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1
Content available Method of identifying a type 2 membership function and application to decision-making problems
Uemura Y.
Control and Cybernetics
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2015
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Vol. 44, no. 3
399--406
EN
Tanaka (1991) suggested that the parameters of a linear regression model should be made fuzzy In order to better reflect the nature of the system, involving a definite degree of variability, and created a fuzzy linear regression model. This model can be formulated in the form of a linear programming problem that minimizes the span between the upper and lower limits under the constraints that include all data. In recent years, all the attention in this context has been focused on a fuzzy number that has an indifferent zone. A fuzzy number that we consider here is defined by using a type 2 membership function. This paper addresses the fact that a type 2 membership function has the upper and lower limits and shows that a type 2 membership function can be identified by expanding a fuzzy linear regression model into a fuzzy linear polynomial regression model. Finally, after a proposed fuzzy polynomial model is identified, a mathematical model is developed for a fuzzy decision-making method that accounts for an indifferent zone.
2
Content available Fuzzy decision making under transition from silence to confusion
Uemura Y.
Control and Cybernetics
|
2015
|
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
Content available Application of fuzzy decision making to the smoking problem
Uemura Y.
Control and Cybernetics
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2015
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Vol. 44, no. 3
413--416
EN
People often fall into a state of waver. A smoker knows ”in the head” that smoking harms his health, but fells a desire to smoke in order to compose himself ”at heart”. In case of an ”observation” (say: illness), a waver gradually sets on – whether to smoke or not. This process can be described as having two states of nature (”in the head” and ”at heart”), one of which is hidden, and only gradually comes to the surface, which leads to an apparent conflict. In this paper, we propose a model for this situation and the respective decision making and a way to solve the resulting problem, using the precepts of the fuzzy set theory.
4
Content available remote Fuzzy satisfactory evaluation method for covering the ability comparison in the context of DEA efficiency
Uemura Y.
Control and Cybernetics
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2006
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Vol. 35, no 2
487-495
EN
Evaluation of efficiency of each of the DMUs (Decision Making Units) in a company is a very important task. Thus, the studies of evaluation of efficiency are being actively carried out, based on production function. Until quite recently, the loglinear production function (the Cobb-Douglas function) has been used for evaluation purposes. The loglinear model evaluates the DMUs by measuring the average efficiency. Of late, the DEA (Data Envelopment Analysis) focussed the interest as the available method, in the form of either the CCR (Charnes-Cooper-Rhodes) or the BCC (Banker-Charnes-Cooper) model. However, the DEA approach does not provide for the lower limit of the production set, but only for the upper one. Hence, considering the fact that in the real-life problems the production set ranges between the lower and the upper limit, it is proposed that the possibility production function be constructed by introducing fuzziness into the loglinear production function. When we try to evaluate efficiency with the help of this possibility function, we can obtain from it two efficiency ratings, corresponding to the upper and lower limits. The DEA and the fuzzy loglinear models perform evaluation in the sense of inclusion of all the DMU data and provide a dual possibility image of efficiency in the sense that the DEA assesses the lower limit of inputs for the given output, while the fuzzy loglinear model assesses the maximum output for the given inputs. Hence, by making full use of this duality, we try to fuse the DEA and the fuzzy loglinear model in the evaluation of DMU efficiency by introducing a fuzzy goal. We propose to construct the fuzzy goal by evaluating the ratings for individual outputs with the help of fuzzy loglinear analysis, and introduce this fuzzy goal into the DEA. This approach can yield both efficiency and ability as obtained from the comparison of the CCR-based efficiencies.
5
Content available 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.
6
Content available Constructing improvement plan for inputs through dialogue with DM about DEA-Efficiency for DMUs
Uemura Y.
Control and Cybernetics
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1999
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Vol. 28, no 1
133-139
EN
Evaluation of efficiency of the DMUs (Decision Making Units) in a company is a very important problem. Thus, the studies of evaluation of efficiency are being actively carried out on the basis of the production functions, for example Cobb-Douglas production function and fuzzy loglinear production function (fuzzy Cobb-Douglas model). Recently, DEA (Data Envelopment Analysis) was applied to evaluation of efficiency, in the sense of benchmarking evaluation. After having evaluated DMUs by DEA, we obtain the improvement plan for every input in the inefficient DMUs. Though we many not be able to decrease inputs at one time according to the DEA plan, it is natural to construct some phased improvement plans for decreasing the inputs. First, we propose to support the construction of some phased improvement plans by the sensitivity analysis for the evaluated efficiency by applicatiion of definite limits to the decrease of inputs. Second, we evaluate this method by applying it to the case of bank data.
7
Content available A satisficing method of introducing the concepts of fuzzy goal and fuzzy constraints into the DEA
Uemura Y.
Control and Cybernetics
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1998
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Vol. 27, no 3
465-469
EN
Evaluation of efficiency of the DMUs (Decision Making Units) in a company can be carried out with the help of DEA (Data Envelopment Analysis). The efficiency calculated for a DMUo with the help of DEA is, however, higher than the maximum efficiency among the single object-single output results. It can be postulated that total efficiency is constrained between the limits thus obtained. Within this context we introduce the concepts of fuzzy goal and fuzzy constraints into the DEA formulation, propose the satisficing method following the precepts of the maximizing decision introduced by Bellman and Zadeh, and the improvement procedure for the satisficing solution using the dialogue with the DM over the tradeoff rate for two inputs, developed by Sakawa.
8
Content available A comparative study of the fuzzy linear model and the DEA in evaluation of efficiency of the DMUs
Uemura Y.
Control and Cybernetics
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1998
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Vol. 27, no 3
471-477
EN
Evaluation of efficiency for every DMU (Decision Making Unit) in a company is a very important issue. Thus, the studies of evaluation of efficiency are being actively carried out on the basis of production functions. Until now, loglinear production function (Cobb-Douglas model) has been used for evaluation. This loglinear model evaluates DMUs by measuring the average. Recently, DEA (Data Envelopment Analysis) has been applied as the available method involving, for example, the CCR (Charnes-Cooper-Rhodes) and BCC (Banker-Charnes-Cooper) models. However, the IDEA models do not have the lower limit on the production set, but only the upper limit. Since, however, we consider that the real problems have the production set extending from the lower limit to the upper limit, we propose the possibility production function obtained by introducing the fuzziness into the loglinear production function. As we try to evaluate the efficiency by this possibility production function we can obtain two efficiency ratings: for the upper and lower limits. Though both DEA and fuzzy loglinear model include all the DMU data, in the DEA approach we obtain the lower limit on inputs for the given output, while in the fuzzy loglinear approach we obtain the possibility maximum output for the given inputs. By making full use of the difference between the two approaches, we try to compare the DEA and the fuzzy loglinear model in the evaluation of efficiency of the DMUs. In terms of two efficiency ratings, fuzzy loglinear model can yield more exact ranking for every DMU than DEA. Genarally, when a DMU has efficiency less that 1 by fuzzy loglinear analysis, it means that there is a possibility of obtaining larger output for the given inputs.
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