Alternative characterizations for the representation of families of sets by fuzzy sets

作者：Saidi Fathi B; Jaballah Ali^*

来源：Information Sciences, 2008, 178(12): 2639-2647.

DOI：10.1016/j.ins.2008.02.006

• representation
• representation by a fuzzy set
• generalized representation
• fuzzy set
• level set
• uniqueness
• existence
• order
• chain
• total order
• isomorphism

We investigate the representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets. This concept of representation is widely used in the literature for the classification and study of fuzzy structures on the same underlying set. Negoita and Ralescu obtained two theorems, both giving necessary and sufficient conditions, one called the representation theorem and the second called the generalized representation theorem. Our aim in this paper is to take a closer look at both theorems, hence establishing some equivalent forms and several constructive remarks, including some directions for future investigations.

• 出版日期2008-6-15