Abstract
In the view of granular computing, some general uncertainty measures are proposed through single-granulation by generalizing Shannon’s entropy. However, in the practical environment we need to describe concurrently a target concept through multiple binary relations. In this paper, we extend the classical information entropy model to a multi-granulation entropy model (MGE) by using a series of general binary relations. Two types of MGE are discussed. Moreover, a number of theorems are obtained. It can be concluded that the single-granulation entropy is the special instance of MGE. We employ the proposed model to evaluate the significance of the attributes for classification. A forward greedy search algorithm for feature selection is constructed. The experimental results show that the proposed method presents an effective solution for feature analysis.
Highlights
Uncertainty analysis represents one of the most significant challenging tasks in intelligent computation.Since Shannon introduced the information entropy to measure the uncertainty of the system, a series of measures were proposed for machine learning, data mining and pattern recognition, etc. [1,2,3].In the field of granular computing, Yu et al introduced the fuzzy entropy for attribute reduction [4].Hu et al presented kernel entropy by extended Yu’s work [5]
The contribution of this paper includes: (1) we extend the classical information entropy model to a multi-granulation entropy model (MGE) by using a series of general binary relations; (2) a number of theorems are obtained; (3) we employ the proposed model to evaluate the significance of the attributes for classification
In MGE model, we introduce optimistic multi-granulation entropy (OMGE) and pessimistic multi-granulation entropy (PMGE) to describe the relations between different granularities
Summary
Uncertainty analysis represents one of the most significant challenging tasks in intelligent computation. It shows that granulation plays a key role in these entropy models. Qian et al proposed multi-granulation rough set (MGRS) according to a user’s different requirements or targets of problem solving. As a matter of fact, we can construct the multi-granulation structure in the process of the information granulation Based on this idea, the contribution of this paper includes:. (1) we extend the classical information entropy model to a multi-granulation entropy model (MGE) by using a series of general binary relations; (2) a number of theorems are obtained; (3) we employ the proposed model to evaluate the significance of the attributes for classification.
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