Learning fuzzy semantic cell by principles of maximum coverage, maximum specificity, and maximum fuzzy entropy of vague concept

Concept modeling and learning have important significance in data mining, machine learning and knowledge discovery. In this paper a fuzzy semantic cell which is composed of a prototype P, a distance function d and a probability density function δ of granularity is considered as the smallest unit of vague concepts and the building brick of concept representation. For each fuzzy semantic cell we introduce three fundamental numeric characteristics, prototype P, expectation granularity R and fuzzy entropy H, to characterize the underlying concept. Then a novel learning strategy for the fuzzy semantic cell is proposed by using the principles of maximum coverage, maximum specificity, and maximum fuzzy entropy. Furthermore a granularity control factor λ is introduced into the learning strategy in order to make these principles coordinate with each other. The ultimate goal is to obtain a fuzzy semantic cell from a given data set which is the most appropriate to describe the data set. Finally the fuzzy semantic cell learning algorithm as well as the crisp semantic cell learning algorithm is formulated. We test the proposed methods on synthetic data and real-world data to demonstrate their feasibility and validity.