ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval

TLDR

Fuzziness may stem from the indistinguishability between a set and its negation. The study investigates the concept of fuzziness and proposes measures derived from fuzzy subsets with unit‑interval membership grades. These measures are obtained via metric‑distance based numeric metrics and compatibility‑based linguistic metrics applied to fuzzy subsets.

Abstract

We investigate the meaning of the concept of fuzziness. It is suggested that fuzziness can be related to the lack of distinction between a set and its negation. Using fuzzy subsets with grades of membership in the unit interval, measures of fuzziness are suggested. First, a class of measures based on metric distances is used to derive numeric measures of fuzziness of a fuzzy set. Finally, the concept of compatibility is used to develop linguistic measures of fuzziness.