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- 저자 : T. O. William-West (검색결과 2 건)
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Shadowed set approximation of fuzzy sets based on nearest quota of fuzziness
T. O. William-West,A. M. Ibrahim,A. F. D. Kana 원광대학교 기초자연과학연구소 2019 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.17 No.2
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.
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On balance of uncertainty in shadowed sets
M. A. Ibrahim,T. O. William-West,A. F. D. Kana,D. Singh 원광대학교 기초자연과학연구소 2020 ANNALS OF FUZZY MATHEMATICS AND INFORMATICS Vol.19 No.3
A shadowed set, $S$, facilitates crisp decision-making with a fuzzy set $F$. It is constructed with the aid of different optimization-based principles. Among these principles, the requirement of uncertainty balance guarantees preservation of the uncertainty of $F$ in $S$. In order to gain further insight on uncertainty balance, some essential mathematical properties which characterize uncertainty-balance-based objective function, $J(\alpha)$, are studied. These properties provide theoretical explanation for interpreting and analyzing $J(\alpha)$ and its ensuing optimum partition threshold $\alpha$. Two senses of uncertainty balance are discussed in this paper. Their combined efficiency in enhancing clustering results is illustrated with the aid of synthetic data set used in shadowed $C$-means clustering. Finally a need for five-region shadowed sets, $S_5$, is pointed out. A closed-form formula for determining its optimum thresholds is proposed and exemplified on typical fuzzy set and synthetic dataset.
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