On Integration Linguistic Factors to Fuzzy Similarity Measures and Intuitionistic Fuzzy Similarity Measures

2019 ◽  
Vol 10 (1) ◽  
pp. 1-37
Author(s):  
Pham Hong Phong ◽  
Vu Thi Hue
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Classification Algorithms ◽  
Classification Problems ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Similarity ◽  
New Concepts ◽  
Fuzzy Linguistic

The article is concerned with integrating linguistic elements into fuzzy similarity measures and intuitionistic fuzzy similarity measure. Some new concepts are proposed: a fuzzy linguistic value (FLv), a fuzzy linguistic vector (FLV), an intuitionistic fuzzy linguistic vector (ILV) and similarity measures. The proposed measures are used to build classification algorithms. As predicted theoretically, experiments show that with the same type of similarity measures, the linguistic-aggregated similarity measures produce better results in classification problems.

scholarly journals The Intuitionistic Fuzzy Linguistic Cosine Similarity Measure and Its Application in Pattern Recognition

Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-11 ◽  
Author(s):  
Donghai Liu ◽  
Xiaohong Chen ◽  
Dan Peng
Keyword(s):  
Similarity Measure ◽  
Similarity Measures ◽  
Cosine Similarity ◽  
Intuitionistic Fuzzy ◽  
Linguistic Term ◽  
Cosine Similarity Measure ◽  
Linguistic Scale Function ◽  
Cosine Similarity Measures ◽  
Fuzzy Linguistic ◽  
Interval Valued

We propose the cosine similarity measures for intuitionistic fuzzy linguistic sets (IFLSs) and interval-valued intuitionistic fuzzy linguistic sets (IVIFLSs), which are expressed by the linguistic scale function based on the cosine function. Then, the weighted cosine similarity measure and the ordered weighted cosine similarity measure for IFLSs and IVIFLSs are introduced by taking into account the importance of each element, and the properties of the cosine similarity measures are also given. The main advantage of the proposed cosine similarity measures is that the decision-makers can flexibly select the linguistic scale function depending on the actual semantic situation. Finally, we present the application of the cosine similarity measures for intuitionistic fuzzy linguistic term sets and interval-valued intuitionistic fuzzy linguistic term sets to pattern recognition and medical diagnosis, and the existing cosine similarity measures are compared with the proposed cosine similarity measures by the illustrative example.

Two Trigonometric Intuitionistic Fuzzy Similarity Measures

2022 ◽  
Vol 14 (1) ◽  
pp. 0-0
Keyword(s):  
Image Processing ◽  
Pattern Recognition ◽  
Edge Detection ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Trigonometric Functions ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Similarity

Intuitionistic Fuzzy Sets(1986) invented by Atanassov(Atanassov, 1986) has gained the wide popularity among various researchers because of its applications in various fields such as image processing, edge detection, medical diagnosis, pattern recognition etc. One of the significant tool by which the decision can be made is Intuitionistic Fuzzy Similarity Measure. In this communication, the authors have introduced two new Intuitionistic fuzzy similarity measures based on the trigonometric functions and its validity is proved. The proposed similarity measure is applied to medical diagnosis and pattern recognition.

Handling Fuzzy Similarity for Data Classification

2011 ◽  
pp. 796-802 ◽  
Author(s):  
Roy Gelbard ◽  
Avichai Meged
Keyword(s):  
Data Mining ◽  
Similarity Measure ◽  
Data Representation ◽  
Classification Algorithms ◽  
Binary Representation ◽  
Fuzzy Data ◽  
Problem Domain ◽  
Data Types ◽  
Fuzzy Similarity ◽  
Set Up

