Fuzzy-Valued Maps

✍ Scribed by J. Ewert

• Publisher: John Wiley and Sons
• Year: 1988
• Tongue: English
• Weight: 456 KB
• Volume: 137
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.19881370108

✦ Synopsis

Let S iind Y be non-empty sets. The notion of a function from S into Y has been generalized in the natural way to a multivaluecl mup as a function from X into the fiimily of all non-empty subsets of Y . I n the same degree is naturnl the second step of generalization which leiids to a fuzzy set-valued map, i.e. to ii function from X into the class of all non-zero fuzzy sets in Y .

*4ny fuzzy set in Y we identify with its membership function, so the family of all fuzzy sets in Y is considered as the family of all functions from X into the unit closed interval [0, 13. For fuzzy sets u, b the symbols u/\b and u V b are used to denote of the infimum and the supremum respectively. We write a zb iff u ( z ) s b(z)

for each xe Y . The characteristic function of a set A is denoted by p.4. Instead of pe and py we will write 0 and 1 too.