ON THE COMPATIBILITY OF A CRISP RELATION WITH A FUZZY EQUIVALENCE RELATION
نویسندگان
1 KERMIT, Department of Mathematical Modelling, Statistics and Bioinformatics, Ghent University, Coupure links 653, B-9000, Gent, Belgium
2 Department of Mathematics, Faculty of Mathematics and Informatics, Med Boudiaf University of Msila, P.O. Box 166 Ichbilia, Msila 28000, Algeria
3 Department of Mathematics, Faculty of Mathematics and Informatics, Med Boudiaf University of Msila, P.O. Box 166 Ichbilia, Msila 28000, Algeria
doi
10.22111/ijfs.2016.2941چکیده
In a recent paper, De Baets et al. have characterized the fuzzytolerance and fuzzy equivalence relations that a given strict order relation iscompatible with. In this paper, we generalize this characterization by consideringan arbitrary (crisp) relation instead of a strict order relation, while payingattention to the particular cases of a reflexive or irreflexive relation. The reasoninglargely draws upon the notion of the clone relation of a (crisp) relation,introduced recently by Bouremel et al., and the partition of this clone relationin terms of three diff erent types of pairs of clones. More specifi cally, reflexive related clones and irreflexive unrelated clones turn out to play a key role in thecharacterization of the fuzzy tolerance and fuzzy equivalence relations that agiven (crisp) relation is compatible with.
