Abstract
Decision making in real problems is done in a fuzzy environment. Thus, Fuzzy-Bayes decision rules have been proposed to cope with a fuzzy state of nature. These decision rules are based on the probability of fuzzy events, or the possibility measure of fuzzy events. Furthermore, a decision rule based on fuzzy utility functions and the possibility distribution of fuzzy events are constructed. However, in these decision rules the fuzziness of the fuzzy expected utility is very big, because these decision rules are based on the extension principle for calculation of the fuzzy expected utility. In this article, avoiding the large fuzziness of the expected utility, we proposed a simple decision rule based on the representation interval of the possibility distributions of fuzzy events and the representation value of the fuzzy utility function. Further, we discuss the application of this simple decision rule to the decision problems, in which the decision maker obtains the one-peak symmetric possibility distribution of a state of nature and the one-peak symmetric membership functions of fuzzy events on a state of nature, by his or her knowledge and his or her belief.
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