Measuring fuzziness: An evaluation problem

The measurement of fuzziness is treated as an evaluation problem. Fuzziness measures can be seen as evaluation mappings, more specifically as approximate solutions of this evaluation problem, satisfying some additional boundary conditions. In this way it is also possible to describe fuzziness in a qualitative manner. A general framework is created in which the most important classes of fuzziness measures, i.e., entropy measures and energy measures, easily fit. The essence of measuring fuzziness is thus reduced to finding a quasi or partial ordering that compares the different alternatives according to some aspect of their fuzziness. Special attention is paid to the quasi or partial orderings underlying entropy measures. The partial ordering of A. De Luca and S. Termini (1979) and some improved versions of it are discussed. The approach of E. Czogala et al. (1982) to energy measures is also discussed and extended