Clustering Methods Using Distance-Based Similarity Measures of Single-Valued Neutrosophic Sets

2014 ◽  
Vol 23 (4) ◽  
pp. 379-389 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Fuzzy Sets ◽  
Clustering Algorithm ◽  
Distance Measure ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Clustering Methods ◽  
Neutrosophic Sets ◽  
Generalized Distance

AbstractClustering plays an important role in data mining, pattern recognition, and machine learning. Single-valued neutrosophic sets (SVNSs) are useful means to describe and handle indeterminate and inconsistent information that fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-valued neutrosophic information, this article proposes single-valued neutrosophic clustering methods based on similarity measures between SVNSs. First, we define a generalized distance measure between SVNSs and propose two distance-based similarity measures of SVNSs. Then, we present a clustering algorithm based on the similarity measures of SVNSs to cluster single-valued neutrosophic data. Finally, an illustrative example is given to demonstrate the application and effectiveness of the developed clustering methods.

scholarly journals Single-Valued Neutrosophic Minimum Spanning Tree and Its Clustering Method

2014 ◽  
Vol 23 (3) ◽  
pp. 311-324 ◽  
Author(s):  
Jun Ye
Keyword(s):  
Machine Learning ◽  
Fuzzy Sets ◽  
Spanning Tree ◽  
Clustering Algorithm ◽  
Minimum Spanning Tree ◽  
Distance Measure ◽  
Intuitionistic Fuzzy Sets ◽  
Clustering Method ◽  
Neutrosophic Sets ◽  
Generalized Distance

AbstractClustering plays an important role in data mining, pattern recognition, and machine learning. Then, single-valued neutrosophic sets (SVNSs) are a useful means to describe and handle indeterminate and inconsistent information, which fuzzy sets and intuitionistic fuzzy sets cannot describe and deal with. To cluster the data represented by single-value neutrosophic information, the article proposes a single-valued neutrosophic minimum spanning tree (SVNMST) clustering algorithm. Firstly, we defined a generalized distance measure between SVNSs. Then, we present an SVNMST clustering algorithm for clustering single-value neutrosophic data based on the generalized distance measure of SVNSs. Finally, two illustrative examples are given to demonstrate the application and effectiveness of the developed approach.

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

2018 ◽  
Vol 27 (2) ◽  
pp. 163-182 ◽  
Author(s):  
Ilanthenral Kandasamy
Keyword(s):  
Fuzzy Sets ◽  
Spanning Tree ◽  
Clustering Algorithm ◽  
Minimum Spanning Tree ◽  
Distance Measure ◽  
Clustering Algorithms ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Inconsistent Information ◽  
Intuitionistic Fuzzy

AbstractNeutrosophy (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. This paper introduces a modified form of a neutrosophic set, called Double-Valued Neutrosophic Set (DVNS), which has these two distinct indeterminate values. Its related properties and axioms are defined and illustrated in this paper. An important role is played by clustering in several fields of research in the form of data mining, pattern recognition, and machine learning. DVNS is better equipped at dealing with indeterminate and inconsistent information, with more accuracy, than the Single-Valued Neutrosophic Set, which fuzzy sets and intuitionistic fuzzy sets are incapable of. A generalised distance measure between DVNSs and the related distance matrix is defined, based on which a clustering algorithm is constructed. This article proposes a Double-Valued Neutrosophic Minimum Spanning Tree (DVN-MST) clustering algorithm, to cluster the data represented by double-valued neutrosophic information. Illustrative examples are given to demonstrate the applications and effectiveness of this clustering algorithm. A comparative study of the DVN-MST clustering algorithm with other clustering algorithms like Single-Valued Neutrosophic Minimum Spanning Tree, Intuitionistic Fuzzy Minimum Spanning Tree, and Fuzzy Minimum Spanning Tree is carried out.

Analysis of Fuzzy Clustering for the Adoption in Data Mining

2014 ◽  
Vol 989-994 ◽  
pp. 2047-2050
Author(s):  
Ying Jie Wang
Keyword(s):  
Machine Learning ◽  
Data Mining ◽  
Mathematical Method ◽  
Big Data ◽  
Fuzzy Clustering ◽  
Clustering Analysis ◽  
Data Clustering ◽  
Clustering Algorithm ◽  
Clustering Methods ◽  
Fuzzy Clustering Methods

Data mining is the general methodology for retrieving useful information from big data. Clustering analysis is a mathematical method of classification for unsupervised machine learning. It can be adopted for data classification in Data mining. This paper combines the clustering process by fuzzy way and then deduces a special clustering algorithm with fast fuzzy c-means (FFCM) method. In summary, the paper illustrates the adoption of a series of fuzzy clustering methods in Data Mining. These methods have improved the computational efficiency with learning as the convergence speed is fast. The methodology of this paper presents significantly meaningful for information retrieval of big data.

