Research On Approximate Reasoning And Decision Making Methods Based On Fuzzy Soft Sets

Due to the complexity of practical problems in real life,people's observation and recognition on objective reality exist uncertainty.The models of uncertain problem have always been a hot spot in the field of artificial intelligence.People put forward a series of mathematical methods for handling uncertain problems,such as,fuzzy set,rough set,soft set and formal concept analysis etc.The theory of soft set emphasizes the description of complex objects from different aspects,and combine relevant description by using appropriate way in order to obtain accurate description of complex objects.Fuzzy soft set,as one of hybrid soft set models,can remedy the single uncertainty of fuzzy set model,and has the characteristics of parameter.Thus,fuzzy soft set model has great research value in the field of uncertainty problem.Currently,approximate reasoning methods of fuzzy soft set are not perfect and lack systematic research.The related uncertain decision making methods are not mature enough.Based on the above considerations,the main contributions of this dissertation are summarized as follows:1.Approximate reasoning methods based on fuzzy soft setsBy using fuzzy logic operators,a fuzzy soft reasoning method based on fuzzy soft similarity for FSMP model is given.According to analyze expansion form and reduction form for Turksen's approximate analogical reasoning approach,we present a method to modify fuzzy soft rules for FSMP model,which is expressed as fuzzy soft relation.By fuzzy implication operators and projection operators,four kinds of fuzzy soft reasoning methods based on fuzzy soft similarity are given,and the reducibility and monotonicity of these reasoning methods are discussed.The basic properties of regular implication operator are studied.Reverse triple I fuzzy soft reasoning method and ?-reverse triple I fuzzy soft reasoning method for FSMP model and FSMT model are given,and the reducibility and monotonicity of reasoning methods are discussed.On basis of the FSMP model and FSMT model,triple I constraint fuzzy soft reasoning methods are studied,triple I constraint principles are proposed,and triple I restriction solutions based on fuzzy logic operators are given.The optimal restriction solutions for Lukasiewicz,Godel and Production implication operators are examined.General triple I fuzzy soft reasoning method for FSMP model,FSMT model and MFSMP model are obtained.We integrate fuzzy soft set into multiple fuzzy rules and construct multiple fuzzy soft rules.We discuss the robustness of general triple I fuzzy soft reasoning method by using fuzzy soft(T,?)-equation.2.Decision making methods based on fuzzy soft setsBy the formal concept analysis,we present the definition of modal-style operator based on fuzzy soft set and discuss some basic properties.Score function for object is constructed by modal operator.The decision making method based on fuzzy soft set is given.Meanwhile,this decision making algorithm based on the fuzzy soft set is compared with three classic decision making algorithms.Based on the conflict analysis problem,the fuzzy conflict information system and pseudo-fuzzy conflict information system are defined by analyzing fuzzy soft set.In the fuzzy conflict information system and pseudo fuzzy conflict information system,similarity and conflict degree based on the objects and attributes are constructed,and then the alliance relationship,neutrality relationship and conflict relationship are described.The alliance relationships are integrated into alliance regions by undirected graph,and then rules are defined to obtain comprehensive strategies for the alliance regions.With the help of coverage,comprehensive strength and comprehensive loss of the alliance areas,a decision making method for resolving conflict problem is given.The decision making method is analyzed and explained with an example.3.Decision making methods based on incomplete fuzzy soft setsAn adjustable fuzzy soft decision making method is given based on the threshold fuzzy set with respect to the attribute set,and the decision making method based on fuzzy soft modal operator and the idealized standard decision object is studied.This method does not need to predict the data of incomplete fuzzy soft set.Considering that different decision attributes have different importance,we define the weighted incomplete fuzzy soft set,put forward a decision making method based on the weighted incomplete fuzzy soft sets by computing score function with respect to attribute weights,and design the corresponding decision algorithm.The incomplete weighted fuzzy soft set model is constructed for analyzing incomplete fuzzy soft sets and incomplete attribute weights.Decision making method based on the incomplete weighted fuzzy soft set is studied.