Three-way Decision-making Methods Based On Pythagorean Fuzzy Information

With the development of artificial intelligence,uncertain information processing has become a hot field in current scientific theory and application research.Scholars have proposed mathematical tools such as fuzzy sets,rough sets,concept lattices and soft sets to deal with uncertain information.Fuzzy sets describe the uncertainty of objects by means of membership.Rough sets describe unknown concepts or knowledge through a pair of precise sets(upper and lower approximation sets).This paper intends to conduct a combined research on Pythagorean fuzzy sets,rough sets,three-way decision method and conflict analysis problems.The specific contents are as follows:First,this paper focuses on the algorithm and information measures of interval-valued Pythagorean fuzzy sets.Pythagorean fuzzy sets,as a new generalization of fuzzy sets and intuitionistic fuzzy sets,have been successfully applied in the fields of intelligent decision-making,knowledge reduction and machine learning.Considering the hesitant attitudes of decision makers and unstable decision-making environment,scholars proposed interval Pythagorean fuzzy sets.Based on the existing measurement methods,this article proposes the axiomatic definition of the information entropy,distance and similarity of the interval-valued Pythagorean fuzzy set,and studies the conversion relationship among the three measures.The rationality of interval-valued Pythagorean fuzzy information entropy,distance and similarity is verified by examples of project evaluation and pattern recognition.Comparative analysis shows that new measures have the characteristics of flexibility and reliability.Secondly,the three-way decision on two universes is a novel mathematical tool for dealing with uncertain information and has been successfully applied in the field of intelligent decision-making.However,in actual decision-making,the classical binary set-valued function cannot describe the uncertain characteristics of the decision object in detail.In response to this problem,the three-way decision model on two universes is extended to the Pythagorean fuzzy multi-attribute information system.By increasing the number of Pythagorean fuzzy mapping,optimistic and pessimistic multi-granular approximation operators are constructed,and four important properties are proposed to prove.Considering the risk preferences of different decision makers,this paper constructs two types of three-way decision models with multi-granularity Pythagorean fuzzy information systems.According to the evaluation criterion of maximum accuracy,a threshold algorithm is given,and the newly proposed model is applied into the example of medical diagnosis.Finally,three-way conflict analysis model for Pythagorean fuzzy information is proposed and studied.As a development of intuitionistic fuzzy sets,Pythagorean fuzzy sets can effectively represent uncertain information,but they are rarely applied to conflict analysis problems.By defining a conflict function,the degree of conflict between any two agents for given events is explored.Then we design a threshold algorithm based on maximum accuracy evaluation,and construct three-way conflict analysis model for Pythagorean fuzzy information.The effectiveness of the new model is explained through an application.In summary,this paper proposes three types of compatible interval-valued Pythagorean fuzzy information measures and explores the conversion relationship between different measures.Any Pythagorean fuzzy mapping is regarded as a granularity,this paper constructs a multi-granularity three-way decision model by increasing the number of Pythagorean fuzzy mappings.Based on the conflict parameters,three-way conflict analysis method for Pythagorean fuzzy information is proposed.These combined studies not only enrich and develop Pythagorean fuzzy sets,three-way decision-making and conflict analysis theories,but also expand their scope of application,and have certain theoretical significance and practical value.