EXTRACTING WEB USER PROFILES USING RELATIONAL COMPETITIVE FUZZY CLUSTERING

2000 ◽  
Vol 09 (04) ◽  
pp. 509-526 ◽  
Author(s):  
OLFA NASRAOUI ◽  
HICHEM FRIGUI ◽  
RAGHU KRISHNAPURAM ◽  
ANUPAM JOSHI
Keyword(s):  
Clustering Algorithm ◽  
Distance Measure ◽  
Similarity Measures ◽  
Unsupervised Classification ◽  
Optimal Number ◽  
Relational Data ◽  
Data Card ◽  
User Profiles ◽  
Clustering Methods ◽  
Access Logs

The proliferation of information on the World Wide Web has made the personalization of this information space a necessity. An important component of Web personalization is to mine typical user profiles from the vast amount of historical data stored in access logs. In the absence of any a priori knowledge, unsupervised classification or clustering methods seem to be ideally suited to analyze the semi-structured log data of user accesses. In this paper, we define the notion of a "user session" as being a temporally compact sequence of Web accesses by a user. We also define a new distance measure between two Web sessions that captures the organization of a Web site. The Competitive Agglomeration clustering algorithm which can automatically cluster data into the optimal number of components is extended so that it can work on relational data. The resulting Competitive Agglomeration for Relational Data (CARD) algorithm can deal with complex, non-Euclidean, distance/similarity measures. This algorithm was used to analyze Web server access logs successfully and obtain typical session profiles of users.

scholarly journals Certain Notions of Neutrosophic Topological K-Algebras

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 234 ◽  
Author(s):  
Muhammad Akram ◽  
Hina Gulzar ◽  
Florentin Smarandache ◽  
Said Broumi
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Point Of View ◽  
Neutrosophic Set ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Research Article

The concept of neutrosophic set from philosophical point of view was first considered by Smarandache. A single-valued neutrosophic set is a subclass of the neutrosophic set from a scientific and engineering point of view and an extension of intuitionistic fuzzy sets. In this research article, we apply the notion of single-valued neutrosophic sets to K-algebras. We introduce the notion of single-valued neutrosophic topological K-algebras and investigate some of their properties. Further, we study certain properties, including C 5 -connected, super connected, compact and Hausdorff, of single-valued neutrosophic topological K-algebras. We also investigate the image and pre-image of single-valued neutrosophic topological K-algebras under homomorphism.

scholarly journals On the Neutrosophic, Pythagorean and Some Other Novel Fuzzy Sets Theories Used in Decision Making: Invitation to Discuss

Entropy ◽  
2021 ◽  
Vol 23 (11) ◽  
pp. 1485
Author(s):  
Pavel Sevastjanov ◽  
Ludmila Dymova ◽  
Krzysztof Kaczmarek
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Short Paper ◽  
Neutrosophic Sets ◽  
Intuitionistic Fuzzy ◽  
Dempster Shafer Theory ◽  
Methodological Problems ◽  
Shafer Theory ◽  
Sets Theory

In this short paper, a critical analysis of the Neutrosophic, Pythagorean and some other novel fuzzy sets theories foundations is provided, taking into account that they actively used for the solution of the decision-making problems. The shortcomings of these theories are exposed. It is stated that the independence hypothesis, which is a cornerstone of the Neutrosophic sets theory, is not in line with common sense and therefore leads to the paradoxical results in the asymptotic limits of this theory. It is shown that the Pythagorean sets theory possesses questionable foundations, the sense of which cannot be explained reasonably. Moreover, this theory does not completely solve the declared problem. Similarly, important methodological problems of other analyzed theories are revealed. To solve the interior problems of the Atanassov’s intuitionistic fuzzy sets and to improve upon them, this being the reason most of the criticized novel sets theories were developed, an alternative approach based on extension of the intuitionistic fuzzy sets in the framework of the Dempster–Shafer theory is proposed. No propositions concerned with the improvement of the Cubic sets theory and Single-Valued Neutrosophic Offset theory were made, as their applicability was shown to be very dubious. In order to stimulate discussion, many statements are deliberately formulated in a hardline form.

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