格值代数系统的解分析

The Solutions of Lattice-valued Fuzzy Algebraic System

引入了格值形式幂级数的概念并建立其运算法则,给出格值形式幂级数特有的性质。重点研究代数系统在格序幺半群下的解的存在性与唯一性问题。扩充定义了V-proper格值代数系统,给出其解的袁达式,研究其与proper格值代数系统的关系,并与定义在自然数半环上的代数系统进行比较,最后得出结论:proper和V-proper格值代数系统都存在唯一强解。体现出格值代数系统具有更好的性质。

In this paper, we have introduced the notions of lattice-valued fuzzy power series, lattice- valued fuzzy algebraic system, and studied the properties of them whose membership values are taken in a commutative lattice-ordered monoid. Some interesting results are obtained, such as r＂ exists for any lattice-valued fuzzy power series if L is a ＊-l-monoid, which does not hold in the semiring S=（ N, ＋, · , 0, 1）. Based on algebraic system, we have introduced some definitions： proper, V-proper lattice valued fuzzy algebraic system and discussed the strong solutions induced by them. We have got that the strong solution exists not only in proper L-AS, but also in V-proper L-AS. Which does not hold in algebraic system based on the semiring S=（N,＋, · ,0,1〉.