FUZZY QUANTIFICATION THEORY TYPE II

Abstract

This paper deals with analyzing fuzzy data according to fuzzy groups. Fuzzy data are characterized qualitatively in the form of fuzzy sets and fuzzy groups are defined by several fuzzy sets. In order to quantify such fuzzy data, a fuzzy mean, a fuzzy variance and a fuzzy variance ratio are defined. Using these definitions, we extend Hayashi's Quantification Theory Type II to the Fuzzy Quantification Theory Type II which can handle fuzzy data and fuzzy groups. Since the qualitative data might be fuzzy in nature, this fuzzy theory is useful for analyzing fuzzy data. A simple example is described to illustrate the Fuzzy Quantification Theory Type II.