Axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model

In "Axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model" [1), Bhattacharjee and Mazumdar have introduced an extension of classical multivalued dependencies for fuzzy relational data models. The authors also proposed a set of sound and complete inference rules to derive more dependencies from a given set of fuzzy multivalued dependencies. We are afraid an important result that was used by the authors to prove the soundness and completeness of the inference rules has been stated incorrectly (Lemma 3.1 [1)). In fact, there are some logically vicious and insufficient reasoning in the proof of the soundness in [1). This paper aims at correction of the above result (Lemma 3.1), gives a proof of its soundness and by the way, proposes some opinions. Tom t~t. Trong bai bao "Axiomatisation of fuzzy multivalued dependencies in a fuzzy relational data model" [1], Bhattacharjee va Mazumdar dil. d'e xufit mot mo' r9ng cila ph u thuoc da trj c5 die'n cho rno hrnh co' so' d ii: li~u mer. Cac tac gia dil. du'a ra mot t%p lu%t suy d[n xac dang v a day dil de' co the' d[n ra them cac phu thuoc t ir met t%p cac phu thuec da trj mer dil. du-o c biet. Chung toi so rhg mot ket qui quan tro ng m a cac tac gia bai bao dung de' chirng minh tinh xac dang v a tinh day dii cda cac lu%t suy d[n dil. duo-c ph at bie'u chira chinh xac (Bo' de 3.1 [1)). Chirng minh tinh xac dang cd a [1) con chu'a day dii va d oi ch6 du'o'ng nhukhong ch~t che ve logic. Trong bai bao nay chung toi chinh xac hoa lai Ht qui n oi tren va de xuat m9t chirng minh cho tinh xac dang, dong thO'i rieu mot so Y kien trao d5i them.