Research On The Uncertainty Of Soft Set And Its Application

With the rapid development of information Science and network technology, human society has entered the digital universe age. We will face unprecedented explosion of information. When people are confronted with massive information, they may aslo have to face the problem of poor data quality containing abundant uncertainty. In the process of dealing with massive information, we need to study and manipulate various types of uncertainties. Actually, most of the concepts we are meeting in real life are vague rather than absolutely precise. Generally, there are various types of uncertainties, such as randomness, fuzziness, vagueness, roughness, inaccuracies, etc. But classical mathematics is no longer suitable for dealing with uncertainty in many cases, with its foundation based on crisp sets and Boolean logic.To solve these difficulties, many mathematical tools for dealing with uncertainty are propsoed, including probability theory, fuzzy set theory and rough set. But all these theories have their inherent difficulties. The reason for these difficulties is, possibly, the inadequency of the parametrization tool of the theories. At the same time, each kind of these theories can only deal with the uncertainty of the specific problem. Consequently, Molodtsov initiated the concept of soft theory as a mathematical tool for dealing with uncertainties which is free from the above difficulties. A soft set is a parametrized family of subsets of the universe and it describes uncertainty by means of domain and parameters’ space. Each parameter corresponds to a crisp set called approximate set which gives an approximate description of the concepts with uncertainty. Soft set theory suggests that complicated concepts with uncertainty should be characterized from many different aspects and all related facets should be organized as a whole. It emphasizes from parameterization angle to study uncertainty, the original idea of soft set is to establish a more general scheme and obtain more powerful tools for dealing with uncertainty. Related studies show there is the essential difference among soft set. fuzzy set and rough set. but they are closely related and privide strong complementarity for each other.In this thesis, we study the algebraic structure of soft sets, some uncertainty measures of soft sets, the text classification based on soft set and related problems. The main achievements are as follows.1. The algebraic structure of soft sets is investigated thoroughly. The different lattice structures of soft sets are constructed with respect to some operations. The concept of soft equality is introduced and some related properties are derived. Some equivalent conditions for soft sets being soft equality are given. It is proved that soft equality is a congruence relation with respect to some operations and the soft quotient algebra is established. The concept of fuzzy soft equality is introduced and some related properties are derived. Some equivalent conditions for fuzzy soft sets being fuzzy soft equality are given. It is proved that fuzzy soft equality is a congruence relation with respect to some operations and the fuzzy soft quotient algebra is established.2. Some uncertainty measures of fuzzy soft sets are studied. We make an analysis of the uncertainty measures of fuzzy soft sets presented in current literature and point out some drawbacks in it. Then the axioms for inclusion measure, similarity measure and entropy of fuzzy soft set are presented. Based on fuzzy implication operators, a new category of inclusion measures, similarity measures and entropies of fuzzy soft sets are given. Our approach is general in the sense that by using different fuzzy implication operators one gets different uncertainty measures. The basic properties of these uncertainty measures are examined.3. Some uncertainty measures of vague soft sets are studied, Firstly, we make an analysis of the uncertainty measures presented in current literature and point out some drawbacks in it. then axiomatic definitions of similarity measure and entropy for vague soft sets are given. Furthermore, we present a new category of similarity measures and entropies for vague soft sets. Our approach is general in the sense that by using different parameters one gets different similarity measures and entropies. The relationships among these measures are analyzed.4. The application of soft set theory in text classification is discussed. One approach of text classification based on soft set theory is presented. We also present a new feature selection algorithms based on NMIFS. Finally we perform some experiments to compare the classification precision and recall to KNN and SVM classification algorithm. Results show that our method is effecitive.