Uncertainty And Knowledge Acquisition Of Generalized Fuzzy Information Systems

Pythagorean fuzzy set is a further extension of intuitionistic fuzzy set.It allows the sum of non-membership and membership degree to be greater than 1,but the sum of the squares of non-membership and membership degree is less than or equal to 1.So,compared with intuitionistic fuzzy set,it has a stronger ability to describe fuzziness and may have wider applications.In this paper,Pythagorean fuzzy information systems is combined with graph theory,evidence theory and three-way decision theory respectively,which provides some new methods for attribute reduction and decision-making of Pythagorean information systems and further enriches the research results of Pythagorean fuzzy information systems.The basic contents of this paper include:(1)Attribute reduction of Pythagorean fuzzy information system is discussed.Firstly,the similarity degree of Pythagorean fuzzy sets based on weighted Euclidean distance is defined.Based on the similarity degree,the discernibility matrix and binary relation which satisfies reflexivity and symmetry are defined.The induced graph of discernibility matrix is constructed by the relationship between vertexes and edges of graph and discernibility attribute sets.The problem of solving reduction of discernibility matrix is transformed into the calculation of minimum vertex cover of the induced graph.Then an algorithm of attribute reduction is proposed.Based on this algorithm,the attribute reduction algorithm of the Pythagorean fuzzy information system with decision attribute is constructed.Then,the effectiveness of the proposed algorithms is demonstrated by examples.Finally,the comparative analysis is given.(2)Belief function of Pythagorean fuzzy rough approximation space and its applications.Firstly,the Pythagorean fuzzy rough upper and lower approximation operators based on binary relation and the concept of the level set of Pythagorean fuzzy set were proposed.Then using these properties,probability measure of Pythagorean fuzzy sets is constructed.And the belief and plausibility functions are studied by using the Pythagorean fuzzy rough upper and lower approximation operators.Finally,we apply the belief function to construct an attribute reduction algorithm,and an example is employed to illustrate the feasibility and validity of the algorithm.(3)Three-way decision models of real value loss function and Pythagorean fuzzy loss function based on three states are proposed.Loss function is the key content of decision-making problem.There are many researches on loss function based on fuzzy set,intuitionistic fuzzy set and interval intuitionistic fuzzy set.All of them are based on the types of two states.Therefore,this paper puts forward the three states of loss function,adding the state of hesitation degree.Then we redefine the expected loss function,which can make the decision to contain more uncertainty.On the basis of Bayesian minimum decision theory,four strategies for dealing with expected loss are proposed and three-way decision models are established respectively.