Neutrosophic Cubic MCGDM Method Based on Similarity Measure (original) (raw)
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Applications of neutrosophic cubic sets in multi-criteria decision making
International Journal for Uncertainty Quantification
In this paper, we investigate the concepts of the weighted average operator (A W) and weighted geometric operator (G W) on neutrosophic cubic sets (NCSs) to aggregate the neutrosophic cubic information. Moreover, on the basis of A W & G W and certain functions, including score, certainty and accuracy, we develop our algorithm to multiple-criteria decision making in NCSs, in which the assessment standards of another possibility on the characteristics yield the technique of neutrosophic cubic numbers (NCNs) to choice greatest necessary ones. Finally, we provide a mathematical example of the technique to determine the application and usefulness of the established technique.
arXiv (Cornell University), 2015
In this paper, we propose three similarity measure methods for single valued neutrosophic refined sets and interval neutrosophic refined sets based on Jaccard, Dice and Cosine similarity measures of single valued neutrosophic sets and interval neutrosophic sets. Furthermore, we suggest two multi-criteria decision making method under single valued neutrosophic refined environment and interval neutrosophic refined environment, and give applications of proposed multi-criteria decision making methods. Finally we suggested a consistency analysis method for similarity measures between interval neutrosophic refined sets and give an application to demonstrate process of the method.
GRA for Multi Attribute Decision Making in Neutrosophic Cubic Set Environment
In this paper, multi attribute decision making problem based on grey relational analysis in neutrosophic cubic set environment is investigated. In the decision making situation, the attribute weights are considered as single valued neutrosophic sets. The neutrosophic weights are converted into crisp weights. Both positve and negative GRA coefficients, and weighted GRA coefficients are determined. Hamming distances for weighted GRA coefficients and standard (ideal) GRA coefficients are determined. The relative closeness coefficients are derived in order to rank the alternatives. The relative closeness coefficients are designed in ascending order. Finally, a numerical example is solved to demonstrate the applicability of the proposed approach.
Multi – Criteria Group Decision Making Model In Neutrosophic Refined Set And Its Application
viXra, 2016
In the paper, multi criteria group decision making model has been presented based on tangent similarity measure of neutrosophic refined set. Simplified form of tangent similarity measure in neutrosophic refined set has been presented. New ranking method has been proposed based on refined tangent similarity measure. The proposed approach has been illustrated by solving a teacher selection problem in neutrosophic refined set environment.
NC-TODIM Based MAGDM under Neutrosophic Cubic Set Environment
Neutrosophic cubic set is the hybridization of the concept of neutrosophic set and interval neutrosophic set. Neutrosophic cubic set has the capacity to express the hybrid information of both the interval neutrosophic set and the single valued neutrosophic set simultaneously. As newly defined, little research on the operations and applications of neutrosophic cubic sets appear in the current literature. In the present paper we propose the score, accuracy functions for neutrosophic cubic sets and prove their basic properties. We firstly develop TODIM method to solve multi attribute group decision making in neutrosophic cubic set environment, which we call NC-TODIM. Also, we solve a MAGDM problem using the proposed NC-TODIM method to show the applicability and effectiveness of the developed method. We also conduct sensitivity analysis to show the impact of ranking order of the alternatives for different values of attenuation factor of losses for multi-attribute group decision making p...
Cosine Measures of Neutrosophic Cubic Sets for Multiple Attribute Decision-Making
Symmetry, 2017
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 t...
Simplified neutrosophic sets and their applications in multi-criteria group decision-making problems
As a variation of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete and inconsistent information that exists in the real world. Simplified neutrosophic sets (SNSs) have been proposed for the main purpose of addressing issues with a set of specific numbers. However, there are certain problems regarding the existing operations of SNSs, as well as their aggregation operators and the comparison methods. Therefore, this paper defines the novel operations of simplified neutrosophic numbers (SNNs) and develops a comparison method based on the related research of intuitionistic fuzzy numbers. On the basis of these operations and the comparison method, some SNN aggregation operators are proposed. Additionally, an approach for multi-criteria group decision-making (MCGDM) problems is explored by applying these aggregation operators. Finally, an example to illustrate the applicability of the proposed method is provided and a comparison with some other methods is made.
Axioms, 2020
In this manuscript, we extend the traditional multi-attributive border approximation area comparison (MABAC) method for the multiple-criteria group decision-making (MCGDM) with triangular fuzzy neutrosophic numbers (TFNNs) to propose the TFNNs-MABAC method. In the proposed method, we utilize the TFNNs to express the values of criteria for each alternative in MCGDM problems. First, we briefly acquaint the basic concept of TFNNs and describe its corresponding some operation laws, the functions of score and accuracy, and the normalized hamming distance. We then review two aggregation operators of TFNNs. Afterward, we combine the traditional MABAC method with the triangular fuzzy neutrosophic evaluation and provide a sequence of calculation procedures of the TFNNs-MABAC method. After comparing it with some TFNNs aggregation operators and another method, the results showed that our extended MABAC method can not only effectively handle the conflicting attributes, but also practically deal...
As the generalization of the fuzzy and similar sets based on Fuzzy sets, neutrosophic sets provide significant possibilities in the case of solving complex decision problems, often related to uncertainty and unreliability. Neutrosophic sets use three values named the truth degree, the indeterminacy degree and the falsity degree, which allow for a more accurate evaluation of alternatives in relation to complex evaluation criteria. As a result of their application in solving numerous different decision-making problems, several approaches to their ranking have been proposed. Therefore, this paper provides a comprehensive overview of the approaches to the ranking of single-valued neutrosophic numbers and a comparison of the results obtained by using them. Finally, numerical illustrations are given.
Multi-Criteria Group Decision Making Based On Linguistic Refined Neutrosophic Strategy
viXra, 2018
Multi-criteria group decision making (MCGDM) strategy, which consists of a group of experts acting collectively for best selection among all possible alternatives with respect to some criteria, is focused on in this study. To develop the paper, we define linguistic neutrosophic refine set. We also define entropy to calculate unknown weights of the criteria and establish basic properties of entropy in linguistic neutrosophy refine set environment. In the developed strategy, the rating of all alternatives is expressed with linguistic variables. All linguistic variables are expressed as refined neutrosophic numbers which are characterized by truth-membership sequences, indeterminacy-membership sequences, and falsitymembership sequences. Linguistic refined neutrosophic score function (LRNSF) and linguistic refined neutrosophic accumulated function (LRNAF) are proposed. Weight of each criterion is unknown to decision maker. Finally, an illustrative example is provided to demonstrate the applicability of the proposed approach.