Quantity of information; Comparison between information systems: 1. Non-fuzzy states

Abstract

In statistical theory, experiments or probabilistic information systems are supposed to be informative, since they reduce the amount of uncertainty associated with the states of nature. For the case that the available information systems are vague (fuzzy information systems), H. Tanaka, T. Okuda and K. Asai have proven, using the ‘measure of information’ as provided by ‘entropy’, that the fuzzy information systems are informative too. Now, we wish to state and to study a criterion in order to compare fuzzy information systems by the ‘quantity of information of a fuzzy information system’ (defined by Tanaka et al.). In this first paper we consider the situation where we require information about the original state space (non-fuzzy state space). The second paper will deal with the situation where we require only information on certain vague states (fuzzy states).