On fuzzy correlations

A general framework for dealing with numerical measurements in an approxima te, uncertain, or fuzzy environment is presented. A fuzzy measurement is defined. It possesses several unique properties, whi ch arise from its physical nature and distinguish it from concepts such as the fuzzy number. These properties, which include the fuzzy correlation ter m and the fuzzy equality relation, follow directly from physical considerat ions. The introduction of the fuzzy correlation term provides a mathematical tool for representing any correlation relations, which may exist between differ ent fuzzy measurements. The main function of the fuzzy correlation term is to eliminate, or filter out, measurement values that are unlikely, given ot her fuzzy measurements. Thus, using the fuzzy correlation term, the range o f possible measurement values is limited by physical realities. The informa tion represented by the fuzzy correlation term is shown to be of great valu e in providing a wider picture of reality than it is possible to obtain by simply considering individual fuzzy measurements. Arithmetic operations on fuzzy measurements and functions of fuzzy measurem ents are also discussed, leading to the derivation of the fuzzy Riemann int egral and its applications.