Uncertainty Measures Of Interval-Valued Fuzzy Soft Sets

Soft set theory was firstly proposed by Molodtsov in 1999, it is a new mathematical tool for dealing with uncertainties. Soft set theory indicates that complicated objects can be described from different parameters. Each of these descriptions leads to an approximate description of the complicated objects. We can get a relatively accurate description of complicated objects by combing these approximate descriptions. Related researches show that soft set theory, fuzzy set theory and rough set theory have inside connections and each of them focus on individual aspect. As a mathematical tool for dealing with uncertain problems, the researches on the related uncertain measures have important significance. Based on the related research works, this thesis discusses the uncertain measures such as similarity measures, distance, entropy for the soft sets and interval-valued fuzzy soft sets, the major achievement are as follows:1 We make an analysis on the existing literatures about similarity measures and distance measures of the soft sets, and point out the inadequacy existed in the literatures. Based on the above discussion, some new formulas to calculate the similarity and distance between soft sets are presented, at the same time, the basic properties of the relevant measures are discussed.2 Based on the uncertainty measures of the fuzzy set and interval-valued fuzzy set, with the help of geometric features of interval-valued fuzzy soft set, some approaches for constructing the similarity measures, distance measures and entropies are given. We discuss the properties of the similarity measures, distance measures and entropy for the interval-valued fuzzy soft sets.