Introduction

Abstract

First like fuzzy logics are logics with fuzzy concepts, by fuzzy statistics we mean statistics with fuzzy data. Data are fuzzy when they are expressed in our natural language. For example, the linguistic value "young" for the age of Tony in "Tony is young" is a fuzzy concept. We use natural language to describe phenomena when precise measurements are not available. The fuzzy concept "young" is intended to describe Tony`s age from our perception. As such it should "contain" the true age of Tony. However, the boundary of a set which supposes to "contain" Tony`s true age is not sharply defined. We will call this vagueness in the meaning of "young" fuzziness. We take fuzzy concepts in our nature language as primitives. We use our natural language to impart knowledge and information. © Springer-Verlag Berlin Heidelberg 2006.