IL-type Triple-I Algorithm And Its Reductor, And Filter Lattices On R₀ Algebra

Today, fuzzy reasoning and fuzzy logic are very attractive research branches of fuzzy system, while logical algebra is an important research topic of fuzzy logic. The purpose of the present paper is to go deep into the trilpe-I algorithms where the implication operator is the implication in a implication lattice, IL-type triple-I algorithms, for short, and MP-filters and quotient-algebras of R₀ algebras.Since, in 1965, professor L.A.Zadeh firstly introduced the concept of fuzzy sets, and in 1973 the theory of approximate reasoning based on fuzzy sets, i.e., the famous compositional rule of inference in fuzzy reasoning, CRI for short. Such a theory has witnessed a great development, and a series of research achievements have appeared. In particular, it has been successfully applied to fuzzy control. However, the theory of fuzzy logic is still not perfect; the method of fuzzy reasoning are still not very reasonvable; and fuzzy logic and fuzzy reasoning are not suitably combined yet. The triple I inference method of fuzzy reasoning was put forward by professor Wang Guojun in 1999. This method reasonably improved the CRI algorithm in fuzzy control. Since the triple I inference method of fuzzy reasoning was presented, it has been well improved and developed. Professor Wang Guojun introduced the concept of implication lattice in order to meet the needs of fuzzy reasoning. In the second chapter of the paper, we turn to the IL-type triple-I algorithm of fuzzy reasoning. The triple-I algorithm, α-triple-I algorithmand and triple-IMT algorithm based on the IL-type implication and their reductor are aslo discussed systematically.Based on the inherent difference between fuzzy logic and classical logic, professor Wang Guojun presented a new formal propositional calculus system L*. Taking the L*-Lindenbaum system algebra as the background, he proposed the R₀ algebras as the semantics of L*. So far, there are many results on the research of the system L* and R₀ algebras. The completeness is the sign of harmonious unity of semantics and syntactics, so a complete logic is a perfect logic system. Professor Wang Guojun introduced the concept of MP filter in R₀ algebras in order to prove the completeness of R₀ algebras. There are some results on the research of MP filter in R₀ algebras. In the third chapter of the paper, we discuss all MP filters as a whole in R₀ algebra.