scholarly journals Intuitionistic Fuzzy Possibilistic C Means Clustering Algorithms

2015 ◽  
Vol 2015 ◽  
pp. 1-17 ◽  
Author(s):  
Arindam Chaudhuri
Keyword(s):  
Fuzzy Sets ◽  
Clustering Algorithm ◽  
Clustering Algorithms ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Mathematical Framework ◽  
Cluster Validity ◽  
Intuitionistic Fuzzy ◽  
Validity Measures ◽  
Interval Valued

Intuitionistic fuzzy sets (IFSs) provide mathematical framework based on fuzzy sets to describe vagueness in data. It finds interesting and promising applications in different domains. Here, we develop an intuitionistic fuzzy possibilistic C means (IFPCM) algorithm to cluster IFSs by hybridizing concepts of FPCM, IFSs, and distance measures. IFPCM resolves inherent problems encountered with information regarding membership values of objects to each cluster by generalizing membership and nonmembership with hesitancy degree. The algorithm is extended for clustering interval valued intuitionistic fuzzy sets (IVIFSs) leading to interval valued intuitionistic fuzzy possibilistic C means (IVIFPCM). The clustering algorithm has membership and nonmembership degrees as intervals. Information regarding membership and typicality degrees of samples to all clusters is given by algorithm. The experiments are performed on both real and simulated datasets. It generates valuable information and produces overlapped clusters with different membership degrees. It takes into account inherent uncertainty in information captured by IFSs. Some advantages of algorithms are simplicity, flexibility, and low computational complexity. The algorithm is evaluated through cluster validity measures. The clustering accuracy of algorithm is investigated by classification datasets with labeled patterns. The algorithm maintains appreciable performance compared to other methods in terms of pureness ratio.

Width-based distance measures on interval-valued intuitionistic fuzzy sets

2021 ◽  
pp. 1-13
Author(s):  
Xi Li ◽  
Chunfeng Suo ◽  
Yongming Li
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Interval Valued ◽  
Dissimilarity Function ◽  
Better Than

An essential topic of interval-valued intuitionistic fuzzy sets(IVIFSs) is distance measures. In this paper, we introduce a new kind of distance measures on IVIFSs. The novelty of our method lies in that we consider the width of intervals so that the uncertainty of outputs is strongly associated with the uncertainty of inputs. In addition, better than the distance measures given by predecessors, we define a new quaternary function on IVIFSs to construct the above-mentioned distance measures, which called interval-valued intuitionistic fuzzy dissimilarity function. Two specific methods for building the quaternary functions are proposed. Moreover, we also analyzed the degradation of the distance measures in this paper, and show that our measures can perfectly cover the measures on a simpler set. Finally, we provide illustrative examples in pattern recognition and medical diagnosis problems to confirm the effectiveness and advantages of the proposed distance measures.

scholarly journals A Dynamic Interval-Valued Intuitionistic Fuzzy Sets Applied to Pattern Recognition

2013 ◽  
Vol 2013 ◽  
pp. 1-16 ◽  
Author(s):  
Zhenhua Zhang ◽  
Min Wang ◽  
Yong Hu ◽  
Jingyu Yang ◽  
Youpei Ye ◽  
...  
Keyword(s):  
Decision Making ◽  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Medical Diagnosis ◽  
Recognition Accuracy ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Simulation Results ◽  
Interval Valued

We present dynamic interval-valued intuitionistic fuzzy sets (DIVIFS), which can improve the recognition accuracy when they are applied to pattern recognition. By analyzing the degree of hesitancy, we propose some DIVIFS models from intuitionistic fuzzy sets (IFS) and interval-valued IFS (IVIFS). And then we present a novel ranking condition on the distance of IFS and IVIFS and introduce some distance measures of DIVIFS satisfying the ranking condition. Finally, a pattern recognition example applied to medical diagnosis decision making is given to demonstrate the application of DIVIFS and its distances. The simulation results show that the DIVIFS method is more comprehensive and flexible than the IFS method and the IVIFS method.

