Fuzzy implications-based transformation approaches from semi-three-way decision spaces to three-way decision spaces and their applications

Three-way decision spaces, as an important component of three-way decisions, greatly enrich their theoretical development and application prospects. Meanwhile, fuzzy implications, as a vital class of fuzzy logic connectives, have made great contributions to the solution of practical problems, especially complex decision-making problems. This paper considers the collaborative effect of the two, which inject new vitality into the theoretical development and application prospects of fuzzy implications and three-way decision spaces. As a vital component of three-way decision spaces, (semi-)decision evaluation functions have been widely studied based on fuzzy logic connectives and become a research hotspot. Specifically, this paper focuses on fuzzy implications-based transformation approaches from semi-three-way decision spaces to three-way decision spaces and their applications. Firstly, we present some novel fuzzy implications-based transformation approaches from semi-decision evaluation functions to decision evaluation functions, and construction approaches of semi-decision evaluation functions involving the existing semi-decision evaluation functions, fuzzy sets, interval-valued fuzzy sets and fuzzy relations. Secondly, we discuss the relationship between our approaches and the known construction approaches of three-way decision spaces. Notably, our approaches cover all existing approaches except the uninorms-based approaches. Finally, by the experiment results, we obtain our approaches are feasible, effective, superior to the known three-way decision spaces approaches and have good anti-noise ability. And, the parameter ρ of our approaches is also effective and stable. •Some novel fuzzy implications-based transformation approaches from S-DEFs to DEFs are given.•Some novel fuzzy implications-based construction approaches of S-DEFs are given.•The proposed approaches are superior to the known related approaches and have good anti-noise ability.