Study On Extension Of Three-way Decision- Theoretic Rough Set Model And Its Related Algorithms

Pawlak Rough Set theory (PRS) is a mathematics tool for processing vague and uncertain problem. Rough Set theory has successfully been applied to the domains of artificial intelligence, machine learning, data mining and pattern recognition etc. Three-way decision-theoretic rough set theory (DTRS) is a probabilistic extension of PRS. Firstly, it introduces three-way decisions theory to interpret the three regions of rough set; secondly, it introduces the Bayesian decision theory to calculate the decision thresholds. Three-way decision-theoretic rough set model(DTRSM) presents tolerance of errors in making incorrect decisions, and it can be transferred into Pawlak rough set model(PRSM) or other probabilistic rough set models. DTRS has recently attracted wide attention of scholars in domestic and overseas because of its unique advantage.After studying three-way decision-theoretic rough set model and its reduction algorithm, this paper analyzes and discusses its defects and algorithm, and it brings in new improved strategies to solve the problem.Firstly, the loss function in DTRSM is generally given by the users, and it is generally a single-valued function. Considering the "uncertainty" character in practical decision making, the loss function should contain some randomness. This paper introduces a fuzzy-number based loss function to deal with a more general decision making problem under uncertainty. First of all, the fuzzy distributions of the decision thresholds are calculated through series of fuzzy operations, and the corresponding decision rules are given. Then this paper presents a different risk preference decision rules and analyzes the sensitivity of decision threshold with respect to the change of loss function. Finally, An example of oil investment was given to illuminate the proposed model in applications.Secondly, as a key concept of rough set theory, an attribute reduction is a subset of attributes that preserves its classification property of the given information table. Attribute reduction is NP-Hard problem, and there doesn’t exist an effective method to calculate it at present, therefore exploring a speedy reduction algorithm is still one of rough set theory research hotspots. At present, attribute reduction in DTRSM mainly categorizes into positive region reduction, non-negative region reduction and minimum cost reduction. This paper mainly studies positive region reduction. First of all, it compares the attribute reduction of PRSM with that of DTRSM, and then a heuristic method for reduction based on the significance of attribute in DTRSM is proposed. By recursively adding the most significance of attributes to an empty set, it ends up with an attribute reduction. As the algorithm has avoided the process for calculating the core of attribute, it is effective. Finally, Experiments results through large amount of data in the UCI machine learning database show the feasibility and validity of this algorithm.Finally, this paper summarizes all work in this research and makes a prospect to the next research direction.