INTUITIONISTIC FUZZY CLUSTERING ALGORITHM BASED ON BOOLE MATRIX AND ASSOCIATION MEASURE

2013 ◽  
Vol 12 (01) ◽  
pp. 95-118 ◽  
Author(s):  
HUA ZHAO ◽  
ZESHUI XU ◽  
ZHONG WANG
Keyword(s):  
Fuzzy Sets ◽  
Clustering Algorithm ◽  
Intuitionistic Fuzzy Sets ◽  
Association Measure ◽  
Association Coefficient ◽  
Intuitionistic Fuzzy ◽  
Intuitionistic Fuzzy Clustering ◽  
Association Matrix ◽  
Interval Valued ◽  
Atanassov’S Intuitionistic Fuzzy Sets

In this paper we develop a measure for calculating the association coefficient between Atanassov's intuitionistic fuzzy sets (A-IFSs), and show its desirable axiomatic properties. Then we present an algorithm for clustering A-IFSs. The algorithm first utilizes the association coefficient of A-IFSs to construct an association matrix, and then calculates the λ-cutting matrix of the association matrix no matter whether it is an equivalent matrix or not. After that, the λ-cutting matrix is used to cluster A-IFSs (if the λ-cutting matrix is just only a similarity matrix, then we can easily transform it into an equivalent matrix). Three examples are used to show the effectiveness of the association coefficient and the algorithm for clustering A-IFSs. Furthermore, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and finally, we use another numerical example to illustrate the latter algorithm.

A Class of New Interval-Valued Intuitionistic Fuzzy Distance Measures and their Applications in Discriminant Analysis

2012 ◽  
Vol 182-183 ◽  
pp. 1743-1745 ◽  
Author(s):  
Hua Zhao ◽  
Ming Fang Ni ◽  
Hai Feng Liu
Keyword(s):  
Discriminant Analysis ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Fuzzy Information ◽  
Fuzzy Distance ◽  
Intuitionistic Fuzzy ◽  
Special Cases ◽  
Interval Valued

In this paper we develop a class of new distance measures for interval-valued intuitionistic fuzzy sets. Then we discuss some of the special cases of it by taking different parameters. Finally we apply them for discriminant analysis with interval-valued intuitionistic fuzzy information.

scholarly journals Some Similarity Measures for Interval-Valued Picture Fuzzy Sets and Their Applications in Decision Making

Information ◽  
2019 ◽  
Vol 10 (12) ◽  
pp. 369 ◽  
Author(s):  
Peide Liu ◽  
Muhammad Munir ◽  
Tahir Mahmood ◽  
Kifayat Ullah
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Real Life ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Distance Measures ◽  
Intuitionistic Fuzzy ◽  
Picture Fuzzy Set ◽  
Picture Fuzzy Sets ◽  
Interval Valued

Similarity measures, distance measures and entropy measures are some common tools considered to be applied to some interesting real-life phenomena including pattern recognition, decision making, medical diagnosis and clustering. Further, interval-valued picture fuzzy sets (IVPFSs) are effective and useful to describe the fuzzy information. Therefore, this manuscript aims to develop some similarity measures for IVPFSs due to the significance of describing the membership grades of picture fuzzy set in terms of intervals. Several types cosine similarity measures, cotangent similarity measures, set-theoretic and grey similarity measures, four types of dice similarity measures and generalized dice similarity measures are developed. All the developed similarity measures are validated, and their properties are demonstrated. Two well-known problems, including mineral field recognition problems and multi-attribute decision making problems, are solved using the newly developed similarity measures. The superiorities of developed similarity measures over the similarity measures of picture fuzzy sets, interval-valued intuitionistic fuzzy sets and intuitionistic fuzzy sets are demonstrated through a comparison and numerical examples.

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