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Abstract

Based on inverse packet sets and fuzzy set, the concept of inverse packet fuzzy sets is proposed in this paper by means of introducing dynamic characteristics into a fuzzy set $A$ and improving the fuzzy set $A$ . The inverse packet fuzzy sets is composed of a pair of fuzzy sets generated by the fuzzy set $A$ and has dynamic characteristic and fuzzy characteristic. Furthermore, on certain conditions, it can be restored to the fuzzy set $A$ or the inverse packet sets generated by the Cantor set $X=\ker(A)$ . As a result, an inverse packet fuzzy sets can be expressed as a series of inverse packet sets by defining its scalar multiplication and its cut sets. Meanwhile some attribute-dependent characteristics of inverse packet fuzzy sets are obtained. The new set model will both enrich the set theory and provide a new basic tool for further practical applications.

Keywords

Inverse packet sets fuzzy set inverse packet fuzzy sets attribute-dependent characteristics

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Inverse packet fuzzy sets and its characteristics

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