Uncertainty Measures Of Fuzzy Soft Sets

Fuzzy soft set is an important theory and tool for dealing with uncertainties, and it is a new concept which has advantages in soft set and fuzzy set, there has been some research results. The paper mainly discusses uncertainty measures of fuzzy soft sets. The specific work is as follows:Distance measure and similarity measure are two important uncertainty measures. Distance measure is a quantitative description of the degree of difference between two objects. Similarity measure is a quantitative description of the degree of similar between two objects. In this paper, fuzzy soft set as the research background, firstly, it is introduced the axiomatic definitions of distance measure and similarity measure, and it is constructed the normalized Hamming distance, the normalized Euclidean distance, the generalized normalized distance, the Type-2generalized normalized distance, the Type-2normalized Euclidean distance, the normalized Hamming—Hausdorff distance and the Chebyshev distance between two fuzzy soft sets. Based on these distance measures, seven similarity measures between two fuzzy soft sets are studied. Secondly, some properties of these distance measures and similarity measures are discussed. Thirdly, comparision analysis on these similarity measures is provided. Moreover, an example is given to illustrate the application of these different similarity measures of fuzzy soft sets in decision making.Entropy is another uncertainty measure of fuzzy soft set, it is a quantitative description of fuzzy degree of a fuzzy soft set. Firstly, according to the axiomatic definition of entropy of fuzzy set, the paper is given the axiomatic definition of entropy of fuzzy soft set and a formula to calculate an entropy of fuzzy soft set. Moreover, according to the results of previous literature, used union operator, intersection operator and complement operator between two fuzzy soft sets, some desirable relations among distance measure, similarity measure and entropy of fuzzy soft sets are studied, which shows that distance measure, similarity measure and entropy of fuzzy soft sets can be deduced from each other.