Abstract
In this note we prove that in the framework of intuitionistic fuzzy sets can be defined connective systems which satisfy some logical rules generalizing the rules of the constructive logic with strong negation (CLSN). As rough set systems defined by a quasiorder serve as models for CLSN, similarly, intuitionistic sets can be viewed as models of its mentioned generalization.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Atanassov, K.T.: Intuitionistic fuzzy sets. In: VII ITKR’s Session, Sofia, 1983 (Deposed in Central Sci. - Techn. Library of Bulg. Acad. of Sci., 1697/84)
Atanassov, K.T.: Intuitionistic fuzzy sets: past, present and future. In: EUSFLAT 3rd Conference, Zittau, pp. 12–19 (2003)
Cignoli, R.: The class of Kleene algebras satisfying an interpolation property and Nelson algebras. Algebra Univers. 23, 262–292 (1986)
Cornelis, C., Deschrijver, G., Kerre, E.E.: Implication in intuitionistic fuzzy and interval-valued fuzzy set theory: construction, classification, application. Int. J. Approx. Reason. 35 (1), 55–95 (2004)
Galatos, N., Jipsen, P., Kowalski, T., Ono, H.: Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Studies in Logic and the Foundations of Mathematics, vol. 151. Elsevier, Amsterdam (2007).
Goertz, G., Mahoney, J.: Concept and measurement: ontology and epistomology. Soc. Sci. Inf. 51 (2), 205–216 (2012)
Grant, J.: Null values in SQL. ACM SIGMOD Rec. 37 (3), 23–25 (2008)
Järvinen, J., Radeleczki, S.: Representation of Nelson algebras by rough sets determined by quasiorders. Algebra Univer. 66, 163–179 (2011)
Järvinen, J., Radeleczki, S.: Monteiro spaces and rough sets determined by quasiorder relations: models for Nelson algebras. Fundam. Inform. 131 (2), 205–215 (2014)
Järvinen, J., Radeleczki, S., Veres, L.: Rough sets determined by quasiorders. Order 26, 337–355 (2009)
Kovács, L., Radeleczki, S.: Uncertainty management in knowledge modelling. In: 8-th International Conference Interdisciplinarity in Engineering, INTER-ENG, Tirgu-Mures (2014)
Liu, J.N.K.: An intelligent system integrated with fuzzy ontology for product recommendation and retrieval. In: Proceedings of the 8th WSEAS International Conference on Fuzzy Systems, pp. 180–185 (2007)
Novák, V., Perfilieva, I., Mockor, J.: Mathematical Principles of Fuzzy Logic, vol. 517. Springer Science & Business Media, New York (2012)
Pawlak, Z.: Rough sets. Int. J. Parall. Program. 11 (5), 341–356 (1982)
Rasiowa, H.: An Algebraic Approach to Non-Classical Logics. North-Holland, Amsterdam (1974)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Kovács, L., Radeleczki, S. (2017). Logical Analogies Between Intuitionistic Fuzzy Sets and Rough Sets. In: Meier, A., Portmann, E., Stoffel, K., Terán, L. (eds) The Application of Fuzzy Logic for Managerial Decision Making Processes. Fuzzy Management Methods. Springer, Cham. https://doi.org/10.1007/978-3-319-54048-1_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-54048-1_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-54047-4
Online ISBN: 978-3-319-54048-1
eBook Packages: Business and ManagementBusiness and Management (R0)