A natural interpretation of fuzzy mappings

✍ Scribed by Mamoru Shimoda

• Book ID: 104291534
• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 277 KB
• Volume: 138
• Category: Article
• ISSN: 0165-0114
• DOI: 10.1016/s0165-0114(02)00568-7

✦ Synopsis

In this paper we present a new and natural interpretation of fuzzy mappings, which is a direct extension of the natural interpretation of fuzzy sets and fuzzy relations shown in our previous paper; A natural interpretation of fuzzy sets and fuzzy relations (Fuzzy Sets and Systems 128 (2002) 135). We interpret fuzzy mappings as mappings in a Heyting valued model for intuitionistic set theory, and present a characterization of fuzzy mappings with membership functions, which seems to be di erent from all kinds of known deÿnitions. This interpretation is quite natural, for it deduces naturally various properties of fuzzy mappings, and it makes clear the meaning of the famous extension principle by Zadeh, which is said to be very important in fuzzy theory.