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On This Book: Clustering, Multisets, Rough Sets and Fuzzy Sets Read chapter Read first chapter

2017 | OriginalPaper | Chapter

A Perspective on Differences Between Atanassov’s Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets

Authors : Eulalia Szmidt, Janusz Kacprzyk

Published in: Fuzzy Sets, Rough Sets, Multisets and Clustering

Publisher: Springer International Publishing

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Abstract

In the paper we show our perspective on some differences between Atanassov’s intuitionistic fuzzy sets (A-IFSs, for short) and Interval-valued fuzzy sets (IVFSs, for short). First, we present some standard operators and extensions for the A-IFSs which have no counterparts for IVFSs. Next, we show on an example a practical application based on one of such operators. We also revisit, and further analyze, the concepts of two possible representations of A-IFSs: the two term one, in which the degrees of membership and non-membership are only involved, and the three term one, in which in addition to the above degrees of membership and non-membership the so called hesitation margin is explicitly accounted for. Though both representations are mathematically correct and may be considered equivalent, the second one involves explicitly an additional, conceptually different information than the degree of membership and non-membership only even if it directly results from these two degrees. We then show on some examples of decision making type problems its intuitive appeal and usefulness for reflecting more sophisticated intentions and preferences of the user which cannot be fully reflected via their counterpart IVFSs based models. Finally, we recall different measures that are important from the point of view of applications. We consider the measures for both types representations of the A-IFSs pointing out some further differences in comparison to the case of the IVFSs.

