Abstract
In this paper, the problem of local properties and local contrast of a fuzzy relation is considered. The importance of these two concepts which measure, in a different way, the influence of neighboring elements on the element itself is studied. Modified versions of the local properties of a fuzzy relation are proposed. Moreover, dependencies between the local properties and local contrast are examined.
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References
Amo, A., Montero, J., Molina, E.: Representation of consistent recursive rules. Euro. J. Oper. Res. 130, 29–53 (2001)
Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)
Bentkowska, U., Pȩkala, B., Rza̧sa, W.: The stability of local properties of fuzzy relations under ordinal equivalence. Inf. Sci. 491, 265–278 (2019)
Beliakov, G., Bustince, H., Calvo, T.: A practical guide to averaging functions. In: Studies in Fuzziness and Soft Computing, vol. 329. Springer (2016)
Bustince, H., Barrenechea, E., Fernandez, J., Pagola, M., Montero, J., Guerra, C.: Contrast of a fuzzy relation. Inf. Sci. 180, 1326–1344 (2010)
Bustince, H., Barrenechea, E., Pagola, M., Fernández, J., Xu, Z., Bedregal, B., Montero, J., Hagras, H., Herrera, F., De Baets, B.: A historical account of types of fuzzy sets and their relationships. IEEE Trans. Fuzzy Syst. 24(1), 174–194 (2016)
Calvo, T., Kolesárová, A., Komorniková, M., Mesiar, R.: Aggregation operators: properties, classes and construction methods. In: Calvo, T., et al. (eds.) Aggregation Operators, pp. 3–104. Physica-Verlag, Heidelberg (2002)
Jahromi, M.Z., Parvinnia, E., John, R.: A method of learning weighted similarity function to improve the performance of nearest neighbor. Inform. Sci. 179(17), 2964–2973 (2009)
Klement, E.P., Mesiar, R., Pap, E.: Triangular Norms. Kluwer Acad. Publ., Dordrecht (2000)
Montero, J., Gómez, D., Bustince, H.: On the relevance of some families of fuzzy sets. Fuzzy Sets Syst. 158, 2429–2442 (2007)
Sambuc, R.: Fonctions \(\phi \)-floues: Application á l’aide au diagnostic en pathologie thyroidienne. Ph.D. Thesis, Universit\(\acute{e}\) de Marseille, France (1975). (in French)
Zadeh, L.A.: Fuzzy sets. Inf. Contr. 8, 338–353 (1965)
Zadeh, L.A.: The concept of a linguistic variable and its application to approximate reasoning-I. Inform. Sci. 8, Part I, 199–251, Part II, 301–357, Inform. Sci. 9. Part III, 43–80 (1975)
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This work was partially supported by the Centre for Innovation and Transfer of Natural Sciences and Engineering Knowledge of University of Rzeszów, Poland, the project RPPK.01.03.00-18-001/10.
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Bentkowska, U., Pȩkala, B. (2021). A Study on Local Properties and Local Contrast in Fuzzy Setting. In: Atanassov, K.T., et al. Advances and New Developments in Fuzzy Logic and Technology. IWIFSGN 2019 2019. Advances in Intelligent Systems and Computing, vol 1308. Springer, Cham. https://doi.org/10.1007/978-3-030-77716-6_7
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DOI: https://doi.org/10.1007/978-3-030-77716-6_7
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