Hybrid Soft Set Models: Application To Decision Making

In order to deal with the uncertainties contained in real-world problems,in the past few decades,researchers have constructed a series of mathematical models,such as fuzzy set model,rough set model and soft set model.Among them,the soft set model is character-ized by its parameterized tools,and it is also its main advantage.By using the soft set model,it is easy to describe and analyze the same thing(or problem)from different attributes(pa-rameters)aspects,and it is also easy to study the uncertainties contained in the same thing(or problem)from different attributes(parameters)aspects.The extended models of soft sets,which are called hybrid soft sets,also contain parameterized tools.Therefore,it is promising to do theoretical researches on hybrid soft sets,as well as their applicationsFrom a theoretical point of view,the theoretical researches on the soft sets and hybrid soft sets are far from enough.For instance,the methods for constructing uncertainty measures for hybrid soft sets are few,few researches carried out comparative analysis on different hybrid soft sets in a systematic way.Based on the above considerations,the following works have been carried out in the current paper1.For interval-valued intuitionistic fuzzy soft sets,the methods for constructing their un-certainty measures are studied.Interval-valued intuitionistic fuzzy soft sets are interval-valued intuitionistic fuzzy extensions of soft sets.In this paper,we provide axiomatic definitions of similarity measure,distance measure,inclusion measure and entropy of Interval-valued intuitionistic fuzzy soft sets.On the basis of the axiomatic definitions,we provide calculation formulas of these measures.The fuzzy equivalence operators are adopted to construct distance measures of interval-valued intuitionistic fuzzy soft sets.Besides,fuzzy equivalence operators are also applied when we study the mutual transformation approaches of these uncertainty measures2.The relationships among different soft rough set models are studied.Based on the com-bination of soft set theory and rough set theory,researchers have constructed several different soft rough set models.These models are not independent of each other,they are closely related.In this paper,we will carry out a systematic study on the relationships among different soft rough set models.Afterwards,by using a soft set as the knowledge,and computing the approximations of another soft set,we construct a novel soft rough set model,called soft rough soft set model.From the perspective of application,soft set and hybrid soft sets have been applied in var-ious fields,such as medical diagnosis,pattern recognition,data mining and so on.Especially,hybrid soft sets show great ability in dealing with decision making problems.However,some existing decision making approaches based on hybrid soft sets still suffer from limitations.Therefore,the following works have been carried out in the current paper:1.Some decision making methods based on fuzzy soft set and rough soft set are improved.The effectiveness and limitations of existing decision-making methods based on fuzzy soft sets and rough soft sets are analyzed.A new adjustable decision making approach is provided,different comparison thresholds could be chosen according to the practical decision demands.A new group decision method based on rough soft set has been pro-vided,decision makers do not need to determine their best alternatives before the group decision making process.2.In order to deal with linguistic information under the framework of soft set theory,we combine soft set theory with the fuzzy linguistic approach to construct a novel hybrid soft set model,which is called CLE soft set model.CLE refers to the comparative lin-guistic expressions.When we apply CLE soft sets to solve decision making problems which contain linguistic information,the decision makers(or the experts)are allowed to provide their assessments on alternatives by using both single linguistic terms and comparative linguistic expressions.3.The data prediction methods based on incomplete fuzzy soft sets are studied.In an in-complete fuzzy soft set,the links among data could be used to predict missing data.We point out some limitations of an existing data prediction method based on incomplete fuzzy soft sets,and then modify this method to make the prediction results more rea-sonable.In addition,by using the similarity measures between fuzzy sets,we propose a new data prediction method based on incomplete fuzzy soft sets.The effectiveness of the new proposed method are examined through experiments.