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Atanassov’s Intuitionistic Fuzzy Sets as a Classification Model.

Montero de Juan, Francisco Javier and Gómez, Daniel and Bustince, H. (2007) Atanassov’s Intuitionistic Fuzzy Sets as a Classification Model. In Foundations of fuzzy logic and soft computing :12th International fuzzy systems association world congress. Lecture Notes in Computer Science (4529). Springer, Berlin, pp. 69-75. ISBN 978-3-540-72917-4

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Abstract

In this paper we show that Atanassov's Intuitionistic Fuzzy sets can be viewed as a classification model, that can be generalized in order to take into account more classes than the three classes considered by Atanassov's (membership, non-membership and non-determinacy). This approach will imply, on one hand, to change the meaning of these classes, so each one will have a positive definition. On the other hand, this approach implies the possibility of a direct generalization for alternative logics and additional valuation states, being consistent with Atanassov's focuss. From this approach we shall stress the absence of any structure within those three valuation states in Atanassov's model. In particular, we consider this is the main cause of the dispute about Atanassov's model: acknowledging that the name intuitionistic is not appropriate, once we consider that a crisp direct graph is defined in the valuation space, formal differences with other three-state models will appear.


Item Type:Book Section
Additional Information:

12th World Congress of the International-Fuzzy-Systems-Association.
JUN 18-21, 2007 Cancun, MEXICO

Uncontrolled Keywords:Atanassov’s Intuitionistic Fuzzy Sets, Interval Valued Fuzzy Sets, Type-2 Fuzzy Sets, L-Fuzzy sets.
Subjects:Sciences > Mathematics > Logic, Symbolic and mathematical
ID Code:16914
References:

A. Amo, D. Gomez, J. Montero and G. Biging (2001): Relevance and redundancy in fuzzy classification systems. Mathware and Soft Computing 8:203–216.

A. Amo, J. Montero, G. Biging and V. Cutello (2004): Fuzzy classification systems.European Journal of Operational Research 156:459–507.

A. Amo, J. Montero, and E. Molina (2001): Representation of consistent recursive ules. European Journal of Operational Research 130:29–53.

K.T. Atanassov (1983): Intuitionistic fuzzy sets. In: V. Sgurev, ed., VII ITKR’s Session, Sofia, June 1983 (deposed in Central Science and Technical Library, Bulgarian Academy of Sciences, 1697/84, in Bulgarian).

K.T. Atanassov (1999): Intuitionistic Fuzzy sets,Physica-Verlag., Heidelberg, New York.

K.T. Atanassov (2005): Answer to D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade’s paper, Terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets. Fuzzy Sets and Systems 156:496–499.

K.T. Atanassov (in press): A personal view on intuitionistic fuzzy sets. In H. Bustince, F. Herrera and J. Montero, eds.: Fuzzy Sets and Their Extensions:Representation,Aggregation and Models, Springer Verlag, Berlin.

T. Calvo, A. Kolesarova, M. Komornikova and R. Mesiar, Aggregation operators (2002): properties, classes and construction methods. In T. Calvo, G. Mayor and R. Mesiar, Eds.: Aggregation Operators, Springer; 3–104.

G. Cattaneo and D. Ciucci (in press): Basic intuitionistic principles in fuzzy set theories and its extensions (a terminological debate on Atanassov IFS).Fuzzy sets and Systems.

P. Cintula (2005): Basics of a formal theory of fuzzy partitions. Proceedings EUSFLAT’05 Conference, Technical University of Catalonia, Barcelona; pp.884–888.

V. Cutello and J. Montero (1999): Recursive connective rules. Int. J. Intelligent Systems 14:3–20.

B. De Baets and R. Mesiar (1998): T-partitions. Fuzzy Sets and Systems 97:211–223.

G. Deschrijver and E.E. Kerre (2003): On the relationship between some extensions of fuzzy sets theory. Fuzzy Sets and Systems 133:227–235.

D. Dubois, S. Gottwald, P. Hajek, J. Kacprzyk and H. Prade (2005): Terminological difficulties in fuzzy set theory - the case of intuitionistic fuzzy sets. Fuzzy Sets and Systems 156:485–491.

P. Fortemps and R. Slowinski (2002): A graded quadrivalent logic for ordinal preference modelling: Loyola-like approach. Fuzzy Optimization and Decision making 1:93–111.

E.P. Klement, R. Mesiar and E. Pap (2002): Triangular Norms, Kluwer Academic Publishers, Dordrecht.

J.M. Mendel (2007): Advances in type-2 fuzzy sets and systems. Information Sciences 117:84–110.

J. Montero (1986): Comprehensive fuzziness. Fuzzy Sets and Systems 20:89–86.

J. Montero (1987): Extensive fuzziness. Fuzzy Sets and Systems 21:201–209.

J. Montero, D. G´omez and H. Bustince (2006): On the relevance of some families of fuzzy sets. Technical report.

E.H. Ruspini (1969): A new approach to clustering. Information and Control 15:22–32.

R. Sambuc (1975): Function Φ-flous, application a l’aide au diagnostic en pathologie thyroidienne.These de doctorat en Medicine, Marseille.

G. Takeuti and S. Titani (1984): Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. Journal of Symbolic Logic 49:851–866.

I.B. T¨urksen (1986): Interval valued fuzzy sets based on normal forms. Fuzzy Sets and Systems 20:191–210.

R.R. Yager and A. Rybalov (1996): Uninorm aggregation operators. Fuzzy Sets and Systems 80:111–120.

R.R. Yager (1988): On ordered averaging aggregation operators in multicriteria decision making. IEEE Transactions on Systems, Man and Cybernetics 18:183–190.

L.A. Zadeh (1965): Fuzzy sets. Information and control 8:338–353.

Deposited On:30 Oct 2012 08:51
Last Modified:07 Feb 2014 09:38

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