Fuzzy Ideal Convergence Of Fuzzy Number And Its Quotient Space Sequence

The study of convergence theory of fuzzy numbers sequence is an impor-tant part of fuzzy analysis.Many scholars have studied the convergence of fuzzy number sequence,and got many very profound conclusions.In this the-sis,based on the formal semantic method,the convergence theory of sequence fuzzifying ideal in fuzzy number and its quotient space is studied deeply,and some important properties of fuzzifying ideal convergence of fuzzy number sequence are obtained.The main contests of this thesis are the following three aspects:Firstly,by giving the definition of fuzzifying ideal convergence?fuzzifying I*-convergence of the fuzzy number sequence and fuzzifying I-Cauchy,we study that fuzzifying ideal convergence of the fuzzy number sequence which have only one limit,satisfy the linear relation.The relations among the fuzzi-fying ideal convergence of the fuzzy number sequence,fuzzifying I*-con-vergence of the fuzzy number sequence are discussed.We shall prove that the fuzzifying ideal convergence of the fuzzy number sequence is equivalent to the fuzzy number sequence is fuzzifying I-Cauchy.On the second part of this thesis,by giving the definition of fuzzifying ideal monotonicity and fuzzifying ideal boundness of the fuzzy number se-quence,we give the decomposition theorem of fuzzifying ideal monotonicity sequence and fuzzifying ideal boundness sequence.Meanwhile,the relation-ship between monotone increasing boundedness of fuzzy number sequence and fuzzifying monotone increasing sequence and fuzzifying boundedness is study.Further confirm that fuzzifying ideal monotonicity sequence is fuzzify-ing ideal boundness of the fuzzy number sequence.At last,by giving the definition of ideal convergence and fuzzifying ideal convergence of sequence in fuzzy number quotient space,and midpoint func-tion ideal uniform bound.A sufficient condition for sequence ideal conver-gence in fuzzy quotient space is obtained.Based on the concept of bounded variation function,the necessary and sufficient conditions for the convergence of level ideal of sequence fuzzifing in quotient space is proved.