Fuzzy Reasoning for Mixture of Fuzzy/Intuitionistic Fuzzy Information Based on Triple I Method

Generalized modus ponens (GMP) is a basic model of approximate reasoning. GMP in fuzzy propositions is called fuzzy modus ponen (FMP) and it is called intuitionistic fuzzy modus ponens (IFMP) when fuzzy propositions are generalized to intuitionistic fuzzy propositions. In this paper, we aim to investigate fuzzy reasoning methods for GMP with mixture of fuzzy/intuitionistic fuzzy information. For mixed types of GMP, we present two basic methods to solve GMP problems based on the triple I method (TIM). One is to transform the GMP problem into two FMP problems by decomposition and aggregate the solutions of TIM for FMP problems to obtain the solution for GMP problem. The other is to transform the GMP problem into the IFMP problem by expansion and aggregate the solutions of TIM for the IFMP problem to obtain the solution for the GMP problem. These two methods are called the decomposition triple I method (DTIM) and expansion triple I method (ETIM), respectively. We analyze the relationship between DTIM and ETIM. Furthermore, we discuss the reversibility of DTIM and ETIM.