模糊软集的不确定度量.pdfVIP

Title: Uncertainty measures of fuzzy soft sets Major: Applied Mathematics Name: Weinan Zheng Signature:_______ Supervisor: Associate Professor Qinrong Feng Signature:_______ A b stra ct 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 discu es 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- 2 generalized normalized distance, the Type-2 normalized 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 discu ed. 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 un