A New Method for Measuring Similarity between Intuitionistic Fuzzy Sets Based on Normal Distribution Functions

2007 ◽  
Author(s):  
Zehua Lv ◽  
Chuanbo Chen ◽  
Wenhai Li
Keyword(s):  
Normal Distribution ◽  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Distribution Functions ◽  
New Method ◽  
Intuitionistic Fuzzy

Vague Correlation Coefficient of Interval Vague Sets and its Applications to Topsis in MADM Problems

2014 ◽  
pp. 140-173
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E. C.
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Numerical Illustration ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Statistical Confidence ◽  
Order Preference ◽  
Novel Method

Various attempts are made by researchers on the study of vagueness of data through Intuitionistic Fuzzy sets and Vague sets, and also it is shown that Vague sets are Intuitionistic Fuzzy sets. However, there are algebraic and graphical differences between Vague sets and Intuitionistic Fuzzy sets. In this chapter, an attempt is made to define the correlation coefficient of Interval Vague sets lying in the interval [0,1], and a new method for computing the correlation coefficient of interval Vague sets lying in the interval [-1,1] using a-cuts over the vague degrees through statistical confidence intervals is also presented by an example. The new method proposed in this work produces a correlation coefficient in the form of an interval. The proposed method produces a correlation coefficient in the form of an interval from a trapezoidal shaped fuzzy number derived from the vague degrees. This chapter also aims to develop a new method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to solve MADM problems for Interval Vague Sets (IVSs). A TOPSIS algorithm is constructed on the basis of the concepts of the relative-closeness coefficient computed from the correlation coefficient of IVSs. This novel method also identifies the positive and negative ideal solutions using the correlation coefficient of IVSs. A numerical illustration explains the proposed algorithms and comparisons are made with some existing methods.

Vague Correlation Coefficient of Interval Vague Sets and its Applications to Topsis in MADM Problems

Fuzzy Systems ◽  
2017 ◽  
pp. 1110-1149
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E. C.
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Numerical Illustration ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Statistical Confidence ◽  
Order Preference ◽  
Novel Method

Various attempts are made by researchers on the study of vagueness of data through Intuitionistic Fuzzy sets and Vague sets, and also it is shown that Vague sets are Intuitionistic Fuzzy sets. However, there are algebraic and graphical differences between Vague sets and Intuitionistic Fuzzy sets. In this chapter, an attempt is made to define the correlation coefficient of Interval Vague sets lying in the interval [0,1], and a new method for computing the correlation coefficient of interval Vague sets lying in the interval [-1,1] using a-cuts over the vague degrees through statistical confidence intervals is also presented by an example. The new method proposed in this work produces a correlation coefficient in the form of an interval. The proposed method produces a correlation coefficient in the form of an interval from a trapezoidal shaped fuzzy number derived from the vague degrees. This chapter also aims to develop a new method based on the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) to solve MADM problems for Interval Vague Sets (IVSs). A TOPSIS algorithm is constructed on the basis of the concepts of the relative-closeness coefficient computed from the correlation coefficient of IVSs. This novel method also identifies the positive and negative ideal solutions using the correlation coefficient of IVSs. A numerical illustration explains the proposed algorithms and comparisons are made with some existing methods.

scholarly journals Evaluating Evidence Reliability on the Basis of Intuitionistic Fuzzy Sets

Information ◽  
2018 ◽  
Vol 9 (12) ◽  
pp. 298 ◽  
Author(s):  
Wenhua Wu ◽  
Yafei Song ◽  
Weiwei Zhao
Keyword(s):  
Fuzzy Sets ◽  
Prior Knowledge ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Intuitionistic Fuzzy ◽  
Combining Evidence ◽  
Basic Probability ◽  
Supporting Degree ◽  
Evaluation Of Evidence ◽  
New Evidence

The evaluation of evidence reliability is still an open topic, when prior knowledge is unavailable. In this paper, we propose a new method for evaluating evidence reliability, in the framework of intuitionistic fuzzy sets. The reliability of evidence was evaluated, based on the supporting degree between basic probability assignments (BPAs). The BPAs were first transformed to intuitionistic fuzzy sets (IFSs). By the similarity degree between the IFSs, we can get the supporting degree between the BPAs. Thus, the reliability of evidence can be evaluated, based on its connection with supporting degree. Based on the new evidence reliability, we developed a new method for combining evidence sources with different reliability degrades. Comparison with other methods was carried out to illustrate the effectiveness of the new method.

Image Thresholding Computation Using Atanassov’s Intuitionistic Fuzzy Sets

2007 ◽  
Vol 11 (2) ◽  
pp. 187-194 ◽  
Author(s):  
H. Bustince ◽  
◽  
E. Barrenechea ◽  
M. Pagola ◽  
R. Orduna
Keyword(s):  
Fuzzy Sets ◽  
Set Theory ◽  
Fuzzy Set ◽  
Fuzzy Set Theory ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Threshold Selection ◽  
Uniform Illumination ◽  
Intuitionistic Fuzzy ◽  
Atanassov’S Intuitionistic Fuzzy Sets

In this paper, a new thresholding technique using Atanassov’s intuitionistic fuzzy sets (A-IFSs) and restricted dissimilarity functions is introduced. In recent years, various thresholding techniques ([18, 24]) based on fuzzy set theory have been introduced to overcome the problem of non-uniform illumination and inherent image vagueness. In this paper we analyze this task and propose a new method for handling the grayness ambiguity and vagueness during the process of threshold selection.

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