Triple I algorithms based on Schweizer–Sklar operators in fuzzy reasoning

In this paper, we focus on the flexible inference method with parameters, that is the parametric triple I method by the combination of Schweizer–Sklar operators and triple I principles for fuzzy reasoning. Because the Schweizer–Sklar parameter m reflects the interaction between propositions in reasoning processes, the new parameterized triple I algorithms are closer to human reasoning in daily life. Also some properties of the new algorithms such as the reductivity, continuity and approximation are discussed. It is shown that some existing results are special cases of the new algorithms given here and in view of the variability of the parameter m the new algorithms have excellent flexibility in reasoning processes.

► A new kind of parameterized triple I algorithms is proposed for fuzzy reasoning.
► Some well-known triple I methods are special cases of new ones which are reductive.
► The new parameterized triple I algorithms are of continuity and approximation.
► New algorithms whose parameter is less than infinity for FMP are robustly stable.
► When the parameter equals 1 for FMT, this new algorithm is of robust stability.