Approximate Reasoning Research Based On Language Quantifiers Of The Fuzzy Integral Semantic

Fuzzy quantifiers (also called language quantifiers) refer to imprecise meaning quantifiers, such as"most","few","about ten","not a few"etc. It is an interdiscipline direction, involving fuzzy mathematics, logistics, linguistics, computer science and intelligent sciences. Therefore, fuzzy quantifiers have attracted attention from many scholars.Zadeh researched fuzzy quantifiers by fuzzy cardinalities. Quantifiers were classified into absolute quantifiers and relative quantifiers. Moreover, the truth value of a lingulstically quantified statement is obtained by caleulating the cardinality of the fuzzy set. Yager used OWA operators to calculate the truth of quantified propositions. In recent years, as uncertain mathematical theory of development, fuzzy quantifiers achieved some new progress. Such as, Chinese scholar M.S.Ying proposed a new approach to model linguistic qualltifiers, German scholar Ingo Glockner proposed computation theory of linguistic qualltifiers.In this article, based on the existing linguistic quantifiers which are modeled by integral theory, we discussed the approximate reasoning with linguistic quantifiers. The main research content of this thesis is following three aspects:(1) Based on Ying's framework for linguistic quantifiers which are modeled by Sugeno integrals, a new logic formal system MTLQ is established by adding general language quantifiers to extend the fuzzy logic system MTL. The logic system MTLQ was added countable truth-constants and book-keeping axioms, and analysised the valuation of MTLQ is closed, the weak completion theorem in MTLQ is proved.(2) Based on linguistic quantifiers which are modeled by Sugeno integrals, we discussed general first-order fuzzy logic axiomatic system with involution andlinguistic quantifiers. We constructed a new logic system IMTLQ* by adding language quantifiers to extend the involutory logic system IMTL, where the variables and constants have different types. Moreover, we discussed some logical properties of the logic system IMTLQ*, and based on IMTLQ*, we gave some formalized mode of fuzzy reasoning, the triple I method extend to fuzzy reasoning with linguistic quantifiers.(3) We discusseed the generalized opposition square with the general language quantifiers. Based on lattice value fuzzy measure, we redefined the various opposition relations of the traditional square of opposition, such as, contradictory, subalternate, contrary, subcontrary. Moreover, based on this, the generalized opposition square was established.