Abstract
Much of decision-making in the real world takes place in an environment in which states of nature, feasible actions and available information are fuzzy. Therefore it is important to study decision problems in such an environment. An example of fuzzy states may be described by such expressions as “It will be warm, ” “It will be cool, ” etc. This fuzziness stems from such adjectives as “warm, ” “cool, ” etc. Since fuzzy states are defined as fuzzy events which are fuzzy sets on a probability space, the decision problem is related to fuzziness and randomness.
The present paper deals with a fuzzy decision problem in this environment.
The application of the fuzzy sets theory and the statistical decision theory to decision problems with fuzzy events leads to a specific formulation of fuzzy decision problems and to the definitions of entropy, worth of information and quantity of information. On the basis of these definitions, this paper gives some analytical results concerning perfect, probabilistic and fuzzy information, which are analogous to those in the statistical decision theory, and shows the advantages for considering the decision problem with fuzzy events.
