Constructions Of Maximal T-S-semitransitive Interior And Minimal T-S-semitransitive Closure

In this thesis,we investigate the constructions of maximal T-S-semitransitive in-terior and minimal T-S-semitransitive closure of two special fuzzy relations.The main work and results are summarized as follows:Firstly,we introduce some basic concepts,properties and symbols involved in this thesis,including fuzzy logical connectives,maximal inner and minimal closure of fuzzy relation.Secondly,we deal with the properties and constructions of maximal T-S-semitransi-tive interior.By the example,we draw a conclusion that there is not necessarily a maximal T-S-semitransitive interior for a fuzzy relation keeping the certain line same.Furthermore,we obtain two important properties of maximal T-S-semitransitive inte-rior.Under the conditions that(T,S,n)is a De Morgan triple7,T is a left-continuous t-norm and its corresponding implication satisfies(CP(n)),we give two construction methods of maximal T-S-semitransitive interior of a fuzzy relation on the universe{a1,a2} proceeding from the first row and the first column respectively.Moreover,we give the construction method of maximal T-*S-semitransitive interior of a special fuzzy relation on the universe {a1,a2,as3} under the same conditions.Finally,we carry out the research on the properties and constructions of minimal T-S-semitransitive closure.By the research on the property of minimal T-S-semitransitive closure,we obtain the indirect method of solving minimal T-S-semitransi-tive closure.For its direct construction method,we show firstly that the method of keeping a row unchanged is no longer suitable by the counter example.Then,the two important properties on the T-S-semitransitive closure of a fuzzy relation are put forward.Under the conditions that(T,S,n)is a De Morgan triple,S is a right-continuous t-conorm and its corresponding implication satisfies(CP(n)),we give the construction methods of minimal T-S'-semitransitive closure of a fuzzy relation on the universe {a1,a2} and a special fuzzy relation on the universe {a1,a2,a3}.