@article{Dai2022, 
author = {Songsong Dai},
title = {Quasi-MV algebras for complex fuzzy logic},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {1},
pages = {1416-1428},
keywords = {complex fuzzy logic, quasi-MV algebra, quasi-Wajsberg algebra},
url = {https://www.sciopen.com/article/10.3934/math.2022083},
doi = {10.3934/math.2022083},
abstract = {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.}
}