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1

The bipolar choquet integrals based on ternary-element sets

Abbas J.

Journal of Artificial Intelligence and Soft Computing Research

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2016

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Vol. 6, No. 1

13--21

EN

This paper first introduces a new approach for studying bi-capacities and the bipolar Choquet integrals based on ternary-element sets. In the second half of the paper, we extend our approach to bi-capacities on fuzzy sets. Then, we propose a model of bipolar Choquet integral with respect to bi-capacities on fuzzy sets, and we give some basic properties of this model.

2

Fuzzy decision making under transition from silence to confusion

Uemura Y.

Control and Cybernetics

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2015

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Vol. 44, no. 3

407--411

EN

Faculty of Education, Mie University, 1515 Kamihamacho, Isu; Mie, Japan uemura0742yahoo.co.jp We often fall into silence. After that, we make a decision through confusion, in most cases. In silence, cool mind runs parallel with warm heart. Traversing over these two, the phenomenon arises, chich can be interpreted as a fuzzy event, which can be called waver. In other words, two states of nature develop into conﬂict, and are covered by a fuzzy event. In confusion, we consider that the states of nature, which had been moving in conﬂict, not only undergo an inversion, but also a transformation takes place from warm heart into dry mind. It is therefore possible to derive a fuzzy function, resulting from the fuzziﬁcation of the transition matrix from silence to confusion, absorbing noise, and taking expectation to link the membership function with the multi-attribute utility function. This short note shows that we can calculate the expected utility by using both the probability of a fuzzy. event and the subjective importance of the two states of nature for the decision maker. Further, we can obtain an optimum action, based on the theory of maximum expected utility.

3

Application of normal possibility decision rule to silence

Uemura Y.

Control and Cybernetics

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2001

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Vol. 30, no 4

465-472

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.