An extensive-form analysis for comparing fuzzy information systems by means of the worth and quietness of information
One of the problems often discussed in statistical literature deals with the comparison of random experiments whose distributions depend upon the same parameter. When several experiments whose distributions depend upon the same parameter are available, but the observer cannot crisply perceive their outcomes, some criteria to compare such experiments have been developed in previous papers by incorporating some notions in the theory of fuzzy sets to the probabilistic framework. In this sense, a criterion to select the most informative experiments, based on the ``worth of information of a fuzzy information system'' (extending to the fuzzy case the well-known ``expected value of sample information'') has been previously proposed by the first two authors and \textit{P. Gil}, Kybernetes 13, 245-251 (1984; Zbl 0552.94030). The present paper involves a criterion that has been suggested to make comparable experiments that are indifferent with respect to the ``worth of information''. This indifference is removed by means of the ``expected quietness of information''. The suitability of this criterion is confirmed with the study of several natural properties it satisfies. Contrasts with other criteria to compare experiments providing fuzzy information are finally developed.
scientific article; zbMATH DE number 4030690
scientific article