Fuzzy Closure Operators with Truth Stressers

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.