Abstract
Preference analysis is a class of important issues in ordinal decision making. As available information is usually obtained from different evaluation criteria or experts, the derived preference decisions may be inconsistent and uncertain. Shannon entropy is a suitable measurement of uncertainty. This work proposes the concepts of preference inconsistence set and preference inconsistence degree. Then preference inconsistence entropy is introduced by combining preference inconsistence degree and Shannon entropy. A number of properties and theorems as well as two applications are discussed. Feature selection is used for attribute reduction and sample condensation aims to obtain a consistent preference system. Forward feature selection algorithm, backward feature selection algorithm and sample condensation algorithm are developed. The experimental results show that the proposed model represents an effective solution for preference analysis.
Highlights
Multiple attribute decision making refers to making preference decisions between available alternatives characterized by multiple, usually conflicting, attributes [1]
In multiple attribute ordinal decision, the derived decisions may be inconsistent and uncertain since the available information is usually obtained from different evaluation criteria or experts
Since the available information is usually obtained from different evaluation criteria or experts
Summary
Multiple attribute decision making refers to making preference decisions between available alternatives characterized by multiple, usually conflicting, attributes [1]. Shannon entropy has been expanded to preference inconsistence entropy and is used to measure the uncertainty of preference decision to conditional attributes Based on this idea, the contributions of this work include: (1) this paper defines a preference inconsistence set and preference inconsistence degree, and some properties are given; (2) based on preference inconsistence degree and Shannon entropy, the notion of preference inconsistence entropy is proposed; (3) relative attribute significance is defined, feature selection is investigated, and a forward feature selection algorithm and backward feature selection algorithm are developed; (4) a sample condensation algorithm is given; (5) some experiments are completed to verify the proposed approach.
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