.png){kind=icon}
.png){kind=icon}
Return
Fuzzy class theory
.png){kind=icon}
PRE
AI
DOI：10.1016/j.fss.2004.12.010.png)
.png){kind=icon}
Original request for help.png){kind=icon}
Share.png){kind=icon}
Save
Abstract
En 中文
The paper introduces a simple, yet powerful axiomatization of Zadeh's notion of fuzzy set, based on formal fuzzy logic. The presented formalism is strong enough to serve as foundations of a large part of fuzzy mathematics. Its essence is elementary fuzzy set theory, cast as two-sorted first-order theory over fuzzy logic, which is generalized to simple type theory. We show a reduction of the elementary fuzzy set theory to fuzzy propositional calculus and a general method of fuzzification of classical mathematical theories within this formalism. In this paper we restrict ourselves to set relations and operations that are definable without any structure on the universe of objects presupposed; however, we also demonstrate how to add structure to the universe of discourse within our framework. (c) 2005 Elsevier B.V. All rights reserved.
Keywords:
formal fuzzy logic
fuzzy set
foundations of fuzzy mathematics
LTI logic
higher-order fuzzy logic
fuzzy type theory
multi-sorted fuzzy logic
Journal
IF:
2.7
Papers:
7.6K
Citations:
1.5W
Organization
No organization information available