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Issue:Pearson's coefficient between intuitionistic fuzzy sets: Difference between revisions

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  | conference      = 15<sup>th</sup> [[ICIFS]], Burgas, 11-12 May 2011
  | conference      = 15<sup>th</sup> [[ICIFS]], Burgas, 11-12 May 2011
  | issue          = Conference proceedings, [[Notes on Intuitionistic Fuzzy Sets/17/2|"Notes on IFS", Volume 17 (2011) Number 2]], pages 25—34
  | issue          = [[Notes on Intuitionistic Fuzzy Sets/17/2|"Notes on Intuitionistic Fuzzy Sets", Volume 17 (2011) Number 2]], pages 25—34
  | file            = NIFS-17-2-25-34.pdf
  | file            = NIFS-17-2-25-34.pdf
  | format          = PDF
  | format          = PDF
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  | abstract        =  
  | abstract        =  


We address the problem of assessing information and knowledge conveyed by an Atanassov's intuitionistic fuzzy set (A-IFS for short). We pay particular attention to the relationship between positive and negative knowledge (expressed by entropy which may be seen as a dual measure to information), and take into account also reliability of the information expressed by the hesitation margin.
The correlation coefficient (Pearson's <math>r</math>) is one of the most frequently used tools in statistics. In this paper we discuss a correlation coefficient between Atanassov's intuitionistic fuzzy sets (A-IFSs). We have constructed the coefficient so it provides the strength of the relationship between A-IFSs and also shows if the considered sets are positively or negatively correlated. Next, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin.


  | keywords        = [[Intuitionistic fuzzy sets]], amount of information, entropy, hesitation margin.
  | keywords        = [[Intuitionistic fuzzy sets]], Correlation coefficient, Hesitation margin
| ams            = 03E72
  | references      =  
  | references      =  


Latest revision as of 11:13, 29 August 2024

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Title of paper: Pearson's coefficient between intuitionistic fuzzy sets
Author(s):
Eulalia Szmidt
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
szmidt@ibspan.waw.pl
Janusz Kacprzyk
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
kacprzyk@ibspan.waw.pl
Paweł Bujnowski
Systems Research Institute - Polish Academy of Sciences, ul. Newelska 6, 01-447 Warsaw, Poland
Presented at: 15th ICIFS, Burgas, 11-12 May 2011
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 17 (2011) Number 2, pages 25—34
Download:  PDF (210  Kb, File info)
Abstract: The correlation coefficient (Pearson's [math]\displaystyle{ r }[/math]) is one of the most frequently used tools in statistics. In this paper we discuss a correlation coefficient between Atanassov's intuitionistic fuzzy sets (A-IFSs). We have constructed the coefficient so it provides the strength of the relationship between A-IFSs and also shows if the considered sets are positively or negatively correlated. Next, the proposed correlation coefficient takes into account not only the amount of information related to the A-IFS data (expressed by the membership and non-membership values) but also the reliability of the data expressed by a so-called hesitation margin.
Keywords: Intuitionistic fuzzy sets, Correlation coefficient, Hesitation margin
AMS Classification: 03E72
References:
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