SISO Intuitionistic Fuzzy Systems: IF- ${t}$ -Norm, IF- ${R}$ -Implication, and Universal Approximators

Abstract

Fuzzy system, as the main method of approximate reasoning, has been widely used to solve practical problems. The existing results on fuzzy systems were based on fuzzy sets, fuzzy <italic>if-then</italic> rule, and fuzzy inference. In this work, we investigate the component of the intuitionistic fuzzy systems, such as the intuitionistic fuzzy triangular norms (IF-<inline-formula> <tex-math notation= LaTeX >${t}$ </tex-math></inline-formula>-norm), the intuitionistic fuzzy residual implications (IF-<inline-formula> <tex-math notation= LaTeX >${R}$ </tex-math></inline-formula>-implication), the intuitionistic fuzzy <italic>if-then</italic> rule, the intuitionistic fuzzy inference, and the intuitionistic defuzzification. Accordingly, the single input single output (SISO) intuitionistic fuzzy systems are built. Some examples are paid to illustrate the methods and their application. Moreover, the approximation properties of the intuitionistic Mamdani, the intuitionistic Larsen, the IF-<inline-formula> <tex-math notation= LaTeX >${t}$ </tex-math></inline-formula>-norm, and the intuitionistic triple-I fuzzy systems are obtained, which show that the SISO intuitionistic fuzzy systems are the universal approximators.