Tense operators in fuzzy logic ?
The aim of the paper is to introduce and describe tense operators in every fuzzy logic which is axiomatized by means of a residuated poset. For this we use the axiomatization of universal quantifiers as a starting point and we modify these axioms for our sake. At first, we show that the operators can be recognized as modal operators and we study the pairs as the so-called dynamic pairs. Further, we get constructions of these operators in the corresponding residuated poset provided a time frame is given. Moreover, we solve the problem of finding a time frame in the case when the tense operators are given. In particular, any tense algebra is representable in its DedekindMacNeille completion.
tense operators fuzzy logic residuated poset modal logic tense logic fuzzy dynamic algebra