Some Studies On The @-Fuzzy Relational Equations

This paper deals with the resolutions of @ -Fuzzy relationalequations and @ -realizable problems of fuzzy matrices. Firstly, we introduce aconcept of continuous meet-irreducible element, investigate some properties ofthe continuous meet-irreducible elements and use it to characterize solutions of@ -Fuzzy relational equations: a necessary and su?cient condition describingthe attainable solution (resp. the unattainable solution) of the @ -Fuzzy rela-tional equation A @ X = b in infinite domains and on completely distributivelattices (where @ denotes inf - @ composition, A = (aj)j∈J,J is an infiniteset) is shown when b is a continuous meet-irreducible element, further, thesolution set is investigated. Secondly, a concept of @ -realizable fuzzy matrixis introduced, a necessary and suffcient condition that a fuzzy matrix is @-realizable is formulated and some properties of the @ -realizable fuzzy matricesare obtained. Finally, an algorithm to calculate the @ -content of @ -realizablefuzzy matrices is given.