Title :
A natural interpretation of fuzzy set theory
Author_Institution :
Shimonoseki City Univ., Japan
Abstract :
We present a new and natural interpretation of fuzzy set theory in a cumulative Heyting valued model for intuitionistic set theory. By this interpretation we can consistently get various notions and properties of fuzzy sets, fuzzy relations and fuzzy mappings. We can consider notions such as operations of fuzzy subsets of different universes, fuzzy relations and mappings between fuzzy subsets. As far as fuzzy sets and fuzzy relations are considered as extensions of crisp sets and relations, this interpretation seems to be most natural
Keywords :
fuzzy logic; fuzzy set theory; crisp sets; cumulative Heyting valued model; fuzzy logic; fuzzy mappings; fuzzy relations; fuzzy set theory; intuitionistic set theory; natural interpretation; Algebra; Equations; Fuzzy set theory; Fuzzy sets; Logic functions; Set theory;
Conference_Titel :
IFSA World Congress and 20th NAFIPS International Conference, 2001. Joint 9th
Conference_Location :
Vancouver, BC
Print_ISBN :
0-7803-7078-3
DOI :
10.1109/NAFIPS.2001.944302
