Fuzzy Relation And Hierarchical Inference Based On Interval-valued Implications

Fuzzy set theory has been widely utilized in many applied fields such as automatic control,artificial intelligence,information processing,data mining,expert system,decisionmaking,classification and prediction and so on.However,there exists some shortcomings to deal with some missing data by the classical fuzzy sets which the membership degrees correspond to the exact values on the unit interval [0,1].Unlike point values,the membership degree of an interval-valued fuzzy set is a subinterval of the unit interval [0,1].Therefore,the interval-valued fuzzy sets with more degrees of freedom have an incomparable advantage over the classical fuzzy sets dealing with the uncertain and fuzzy information.It is well known that interval-valued implication not only can be used to realize fuzzy reasoning,but also plays an important role in fuzzy relation.In order to better describe the interval-valued fuzzy relation and apply the interval-valued fuzzy hierarchical inference system in practice,this dissertation mainly analyzes the properties of fuzzy relations based on interval-valued implications and constructs the interval-valued fuzzy hierarchical inference algorithm with Bandler-Kohout subproduct(BKS)composition.And then,this interval-valued fuzzy hierarchical inference is used to assess the risk of Marine pollution in the yellow river mouth.Specifically,the main research contents of this paper include:1.To study the properties of fuzzy equivalence relation based on interval-valued implications.Firstly,the properties of fuzzy equivalence relation and fuzzy partition based on interval-valued implication are analyzed.Further,the relationship between a fuzzy equivalence relation and a fuzzy partition based on interval-valued implication is discussed.And the necessary and sufficient conditions for an one-to-one correspondence between them are sought.2.To construct an interval-valued hierarchical inference algorithm based on BKS composition.In particular,we firstly seek some interval-valued t-norms for well-known interval-valued implications such that they satisfy the law of importation.A multi-inputsingle-output hierarchical inference system based on BKS composition is further constructed with the interval-valued implications satisfying the law of importation.Finally,taking the real data of dissolved oxygen concentration and suspended solids concentration in coastal waters of the yellow river mouth in 2022 as the research object,this interval-valued fuzzy hierarchical inference is used to establish a marine pollution assessment model.