Shadowed set approximation of fuzzy sets based on nearest quota of fuzziness
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Shadowed set approximation of fuzzy sets has been introduced and enhanced to exploit some optimization-based principles which define the quality of its approximation. It found its applications in granular computing, cluster computing and recommender systems. This paper introduces a new approach accompanied with an algorithm; based on a principle of uncertainty invariance, to simplify fuzzy sets by inducing its best approximation which possesses the nearest quota of fuzziness as encountered in the original fuzzy set. Some numerical examples are provided to demonstrate how to implement the proposed method. The new approach is useful in preserving the uncertainty and information inherently associated with a given fuzzy set. A comparative study is made with related methods. The results of some evaluation indices on the approximation effectiveness illustrate the essence of the proposed method.
Abstract
Shadowed set approximation of fuzzy sets has been introduced and enhanced to exploit some optimization-based principles which define the quality of its approximation. It found its applications in granular computing, cluster computing and recommender systems. This paper introduces a new approach accompanied with an algorithm; based on a principle of uncertainty invariance, to simplify fuzzy sets by inducing its best approximation which possesses the nearest quota of fuzziness as encountered in the original fuzzy set. Some numerical examples are provided to demonstrate how to implement the proposed method. The new approach is useful in preserving the uncertainty and information inherently associated with a given fuzzy set. A comparative study is made with related methods. The results of some evaluation indices on the approximation effectiveness illustrate the essence of the proposed method.
참고문헌 (18)
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