Abstract
Twenty years after their inception, intuitionistic fuzzy sets are on the rise towards making their “claim to fame”. Competing alongside various other, often closely related, formalisms, they are catering to the needs of a more demanding and rapidly expanding knowledge-based systems industry. In this paper, we develop the notion of a graded inclusion indicator within this setting, drawing inspiration from related concepts in fuzzy set theory, yet keeping a keen eye on those particular challenges raised specifically by intuitionistic fuzzy set theory. The use of our work is demonstrated by its applications in approximate reasoning and non-probabilistic entropy calculation.
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References
Atanassov, K.T.: Intuitionistic Fuzzy Sets. Physica-Verlag, Heidelberg (1999)
Bandler, W., Kohout, L.: Fuzzy power sets and fuzzy implication operators. Fuzzy Sets and Systems 4, 13–30 (1980)
Cornelis, C., De Cock, M., Kerre, E.: Intuitionistic fuzzy rough sets: on the crossroads of imperfect knowledge. Accepted to: Expert Systems (2003)
Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic and interval– Valued fuzzy set theory: construction, classification, application. Submitted to: International Journal of Approximate Reasoning (2002)
Cornelis, C., Kerre, E.E.: A Fuzzy Inference Methodology Based on the Fuzzification of Set Inclusion. In: Abraham, A., Jain, L., Kacprzyk, J. (eds.) Recent Advances in Intelligent Paradigms and Applications, pp. 71–89. Physica-Verlag, Heidelberg (2002)
Cornelis, C., Kerre, E.E.: On the structure and interpretation of an intuitionistic fuzzy expert system. In: De Baets, B., Fodor, J., Pasi, G. (eds.) Proceedings of EUROFUSE 2002, pp. 173–178 (2002)
Cornelis, C., Van Der Donck, C., Kerre, E.E.: Sinha–Dougherty approach to the fuzzification of set inclusion revisited. Fuzzy Sets and Systems 134(2), 283–295 (2003)
Fodor, J., Yager, R.: Fuzzy set theoretic operators and quantifiers. In: Dubois, D., Prade, H. (eds.) Fundamentals of Fuzzy Sets, pp. 125–193. Kluwer, Boston (2000)
Fortemps, P., Slowinski, R.: A graded quadrivalent logic for ordinal preference modelling: Loyola–like approach. Fuzzy Optimization and Decision Making 1, 93–111 (2002)
Goguen, J.: L–fuzzy Sets. J. Math. Anal. Appl. 18, 145–174 (1967)
Kitainik, L.: Fuzzy decision procedures with binary relations. Kluwer, Dordrecht (1993)
Kosko, B.: Fuzzy entropy and conditioning. Kluwer, Dordrecht (1993)
Mendel, J.M.: Uncertain rule–based fuzzy logic systems. Prentice Hall PTR, Upper Saddle River (2001)
Sinha, D., Dougherty, E.R.: Fuzzification of set inclusion: theory and applications. Fuzzy Sets and Systems 55(1), 15–42 (1993)
Stickel, M.E.: Fuzzy four–valued logic for inconsistency and uncertainty. In: Proceedings of the Eighth International Symposium on Multiple–Valued Logic (1978)
Szmidt, E., Kacprzyk, J.: Entropy for intuitionistic fuzzy sets. Fuzzy Sets and Systems 118(3), 467–477 (2001)
Takeuti, G., Titani, S.: Intuitionistic fuzzy logic and intuitionistic fuzzy set theory. Journal of Symbolic Logic 49(3), 851–866 (1984)
Young, V.: Fuzzy subsethood. Fuzzy Sets and Systems 77(3), 371–384 (1996)
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Cornelis, C., Kerre, E. (2003). Inclusion Measures in Intuitionistic Fuzzy Set Theory. In: Nielsen, T.D., Zhang, N.L. (eds) Symbolic and Quantitative Approaches to Reasoning with Uncertainty. ECSQARU 2003. Lecture Notes in Computer Science(), vol 2711. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-45062-7_28
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DOI: https://doi.org/10.1007/978-3-540-45062-7_28
Publisher Name: Springer, Berlin, Heidelberg
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