TY  - JOUR
AU  - Dai, Songsong
PY  - 2022
TI  - Quasi-MV algebras for complex fuzzy logic
JO  - AIMS Mathematics
SP  - 1416
EP  - 1428
VL  - 7
IS  - 1
AB  - Complex fuzzy logic (CFL) is an emerging topic of research in fuzzy logic. Due to the circle structured codomain of the complex membership function, algebraic structure (including MV-algebra) in traditional fuzzy logic cannot be easily transplanted to CFL. Quasi-MV algebras are almost identical to MV algebras, except    α  ⊕      0    =  α does not always hold. In this paper, our goal is to derive some algebraic structures for CFL. We first construct a quasi-MV algebra in complex fuzzy logic by introducing negation and truncated sum in the unit disc of the complex plane        S  . Next we construct a        ¬   quasi-MV algebra over        S   by adding an operation of square root of the negation. Moreover, implication connective and some derived connectives on        S   are introduced. Furthermore, we construct a quasi-Wajsberg algebra over        S   in which implication is a primitive connective. These algebraic structures are suitable for CFL.
UR  - https://doi.org/10.3934/math.2022083
DO  - 10.3934/math.2022083