Application of normal possibility decision rule to silence

• Autorzy: Uemura Y.
• Języki publikacji: EN

Abstrakty

EN

We often fall into silence. This often happens when we have two conflicting objectives and utilities, related to "cool head" and "warm heart" . This case has two different states of nature, associated with "cool head" and "warm heart" . We try to fuse the two decision problems referring to these different states of nature by introducing two-dimensional fuzzy events based on "cool head" and "warm heart" . We construct a decision rule based on one-dimensional fuzzy events. Thus, we propose the normal possibility decision rule based on the normal possibility theory. In the example of this paper, we consider fuzzy events named "astray" state and "lost" state, related to the "cool head" and "warm heart". We can obtain the fuzzy utility functions by the extension principle for a mapping, and the fuzzy expected utility functions by the extension principle for the sum and the product. We assume that the DM (decision-maker) defines the weights for the individual states of nature and the two problems. We make full use of these weights and the fuzzy utility functions are transformed into the one-dimensional function. As we make full use of indexes for ordering of fuzzy numbers, we can order the weighted fuzzy expected utility and select the optimal decision. For the example of this paper, we assume that the possibility of a fuzzy event is normal possibility distributed, and a DM is risk neutral. Consequently, both any fuzzy utility function and any fuzzy expected possibility function are normal possibility distributed. A decision rule is introduced, based on the ordering of only means of these normal possibility distributions for the fuzzy expected utilities, so that we do not need an index for ordering. When DM is of another type, the fuzzy expected possibility function is in general not normally possibility distributed. In this case, the DM needs the indexes for the ordering of the fuzzy numbers. This fuzzy-Bayes decision rule provides for a natural extension of the scope of our study by increasing the dimension of the possibility function of a fuzzy event.

Słowa kluczowe

EN

fuzzy event; normal possibility theory; two competing decision problems

PL

dwa problemy decyzyjne uzupełniające się; normalna teoria możliwości; zderzenie rozmyte

• Wydawca: Systems Research Institute, Polish Academy of Sciences
• Czasopismo: Control and Cybernetics
• Rocznik: 2001
• Tom: Vol. 30, no 4
• Strony: 465--472
• Opis fizyczny: Bibliogr. 6 poz.,

Twórcy

autor

Uemura Y.