模糊数的正向和反向表述及模糊数运算的拓展  

The Positive(Reverse) Direction Expression of Fuzzy Number and the Expansion of Fuzzy Number Operation

作　　者：岳立柱[1] 闫艳[1] 仲维清[1] 

机构地区：[1]辽宁工程技术大学工商管理学院

出　　处：《数学的实践与认识》2010年第14期159-165,共7页Mathematics in Practice and Theory

基　　金：辽宁省教育厅高效创新团队项目计划(2006T076,2006T077)

摘　　要：模糊数运算的存在不可逆等问题，主要在于传统（正向）区间数严格限定所致．因此，提出了“反向区间数”的概念，利用该概念，能够给经典模糊分解定理、扩张原理新的表达形式．之后，分别以正（反）向区间为基础，分析模糊数的结构元表达形式，得到正（反）向区间对应结构元理论中单调增（减）函数．定义了反向区间数和反向区间数加、乘运算法则，利用结构元理论，证明了正、反向模糊数的加、乘运算解析表达式，得到了模糊方程解的判断定理．在保持传统运算法则不变的同时，对模糊数概念进行正（反）向的表述，并定义了二者的运算法则，这拓展了传统模糊数解的空间，进而解决模糊方程求解、不可逆等问题．通过算例看出，这两种表述在实际的计算过程中具有明显的意义．The main reason of the irreversible problems in Fuzzy number operations is the strict limit of traditional （positive-direction） interval number. Therefore, the ＂reverse interval number＂ is put forward, using the concept give the classic decomposition theorem and the principle of expansion a new expression, and then on the basis of positive （reverse） direction interval analyze the expression of fuzzy numbers with structured element respectively, positive （reverse） direction interval are structure corresponding to monotony increasing（decreasing） function in structured element, the reverse direction interval is defined and the algorithms of addition and multiplication, by using the theory of structured element prove how to express the addition and multiplication of positive （reverse） direction fuzzy numbers, then there is judged-theorem the Solutions of fuzzy equation. Traditional algorithms is not changed, and At the same time, the concept of fuzzy number is expressed in positive （reverse） direction and the algorithms is defined for which, and this expand the scope for the traditional solutions of fuzzy number, thus the problem of how to solve the fuzzy equation and the irreversible problems is solved, with An example it can be seen that it is obviously significant by using two expression in the actual calculation.

关 键 词：模糊数 结构元 区间数 模糊方程 

分 类 号：O159[理学—数学]