LK-INTERIOR SYSTEMS AS SYSTEMS OF “ALMOST OPEN” L-SETS

Document Type : Research Paper

Author

Department of Mathematics, Technical University of Ostrava, 17. listopadu, CZ-708 30,Ostrava , Czech Republic

Abstract

We study interior operators and interior structures in a fuzzy setting.
We investigate systems of “almost open” fuzzy sets and the relationships
to fuzzy interior operators and fuzzy interior systems.

Keywords


[1] W. Bandler and L. Kohout, Special properties, closures and interiors of crisp and fuzzy
relations, Fuzzy Sets and Systems, 26(3)(1988), 317–331.
[2] R. Bˇelohl´avek and T. Funiokov´a, Fuzzy interior operators, Int. J. General Systems,
33(4)(2004), 315–330.
[3] R. Bˇelohl´avek, Fuzzy closure operators, J. Math. Anal. Appl., 262(2001), 473-489.
[4] R. Bˇelohl´avek, Fuzzy closure operators II, Soft Computing, 7(1)(2002), 53-64.
[5] R. Bˇelohl´avek, Fuzzy relational systems: foundations and principles, Kluwer Academic/
Plenum Press, New York, 2002.
[6] G. Gerla, Fuzzy logic. mathematical tools for approximate reasoning, Kluwer, Dordrecht,
2001.
[7] J. A. Goguen, L-fuzzy sets, J. Math. Anal. Appl., 18(1967), 145–174.
[8] J. A. Goguen, The logic of inexact concepts, Synthese 18(1968-9), 325–373.
[9] S. Gottwald, A Treatise on many-valued logics, Research Studies Press, Baldock, Hertfordshire,
England, 2001.
[10] P. H´ajek, Metamathematics of fuzzy logic, Kluwer, Dordrecht, 1998.
[11] U. H¨ohle, Commutative, residuated l-monoids., In: U, H¨ohle and E. P. Klement (Eds.),
Non-classical logics and their applications to fuzzy subsets. Kluwer, Dordrecht, 1995.
[12] U. H¨ohle, On the fundamentals of fuzzy set theory, J. Math. Anal. Appl., 201(1996), 786–826.
[13] A. S. Mashour and M. H. Ghanim, Fuzzy closure spaces, J. Math. Anal. Appl., 106(1985),
154–170.
[14] R. O. Rodr´ıguez, F. Esteva, P. Garcia and L. Godo, On implicative closure operators in
approximate reasoning, Int. J. Approximate Reasoning, 33(2003), 159–184.