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previous chapter L-Fuzzy Bags
next chapter Attribute Importance Degrees Corresponding to Several Kinds of Attribute Reduction in the Setting of the Classical Rough Sets
Literature
1.
Atanassov K.T. (1983) Intuitionistic Fuzzy Sets. VII ITKR Session. Sofia (Deposed in Centr. Sci.-Techn. Library of Bulg. Acad. of Sci., 1697/84) (in Bulgarian).
2.
3.
4.
Atanassov K.T. (1991) Temporal intuitionistic fuzzy sets. Comptes Rendus de l’Academie Bulgare des Sciences, Tome 44, No. 7, 5–7.
5.
Atanassov K.T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications. Springer-Verlag.
6.
Atanassov K.T. (2006) Intuitionistic fuzzy sets and interval valued fuzzy sets. First Int. Workshop on IFSs, GNs, KE, London, 6–7 Sept. 2006, 1–7.
7.
Atanassov K.T. (2012) On Intuitionistic Fuzzy Sets Theory. Springer-Verlag.
8.
9.
Atanassov K., Tasseva V, Szmidt E. and Kacprzyk J. (2005): On the geometrical interpretations of the intuitionistic fuzzy sets. In: Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. (Eds. Atanassov K., Kacprzyk J., Krawczak M., Szmidt E.), EXIT, Warsaw, 11–24.
10.
Atanassova V. (2004) Strategies for Decision Making in the Conditions of Intuitionistic Fuzziness. Int. Conf. 8th Fuzzy Days, Dortmund, Germany, 263–269.
11.
Bujnowski P., Szmidt E., Kacprzyk J. (2014): Intuitionistic Fuzzy Decision Trees - a new Approach. In: Rutkowski L., Korytkowski M., Scherer R., Tadeusiewicz R., Zadeh L., urada J. (Eds.): Artificial Intelligence and Soft Computing, Part I. Springer, Switzerland, 181–192.
12.
Bustince H., Mohedano V., Barrenechea E., and Pagola M. (2005): Image thresholding using intuitionistic fuzzy sets. In: Issues in the Representation and Processing of Uncertain and Imprecise Information. Fuzzy Sets, Intuitionistic Fuzzy Sets, Generalized Nets, and Related Topics. (Eds. Atanassov K., Kacprzyk J., Krawczak M., Szmidt E.), EXIT, Warsaw.
13.
Bustince H., Mohedano V., Barrenechea E., and Pagola M. (2006): An algorithm for calculating the threshold of an image representing uncertainty through A-IFSs. IPMU’2006, 2383–2390.
14.
Bustince H., Barrenechea E., Pagola M., Fernandez J., Xu Z., Bedregal B., Montero J., Hagras H., Herrera F., and De Baets B., A Historical Account of Types of Fuzzy Sets and Their Relationships. IEEE Transactions on Fuzzy Systems, 24 (1), 2016, 179–194.CrossRef
15.
Deng-Feng Li (2005): Multiattribute decision making models and methods using intuitionistic fuzzy sets. Journal of Computer and System Sciences, 70, 73–85.MathSciNetCrossRefMATH
16.
Dubois D., Prade H.(2008): An introduction to bipolar representations of information and preference. Int. J. Intell. Syst. 23(8), 866–877.CrossRefMATH
17.
Feys R. Modal logic. Foundation Universitaire de Belgique, Paris 1965.MATH
18.
Grabisch M., Greco S., Pirlot M. (2008): Bipolar and bivariate models in multicriteria decision analysis: Descriptive and constructive approaches. International Journal of Intelligent Systems, 23 (9), 930–969.CrossRefMATH
19.
Kuratowski K. (1966) Topology, Vol. 1, New York, Acad. Press.MATH
20.
Montero J., Gmez D., Bustince Sola H. (2007): On the relevance of some families of fuzzy sets. Fuzzy Sets and Systems 158(22), 2429–2442.MathSciNetCrossRefMATH
21.
Narukawa Y. and Torra V. (2006): Non-monotonic fuzzy measure and intuitionistic fuzzy set. MDAI 2006, LNAI 3885, 150–160, Springer-Verlag.
22.
Roeva O. and Michalikova A. (2013) Generalized net model of intuitionistic fuzzy logic control of genetic algorithm parameters. In: Notes on Intuitionistic Fuzzy Sets. Academic Publishing House, Sofia, Bulgaria. Vol. 19, No. 2, 71–76. ISSN 1310-4926.
23.
Szmidt E. (2014): Distances and Similarities in Intuitionistic Fuzzy Sets. Springer.
24.
Szmidt E. and Baldwin J. (2003) New similarity measure for intuitionistic fuzzy set theory and mass assignment theory.
25.
Szmidt E. and Baldwin J. (2004) Entropy for intuitionistic fuzzy set theory and mass assignment theory. Notes on IFSs, 10 (3), 15–28.
26.
Szmidt E. and Baldwin J. (2006): Intuitionistic Fuzzy Set Functions, Mass Assignment Theory, Possibility Theory and Histograms. 2006 IEEE World Congress on Computational Intelligence, 237–243.
27.
Szmidt E. and Kacprzyk J. (1997): On measuring distances between intuitionistic fuzzy sets. Notes on IFS, 3(4), 1–13.MathSciNetMATH
28.
Szmidt E. and Kacprzyk J. (1999): Probability of Intuitionistic Fuzzy Events and their Applications in Decision Making. EUSFLAT-ESTYLF, Palma de Mallorca, 457–460.
29.
Szmidt E. and Kacprzyk J. (1999b): A Concept of a Probability of an Intuitionistic Fuzzy Event. FUZZ-IEEE’99, Seoul, Korea, III 1346–1349.
30.
31.
Szmidt E., Kacprzyk J. (2001): Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems, 118, Elsevier, 467–477.
32.
Szmidt E., Kacprzyk J. (2006): Distances Between Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 3rd International IEEE Conference Intelligent Systems IEEE IS’06, London, 716–721.
33.
Szmidt E. and Kacprzyk J. (2007): Some problems with entropy measures for the Atanassov intuitionistic fuzzy sets. Applications of Fuzzy Sets Theory. LNAI 4578, Springer-Verlag, 291–297
34.
Szmidt E. and Kacprzyk J. (2007a): A New Similarity Measure for Intuitionistic Fuzzy Sets: Straightforward Approaches may not work. 2007 IEEE Conf. on Fuzzy Systems, 481–486
