(T, S)-Based Single-Valued Neutrosophic Number Equivalence Matrix and Clustering Method
(T, S)-Based Single-Valued Neutrosophic Number Equivalence Matrix and Clustering Method

Author: Jiongmei Mo

Publisher: Infinite Study

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Total Pages: 16

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Fuzzy clustering is widely used in business, biology, geography, coding for the internet and more. A single-valued neutrosophic set is a generalized fuzzy set, and its clustering algorithm has attracted more and more attention. An equivalence matrix is a common tool in clustering algorithms. At present, there exist no results constructing a single-valued neutrosophic number equivalence matrix using t-norm and t-conorm.

New Distance Measure of Single-Valued Neutrosophic Sets and Its Application
New Distance Measure of Single-Valued Neutrosophic Sets and Its Application

Author: Han-Liang Huang

Publisher: Infinite Study

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Total Pages: 12

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A single-valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which can be used to handle uncertainty, imprecise, indeterminate, and inconsistent information in real life. In this paper, a new distance measure between two SVNSs is deļ¬ned by the full consideration of truthmembership function, indeterminacy-membership function, and falsity-membership function for the forward and backward differences. Then the similarity measure, the entropy measure, and the index of distance are also presented. Finally, two illustrative examples are given to demonstrate the effectiveness of the proposed clustering method and multicriteria decision-making method based on the distance (similarity) measure between SVNSs.

Single valued Neutrosophic clustering algorithm Based on Tsallis Entropy Maximization
Single valued Neutrosophic clustering algorithm Based on Tsallis Entropy Maximization

Author: Qiaoyan Li

Publisher: Infinite Study

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Total Pages: 12

ISBN-13:

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Data clustering is an important field in pattern recognition and machine learning. Fuzzy c-means is considered as a useful tool in data clustering. Neutrosophic set, which is extension of fuzzy set, has received extensive attention in solving many real life problems of uncertainty, inaccuracy, incompleteness, inconsistency and uncertainty.

NEUTROSOPHIC TRIPLET STRUCTURES, Volume I
NEUTROSOPHIC TRIPLET STRUCTURES, Volume I

Author: Memet Sahin

Publisher: Infinite Study

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Total Pages: 23

ISBN-13:

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A bipolar neutrosophic set (BNS) is an instance of a single- valued neutrosophic set. To do this, we firstly propose distance measure between two BNSs is defined by the full consideration of positive membership function and negative membership function for the forward and backward differences. Then the similarity measure, the entropy measure and the index of distance are also presented. Then, two examples are shown to verify the feasibility of the proposed method. Finally, the decision results of different similarity measures demonstrate the practicality and effectiveness of the developed method in this paper.

Double-Valued Neutrosophic Sets, their Minimum Spanning Trees, and Clustering Algorithm
Double-Valued Neutrosophic Sets, their Minimum Spanning Trees, and Clustering Algorithm

Author: Ilanthenral Kandasamy

Publisher: Infinite Study

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Total Pages: 20

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Neutrosophy (neutrosophic logic) is used to represent uncertain, indeterminate, and inconsistent information available in the real world. This article proposes a method to provide more sensitivity and precision to indeterminacy, by classifying the indeterminate concept/value into two based on membership: one as indeterminacy leaning towards truth membership and the other as indeterminacy leaning towards false membership.

Two Ranking Methods of Single Valued Triangular Neutrosophic Numbers to Rank and Evaluate Information Systems Quality
Two Ranking Methods of Single Valued Triangular Neutrosophic Numbers to Rank and Evaluate Information Systems Quality

Author: Samah Ibrahim Abdel Aal

Publisher: Infinite Study

Published:

Total Pages: 10

ISBN-13:

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The concept of neutrosophic can provide a generalization of fuzzy set and intuitionistic fuzzy set that make it is the best fit in representing indeterminacy and uncertainty. Single Valued Triangular Numbers (SVTrN-numbers) is a special case of neutrosophic set that can handle ill-known quantity very difficult problems.

RANKING METHODS OF SINGLE VALUED NEUTROSOPHIC NUMBERS AND ITS APPLICATIONS TO MULTIPLE CRITERIA DECISION MAKING
RANKING METHODS OF SINGLE VALUED NEUTROSOPHIC NUMBERS AND ITS APPLICATIONS TO MULTIPLE CRITERIA DECISION MAKING

Author: Dragisa Stanujkic

Publisher: Infinite Study

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Total Pages: 7

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Decision making is a very important and actual process. It is exactly as such the most important to managers to whom it is a primary task. Taking into account the more possibilities of the action lines that can be implemented, the outcome of the decision-making process must be the solution of this situation, i.e., defining the directions for further action.

Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems
Interval Neutrosophic Sets and Their Application in Multicriteria Decision Making Problems

Author: Hong-yu Zhang

Publisher: Infinite Study

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Total Pages: 15

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As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number.However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decisionmakingmethod. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, amethod formulticriteria decisionmaking problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.