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arXiv · 2404.11629

Rules and Algorithms for Objective Construction of Fuzzy Sets

Lei Zhou
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Abstract

This paper aims to present objective methods for constructing new fuzzy sets from known fuzzy or classical sets, defined over the elements of a finite universe's superstructure. The paper proposes rules for assigning membership functions to these new fuzzy sets, leading to two important findings. Firstly, the property concerning the cardinality of a power set in classical theory has been extended to the fuzzy setting, whereby the scalar cardinality of a fuzzy set $\tilde B$ defined on the power set of a finite universe of a fuzzy set $\tilde A$ satisfies $\text{card}(\tilde B)=2^{\text{card}(\tilde A)}$. Secondly, the novel algorithms allow for an arbitrary membership value to be objectively achieved and represented by a specific binary sequence.

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Lei Zhou. 2024-11-07. Rules and Algorithms for Objective Construction of Fuzzy Sets. https://arxiv.org/abs/2404.11629

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