The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

Abstract

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

Intuitionistic Neuro-Fuzzy Optimization in the Management of Medical Diagnosis

“…Intuitionistic fuzzy logic has also been used in many medical diagnosis tools. Sang and Zhang gave an approach which was based on Intuitionistic Fuzzy Information [24]. Barrenechea, E. et al generalized the work of Atanassov's intuitionistic fuzzy index construction method [25], Hájek, P. and Olej, V. solved the regression problems by using an adaptive intuitionistic fuzzy inference system of Takagi-Sugeno type approach, afterwards they used again Takagi-Sugeno type intuitionistic Fuzzy Inference System (FIS) by using defuzzification methods to solve the matter of incorporated liquidation forecast, followed by these two works they added Intuitionistic Fuzzy Neural Network, a new approach in their work and got results for the situation of credit scoring using text acquaintance [26] [27] [28].…”