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Logic Journal of IGPL 2005 13(5):503-513; doi:10.1093/jigpal/jzi038
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© The Author, 2005. Published by Oxford University Press. All rights reserved.

Original Articles

Fuzzy Closure Operators with Truth Stressers

Radim Belohlávek1, Tatána Funioková2 and Vilém Vychodil3

1 Dept. Computer Science, Palacky University, Tomkova 40, CZ-779 00, Olomouc, Czech Republic. E-mail: radim.belohlavek{at}upol.cz, 2 Dept. of Mathematics, Technical University of Ostrava, 17. listopadu, CZ-708 30, Ostrava, Czech Republic. E-mail: tatana.funiokova{at}vsb.cz, 3 Dept. Computer Science, Palacky University, Tomkova 40, CZ-779 00, Olomouc, Czech Republic. E-mail: vilem.vychodil{at}upol.cz

We study closure operators and closure structures in a fuzzy setting. Our main interest is the monotony condition of closure operators. In a fuzzy setting, the monotony condition may take several particular forms, all of them equivalent in the bivalent case. We study closure operators, called fuzzy closure operators with truth stresser, satisfying the monotony condition which can be linguistically described as "if it is (very) true that A is included in B then the closure of A is included in the closure of B." We present examples of closure operators with truth stresser, investigate their basic properties and related structures.

Key Words: closure operator, closure system, Galois connection, fuzzy set, residuated lattice


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