区间值犹豫模糊信息系统中的信息熵研究

Study of the Information Entropy in Interval-valued Hesitant Fuzzy Information Systems

借鉴已有处理区间值犹豫模糊集中犹豫模糊元素中元素个数不等问题的研究方法,对区间值犹豫模糊集进行了处理,使区间值犹豫模糊集中犹豫模糊元素中元素个数达到相等,方便了区间值犹豫模糊集中运算和关系的定义.基于区间值犹豫模糊二元关系,给出了区间值犹豫模糊粒度结构概念和区间值犹豫模糊粒的基数概念,讨论了区间值犹豫模糊粒度结构上的三种偏序关系.基于区间值犹豫模糊粒的基数概念,结合Shannon熵给出了区间值犹豫模糊信息熵、联合熵、条件熵概念,讨论了区间值犹豫模糊信息熵的偏序性,并通过实例验证了有关概念的和定理的正确性.

Drawing on existing research methods about handling unequal problem of the number of elements of the hesitant fuzzy ele- ments in interval-valued hesitant fuzzy sets, this paper deals with interval-valued hesitant fuzzy sets, providing the convenience for the definition of the operations and relationships in interval-valued hesitant fuzzy sets. In the paper,the concepts of interval-valued hesitant fuzzy granular structures and the cardinalities of interval-valued hesitant fuzzy granularity are given base on the interval-valued hesitant fuzzy binary relation, three new partial order relations in interval-valued hesitant fuzzy granular structures are discussed, the concepts of hesitant fuzzy information entropy,joint entropy,condition entropy in relation to the concepts of Shannon＇s entropy are given base on the concepts of cardinalities of the interval-valued hesitant fuzzy granularity and the partial order of hesitant fuzzy information entropy is explored. In addition,an example is provided to show the validity of the related concepts and theorems.