Abstract
The aim of this paper is, first, to recall fuzzy relational compositions (products) and, to introduce an idea, how the so-called excluding features could be incorporated into the theoretical background. Apart from rather natural definitions, we provide readers with a theoretical investigation that provides and answer to a rather natural question, under which conditions, in terms of the underlying algebraic structures, the proposed incorporation of excluding features preserves the same properties as the incorporation in the classical relational compositions. The positive impact of the incorporation on reducing the suspicions provided by the basic “circlet” composition without losing the possibly correct suspicion, as in the case of the use of the Bandler-Kohout products, is demonstrated on an example.
M. Štěpnička—This research was partially supported by the NPU II project LQ1602 “IT4Innovations excellence in science” provided by the MŠMT.
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Notes
- 1.
Instead of the term composition, one may often encounter the term “product” denoting the same mappings or objects. This terminology naturally comes from the product-like matrix calculation of the compositions.
References
Pedrycz, W.: Applications of fuzzy relational equations for methods of reasoning in presence of fuzzy data. Fuzzy Sets Syst. 16, 163–175 (1985)
Štěpnička, M., Jayaram, B.: On the suitability of the Bandler-Kohout subproduct as an inference mechanism. IEEE Trans. Fuzzy Syst. 18(2), 285–298 (2010)
Bandler, W., Kohout, L.: Semantics of implication operators and fuzzy relational products. Int. J. Man-Mach. Stud. 12(1), 89–116 (1980)
Bandler, W., Kohout, L.: Relational-product architectures for information processing. Inf. Sci. 37, 25–37 (1985)
Dubois, D., Prade, H.: Semantics of quotient operators in fuzzy relational databases. Fuzzy Sets Syst. 78, 89–93 (1996)
De Baets, B., Kerre, E.: Fuzzy relational compositions. Fuzzy Sets Syst. 60, 109–120 (1993)
Běhounek, L., Daňková, M.: Relational compositions in fuzzy class theory. Fuzzy Sets Syst. 160(8), 1005–1036 (2009)
Novák, V., Perfilieva, I., Močkoř, J.: Mathematical Principles of Fuzzy Logic. Kluwer Academic Publishers, Boston (1999)
Bandler, W., Kohout, L.: Fuzzy power sets and fuzzy implication operators. Fuzzy Sets Syst. 4, 183–190 (1980)
Pedrycz, W.: Fuzzy relational equations with generalized connectives and their applications. Fuzzy Sets Syst. 10, 185–201 (1983)
Chung, F., Lee, T.: Analytical resolution and numerical identification of fuzzy relational systems. IEEE Trans. Syst. Man Cybern. 28, 919–924 (1998)
Štěpnička, M., Holčapek, M.: Fuzzy relational compositions based on generalized quantifiers. In: Laurent, A., Strauss, O., Bouchon-Meunier, B., Yager, R.R. (eds.) IPMU 2014, Part II. CCIS, vol. 443, pp. 224–233. Springer, Heidelberg (2014)
Cao, N., Štěpnička, M.: An existence of fuzzy relational compositions using generalized quantifiers. In: Proceedings of the 16th World Congress of the International Fuzzy Systems Association (IFSA), 9th Conference of the European Society for Fuzzy-Logic, Technology (EUSFLAT). Advances in Intelligent Systems Research, vol. 89, pp. 49–58. Atlantis press, Gijón (2015)
Murinová, P., Novák, V.: A formal theory of generalized intermediate syllogisms. Fuzzy Sets Syst. 186(1), 47–80 (2012)
Dvořák, A., Holčapek, M.: L-fuzzy quantifiers of type \(\langle 1\rangle \) determined by fuzzy measures. Fuzzy Sets Syst. 160(23), 3425–3452 (2009)
Lim, C., Chan, C.: A weighted inference engine based on interval-valued fuzzy relational theory. Expert Syst. with Appl. 42, 3410–3419 (2015)
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Cao, N., Štěpnička, M. (2016). How to Incorporate Excluding Features in Fuzzy Relational Compositions and What for. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_38
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