(┬,┴,N) Fuzzy logic

Abstract

To investigate more reasonable fuzzy reasoning model in expert systems as well as more effective logical circuit in fuzzy control, a $(\top, \bot, N)$ fuzzy logic is proposed in this paper by using $\top$-norm, $\bot$-norm and pseudo-complement $N$ as the logical connectives. Two aspects are discussed: (1) some concepts of ($\top, \bot, N)$ fuzzy logic are introduced and some properties of ($\top, \bot, N)$ fuzzy logical formulae are discussed. (2) $G$-fuzzy truth (falsity) of $(\top, \bot, N)$ fuzzy logical formulae are investigated and also the relation between the Boolean truth (falsity) of $\bot$-normal forms ($\top$-normal forms) and the $G$-fuzzy truth (falsity) of them are analyzed.\