35.
Szmidt E. and Kacprzyk J. (2008) A new approach to ranking alternatives expressed via intuitionistic fuzzy sets. In: D. Ruan et al. (Eds.) Computational Intelligence in Decision and Control. World Scientific, 265–270.
36.
Szmidt E. and Kacprzyk J.: Ranking of Intuitionistic Fuzzy Alternatives in a Multi-criteria Decision Making Problem. In: Proceedings of the conference: NAFIPS 2009, Cincinnati, USA, June 14–17, 2009, IEEE, ISBN: 978-1-4244-4577-6.
37.
Szmidt E., Kacprzyk J. (2011) Intuitionistic fuzzy sets – Two and three term representations in the context of a Hausdorff distance. Acta Universitatis Matthiae Belii, Series Mathematics, available at http://​ACTAMTH.​SAVBB.​SK, Vol.19, No. 19, 2011, 53–62.
38.
Szmidt E. and Kacprzyk J. (2009) Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives. In: Recent Advances in decision Making, SCI 222. E. Rakus-Andersson, R. Yager, N. Ichalkaranje, L.C. Jain (Eds.), Springer-Verlag, 7–19.
39.
Szmidt E. and Kacprzyk J. (2010): Correlation between intuitionistic fuzzy sets. LNAI 6178 (Computational Intelligence for Knowledge-Based Systems Design, Eds. E.Hullermeier, R. Kruse, F. Hoffmann), 169–177.
40.
Szmidt E. and Kacprzyk J. (2010): The Spearman rank correlation coefficient between intuitionistic fuzzy sets. In: Proc. 2010 IEEE Int. Conf. on Intelligent Systems IEEE’IS 2010, London, 276–280.
41.
Szmidt E., Kacprzyk J., Bujnowski P. (2011): Measuring the Amount of Knowledge for Atanassov’s Intuitionistic Fuzzy Sets. Fuzzy Logic and Applications, Lecture Notes in Artificial Intelligence, Vol. 6857, 2011, 17–24.MATH
42.
Szmidt E., Kacprzyk J. and Bujnowski P. (2011) Pearson’s coefficient between intuitionistic fuzzy sets. Notes on Intuitionistic Fuzzy Sets, 17 (2), 25–34.MATH
43.
Szmidt E. and Kacprzyk J. (2011) The Kendall Rank Correlation between Intuitionistic Fuzzy Sets. In: Proc.: World Conference on Soft Computing, San Francisco, CA, USA, 23/05/2011-26/05/2011.
44.
Szmidt E. and Kacprzyk J. (2011) The Spearman and Kendall rank correlation coefficients between intuitionistic fuzzy sets. In: Proc. 7th conf. European Society for Fuzzy Logic and Technology, Aix-Les-Bains, France, Antantic Press, 521–528.
45.
Szmidt E., Kacprzyk J., Bujnowski P. (2012): Advances in Principal Component Analysis for Intuitionistic Fuzzy Data Sets. 2012 IEEE 6th International Conference ,,Intelligent Systems”, 194–199.
46.
Szmidt E. and Kacprzyk J. (2012) A New Approach to Principal Component Analysis for Intuitionistic Fuzzy Data Sets. S. Greco et al. (Eds.): IPMU 2012, Part II, CCIS 298, 529–538, Springer-Verlag Berlin Heidelberg.
47.
Szmidt E. and Kacprzyk J. (2015) Two and Three Term Representations of Intuitionistic Fuzzy Sets: Some Conceptual and Analytic Aspects. IEEE International Conference on Fuzzy Systems (FUZZ-IEEE 2015), Istanbul, Turkey, August 2–5, 2015, IEEE, ss. 1-8.
48.
Szmidt E., Kacprzyk J. and Bujnowski P. (2012) Advances in Principal Component Analysis for Intuitionistic Fuzzy Data Sets. 2012 IEEE 6th International Conference “Intelligent Systems”, 194–199.
49.
Szmidt E., Kacprzyk J. and Bujnowski P. (2012): Correlation between Intuitionistic Fuzzy Sets: Some Conceptual and Numerical Extensions. WCCI 2012 IEEE World Congress on Computational Intelligence, Brisbane, Australia, 480–486.
50.
Szmidt E., Kacprzyk J., Bujnowski P. (2014): How to measure the amount of knowledge conveyed by Atanassov’s intuitionistic fuzzy sets. Information Sciences, 257, 276–285.MathSciNetCrossRefMATH
51.
Szmidt E., Kreinovich V. (2009) Symmetry between true, false, and uncertain: An explanation. Notes on Intuitionistic Fuzzy Sets 15, No. 4, 1–8.MATH
52.
Szmidt E. and Kukier M. (2006): Classification of Imbalanced and Overlapping Classes using Intuitionistic Fuzzy Sets. IEEE IS’06, London, 722–727.
53.
Szmidt E. and Kukier M. (2008): A New Approach to Classification of Imbalanced Classes via Atanassov’s Intuitionistic Fuzzy Sets. In: Hsiao-Fan Wang (Ed.): Intelligent Data Analysis : Developing New Methodologies Through Pattern Discovery and Recovery. Idea Group, 85–101.
54.
Szmidt E., Kukier M. (2008): Atanassov’s intuitionistic fuzzy sets in classification of imbalanced and overlapping classes. In: P. Chountas, I. Petrounias, J. Kacprzyk (Eds.): Intelligent Techniques and Tools for Novel System Architectures. Series: Studies in Computational Intelligence, Vol. 109, Springer, Berlin Heidelberg 2008, 455–471.
55.
Tan Ch. and Zhang Q. (2005): Fuzzy multiple attribute TOPSIS decision making method based on intuitionistic fuzzy set theory. IFSA 2005, 1602–1605.
56.
Tasseva V., Szmidt E. and Kacprzyk J. (2005): On one of the geometrical interpretations of the intuitionistic fuzzy sets. Notes on IFS, 11 (3), 21–27.
57.
Metadata
Title
A Perspective on Differences Between Atanassov’s Intuitionistic Fuzzy Sets and Interval-Valued Fuzzy Sets
Authors
Eulalia Szmidt
Janusz Kacprzyk
Copyright Year
2017
Book
Fuzzy Sets, Rough Sets, Multisets and Clustering

Print ISBN: 978-3-319-47556-1

Electronic ISBN: 978-3-319-47557-8

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-47557-8_13

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