Representing and consequently processing fuzzy data in standard and binary databases is problematic. The problem is further amplified in binary databases where continuous data is represented by means of discrete ‘1’ and ‘0’ bits. As regards classification, the problem becomes even more acute. In these cases, we may want to group objects based on some fuzzy attributes, but unfortunately, an appropriate fuzzy similarity measure is not always easy to find. The current paper proposes a novel model and measure for representing fuzzy data, which lends itself to both classification and data mining. Classification algorithms and data mining attempt to set up hypotheses regarding the assigning of different objects to groups and classes on the basis of the similarity/distance between them (Estivill-Castro & Yang, 2004) (Lim, Loh & Shih, 2000) (Zhang & Srihari, 2004). Classification algorithms and data mining are widely used in numerous fields including: social sciences, where observations and questionnaires are used in learning mechanisms of social behavior; marketing, for segmentation and customer profiling; finance, for fraud detection; computer science, for image processing and expert systems applications; medicine, for diagnostics; and many other fields. Classification algorithms and data mining methodologies are based on a procedure that calculates a similarity matrix based on similarity index between objects and on a grouping technique. Researches proved that a similarity measure based upon binary data representation yields better results than regular similarity indexes (Erlich, Gelbard & Spiegler, 2002) (Gelbard, Goldman & Spiegler, 2007). However, binary representation is currently limited to nominal discrete attributes suitable for attributes such as: gender, marital status, etc., (Zhang & Srihari, 2003). This makes the binary approach for data representation unattractive for widespread data types. The current research describes a novel approach to binary representation, referred to as Fuzzy Binary Representation. This new approach is suitable for all data types - nominal, ordinal and as continuous. We propose that there is meaning not only to the actual explicit attribute value, but also to its implicit similarity to other possible attribute values. These similarities can either be determined by a problem domain expert or automatically by analyzing fuzzy functions that represent the problem domain. The added new fuzzy similarity yields improved classification and data mining results. More generally, Fuzzy Binary Representation and related similarity measures exemplify that a refined and carefully designed handling of data, including eliciting of domain expertise regarding similarity, may add both value and knowledge to existing databases.

scholarly journals A New Similarity Measure between Intuitionistic Fuzzy Sets and Its Application to Pattern Recognition

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Yafei Song ◽  
Xiaodan Wang ◽  
Lei Lei ◽  
Aijun Xue
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Membership Degree ◽  
Intuitionistic Fuzzy ◽  
Axiomatic Definition

As a generation of ordinary fuzzy set, the concept of intuitionistic fuzzy set (IFS), characterized both by a membership degree and by a nonmembership degree, is a more flexible way to cope with the uncertainty. Similarity measures of intuitionistic fuzzy sets are used to indicate the similarity degree between intuitionistic fuzzy sets. Although many similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity or provide counterintuitive cases. In this paper, a new similarity measure and weighted similarity measure between IFSs are proposed. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counterintuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating difference between patterns.

Generalized Entropy and Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets With Application in Decision Making

2021 ◽  
Vol 10 (1) ◽  
pp. 64-93
Author(s):  
Pratiksha Tiwari
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Extended Family ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Optimal Point ◽  
Generalized Entropy ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

Interval-valued intuitionistic fuzzy environment is appropriate for most of the practical scenarios involving uncertainty, vagueness, and insufficient information. Entropy, similarity, distance, inclusion, and cross entropy measures are a few methods used for measuring uncertainty and classifying fuzzy sets and its generalizations. Entropy of a fuzzy set describes fuzziness degree of the set and similarity measure measures similarity between two fuzzy or members of its extended family. This paper presents generalized entropy and similarity measures for interval-valued intuitionistic fuzzy sets. Further, the proposed similarity measure is compared with some existing measure of similarity with the help of an illustrative example, and a method is used to define optimal point using the existing information. Finally, entropy and similarity measures are used to identify best alternatives to solve multi-attribute decision making.

A New Similarity Measure of Intuitionistic Fuzzy Sets Considering Abstention Group Influence and Its Applications

2016 ◽  
Vol 25 (2) ◽  
pp. 197-208 ◽  
Author(s):  
Bei Zhou
Keyword(s):  
Fuzzy Sets ◽  
Similarity Measure ◽  
Group Decision ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Group Influence ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Group A ◽  
Multicriteria Group Decision Making

AbstractThe issue of similarity measures of intuitionistic fuzzy sets (IFSs) is considered in this paper. Many existing similarity measures for two IFSs fail to take the abstention group influence into consideration and may lead to counterintuitive results in some cases. To deal with the problem, this paper first discusses the limitations of the existing similarity measures by some numerical examples, then, by considering the influence of abstention group, a new similarity measure of intuitionistic fuzzy sets is proposed, and the same numerical examples are given to demonstrate the validity of the proposed measure. Finally, the proposed similarity measure is applied to pattern recognition, multicriteria group decision making, and medical diagnosis.

scholarly journals A Novel Similarity Measure for Interval-Valued Intuitionistic Fuzzy Sets and Its Applications

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 441 ◽  
Author(s):  
Minxia Luo ◽  
Jingjing Liang
Keyword(s):  
Pattern Recognition ◽  
Fuzzy Sets ◽  
Similarity Measure ◽  
Medical Diagnosis ◽  
Fuzzy Numbers ◽  
Similarity Measures ◽  
Intuitionistic Fuzzy Sets ◽  
Numerical Examples ◽  
Intuitionistic Fuzzy ◽  
Interval Valued

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems.

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