The Aggregation Properties Of Some Kinds Of Fuzzy Relations

Fuzzy relation not only is an important part of fuzzy set theory but also plays an essential role in some applied fields,e.g.,fuzzy control,decision making,artificial intelligence,data mining and machine learning.These applications stimulate many researchers to construct different fuzzy relations to satisfy various demands in practice.Therefore,it proves to be one of meaningful topics to investigate properties of fuzzy relations from the view of theoretics and their applications perspective.It is well-known that aggregation functions play an indispensable role in decision-making.To make better decision in imprecise or uncertain environment,it is necessary to use some aggregation functions or appropriate n-ary functions to aggregate a series of fuzzy relations and study the preservation of the original properties of these fuzzy relations after aggregating.To make a better application of fuzzy relations in uncertainty reasoning and decision making according to the practical requirement,it is significant to investigate the preservation of well-known properties in the aggregation of fuzzy relations.Therefore,this thesis will investigate the aggregation of BKS(Bandler-Kohout subproduct)fuzzy relations,Ⅰ-transitive fuzzy relations and fuzzy preference relations respectively,and discuss the retainment of their common properties after aggregating.This thesis contents mainly include:1.For some well-known fuzzy implications,we seek the aggregation functions that satisfy the aggregation of BKS fuzzy relations(BK-GHS for short)property.First of all,we use the method of automorphism transformation to study the sufficient conditions for the continuous(S,N)-implications and noncontinuous(S,N)-implications to fulfill the(BKGHS)property.Then we investigate the corresponding conditions that residual implications generated by aggregation functions A,the T-power implications generated by the continuous t-norms T and QL-implications generated by t-conorms S and strict fuzzy negations N satisfy the(BK-GHS)property.Finally,the basic properties of fuzzy implications are used to discuss the necessary and sufficient conditions for g-implications,f-implications,probability implications and probability S-implications to satisfy the(BKGHS)property.2.Analyzing the preservation of the original properties of Ⅰ-transitive fuzzy relations and fuzzy preference relations after aggregating by aggregation functions or appropriate nary functions.We firstly characterize the n-ary functions preserving some properties in the aggregation of Ⅰ-transitive fuzzy relations.And then the conditions for the preservation of aggregating some special Ⅰ-transitive fuzzy relations are investigated.Furthermore,two aggregation functions are constructed to preserve some relevant well-known properties in the aggregation of some fuzzy relations preference relations.Especially,focused on the T-S consistency of fuzzy preference relations,we further investigate the retainment in the aggregation of T-S consistent fuzzy preference relations.