Research On Three-way Decision Based On Intuitionistic Fuzzy Information Systems

The main idea of the three-way decision theory is divided into three parts,which aims to think and deal with problems from three aspects or three levels,and provides an effective method for making complicated problems.In recent years,many three-way decision models have been proposed by scholars.As a representative one,the three-way decision on two universes has been widely used in the decision-making field.Most of the existing three-way decision models on two universes are studied under crisp settings,but the problems faced in real life are usually fuzzy.In order to solve this problem,this paper will study the three-way decision models of complete intuitionistic fuzzy information systems and incomplete intuitionistic fuzzy information systems.1.A three-way decision model based on complete intuitionistic fuzzy information systems is proposed.Firstly,a similarity function of intuitionistic fuzzy sets is given,which is composed of fuzzy factor,mean factor and probability factor.Secondly,a three-way decision model of complete intuitionistic fuzzy information systems based on similarity function is established and it is pointed out that this model theoretically unifies the existing two-universe models.Then,a new partition measure,the weighted information entropy,is proposed by improving the information entropy,and it is proved that the smaller the partition is,the larger the weighted information entropy is.At the same time,according to the property of the weighted information entropy,a reasonable explanation of optimal tri-partition is given,that is,the larger the entropy value is,the more accurate the corresponding partition is expressed,and a new method of solving the thresholds value and determining the optimal tri-partition based on the weighted information entropy is proposed.Finally,the proposed new method is compared with the traditional method,which is based on Bayesian minimum risk decision principle.2.A three-way decision model of incomplete intuitionistic fuzzy information systems is discussed.Firstly,the incomplete intuitionistic fuzzy information system is completed,that is,the method of completing the missing value is given.Secondly,a divergence function based on membership degree and non-membership degree is defined.Then,a three-way decision model of incomplete intuitionistic fuzzy information systems based on the divergence function is established and it is pointed out that this model theoretically unifies the existing two-universe models including the three-way decision model of complete intuitionistic fuzzy information systems.Next,considering the different weights of objects in the universe,the weighted rough entropy is proposed,and the property that the finer the partition is,the smaller the weighted rough entropy is proved.At the same time,according to the property of the weighted rough entropy,a reasonable explanation of optimal tri-partition is given,that is,the smaller the entropy value is,the more accurate the corresponding partition is expressed,and a method of solving the thresholds and determining the optimal tri-partition based on the weighted rough entropy is proposed.Finally,an example is given to compare the two methods proposed in this paper.In conclusion,this paper mainly researches three-way decision models of complete intuitionistic fuzzy information systems and incomplete intuitionistic fuzzy information systems.These contents not only enrich the study of the three-way decision theory,but also provide new ideas for the expansion of the three-way decision models.