Vague Sets or Intuitionistic Fuzzy Sets for Handling Vague Data: Which One Is Better?

2005 ◽  
pp. 401-416 ◽  
Author(s):  
An Lu ◽  
Wilfred Ng
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Vague Data

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.

A Short Primer on the Correlation Coefficient of Vague Sets

2011 ◽  
Vol 1 (2) ◽  
pp. 55-69 ◽  
Author(s):  
John Robinson P. ◽  
Henry Amirtharaj E.C.
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Real Life ◽  
Detailed Comparison ◽  
Intuitionistic Fuzzy Sets ◽  
Vague Set ◽  
Practical Applications ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Life Problems

Intuitionistic fuzzy sets and vague sets are generalizations of the concept of fuzzy sets. Various researchers have studied the vagueness of data through vague sets, and it was later demonstrated that vague sets are indeed intuitionistic fuzzy sets. Since its entry in the literature, vague set theory has received increased attention. Many real life problems involve information in the form of vague values, due to the increasing complexity of the socio-economic environment and the vagueness of the inherent subjective nature of human thinking. Instead of using point-based membership as in fuzzy sets, interval-based membership is used in a vague set. This paper presents a detailed comparison between vague sets and intuitionistic fuzzy sets, from various perspectives of algebraic properties, graphical representations, and practical applications. Methods of calculating the correlation coefficient of intuitionistic fuzzy sets and interval-valued intuitionistic fuzzy sets are already found in the literature. This paper defines the correlation coefficient of vague sets through simple examples.

Generalized Set Theories Applied in Uncertain Information Processing

2014 ◽  
Vol 644-650 ◽  
pp. 2419-2423
Author(s):  
Qing Bo Yang ◽  
Jian Long Zhou
Keyword(s):  
Information Processing ◽  
Fuzzy Sets ◽  
Rough Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Uncertain Information ◽  
Vague Sets ◽  
Intuitionistic Fuzzy

Uncertain factors in information bring us serious challenges. In order to apply information effectively, many researchers are committed to the research on uncertain information processing. Generalized set theories are widely used in the research. Several kinds of theories such as Fuzzy sets, Intuitionistic fuzzy sets, Vague sets, Rough sets and Extension sets are introduced in this paper. And a comparation and analysis of them is given in the following.

Vague sets are intuitionistic fuzzy sets

1996 ◽  
Vol 79 (3) ◽  
pp. 403-405 ◽  
Author(s):  
H. Bustince ◽  
P. Burillo
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Vague Sets ◽  
Intuitionistic Fuzzy

Vague Correlation Coefficient of Interval Vague Sets

2012 ◽  
Vol 2 (1) ◽  
pp. 18-34 ◽  
Author(s):  
P. John Robinson ◽  
E. C. Henry Amirtharaj
Keyword(s):  
Fuzzy Sets ◽  
Correlation Coefficient ◽  
Confidence Intervals ◽  
Intuitionistic Fuzzy Sets ◽  
New Method ◽  
Vague Sets ◽  
Intuitionistic Fuzzy ◽  
Statistical Confidence

Various attempts have been made by researchers on the study of vagueness of data through intuitionistic fuzzy sets and vague sets, and also it was shown that vague sets are intuitionistic fuzzy sets. But there are algebraic and graphical differences between vague sets and intuitionistic fuzzy sets. In this paper 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 presented by an example. The new method proposed in this paper produces a correlation coefficient in the form of an interval.

One Hundredth of Intuitionistic Fuzzy Sets

2019 ◽  
Vol 10 (3) ◽  
pp. 445-453
Author(s):  
R. Nagalingam ◽  
S. Rajaram
Keyword(s):  
Fuzzy Sets ◽  
Intuitionistic Fuzzy Sets ◽  
Intuitionistic Fuzzy
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