrate the effectiveness and rationality of the proposed method.

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.

Some Single-Valued Neutrosophic Dombi Weighted Aggregation Operators for Multiple Attribute Decision-Making

The Dombi operations of T-norm and T-conorm introduced by Dombi can have the advantage of good flexibility with the operational parameter. In existing studies, however, the Dombi operations have so far not yet been used for neutrosophic sets. To propose new aggregation operators for neutrosophic sets by the extension of the Dombi operations, this paper firstly presents the Dombi operations of single-valued neutrosophic numbers (SVNNs) based on the operations of the Dombi T-norm and T-conorm, and then proposes the single-valued neutrosophic Dombi weighted arithmetic average (SVNDWAA) operator and the single-valued neutrosophic Dombi weighted geometric average (SVNDWGA) operator to deal with the aggregation of SVNNs and investigates their properties. Because the SVNDWAA and SVNDWGA operators have the advantage of good flexibility with the operational parameter, we develop a multiple attribute decision-making (MADM) method based on the SVNWAA or SVNWGA operator under a SVNN environment. Finally, an illustrative example about the selection problem of investment alternatives is given to demonstrate the application and feasibility of the developed approach.

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.