円谷 友英

We improve the efficiency interval of a DMU by adjusting its given inputs and outputs. The Interval DEA model has been formulated to obtain an efficiency interval consisting of evaluations from both the optimistic and pessimistic viewpoints. DMUs which are not rated as efficient in the conventional sense are improved so that their lower bounds become as large as possible under the condition that their upper bounds attain the maximum value one. The adjusted inputs and outputs keep each other balanced by improving the lower bound of efficiency interval, since the lower bound becomes small if all the inputs and outputs are not proportioned. In order to improve the lower bound of efficiency interval, different target points are defined for different DMUs. The target point can be regarded as a kind of benchmark for the DMU. First, a new approach to improvement by adjusting only outputs or inputs is proposed. Then, the combined approach to improvement by adjusting both inputs and outputs simultaneously is proposed. Lastly, numerical examples are shown to illustrate our proposed approaches. © 2004 Elsevier B.V. All rights reserved.

Even if the given data are crisp, there exists uncertainty in decision making process and inconsistency based on human judgements. The purpose of this paper is to obtain the evaluations which reflect such an uncertainty and inconsistency of the given information. Based on the idea that intervals are more suitable than crisp values to represent evaluations in uncertain situations, we introduce this interval analysis concept into two well-known decision making models, DEA and AHP. In the conventional DEA, the relative efficiency values are measured and in the proposed interval DEA, the efficiency values are defined as intervals considering various viewpoints of evaluations. In the conventional AHP, the priority weights of alternatives are obtained and in the proposed interval AHP, the priority weights are also defined as intervals reflecting the inconsistency among the given judgements. © Springer-Verlag Berlin Heidelberg 2006.

Analytic Hierarchical Process(AHP) is proposed to give the priority weight with respect to many items. The priority weights are obtained from the pairwise comparison matrix whose elements are given by a decision maker as crisp values. We extend the crisp pairwise comparisons to fuzzy ones based on uncertainty of human judgement. To give uncertain information as a fuzzy value is more rational than as a crisp value. We assume that the item's weight is a fuzzy value, since the comparisons are based on human intuition so that they must be inconsistent each other. We propose a new AHP, where the item's weight is given as a fuzzy value, in order to deal with inconsistency in the given matrix. The purpose is to obtain fuzzy weights so as to include all the given fuzzy pairwise comparisons, in the similar way to the upper approximation in interval regression analysis. © 2006 Springer.

The decision problem in Analytic Hierarchy Process (AHP) is structured hierarchically as several criteria and alternatives. It is proposed to determine the global weights of alternatives considering the referenced priority weights of criteria and local weights of alternatives. We assume them as intervals, since they are obtained from the corresponding pairwise comparison matrices given by a decision maker based on his/her intuition. The width represents the possibility of each weight reflecting the inconsistency of the given comparisons. Then, the global weights calculated with them should be also intervals and such intervals tend to contain redundant parts. We propose the models to modify the intervals so as to be normalized keeping their possibilities. Instead of crisp normalization, the interval probability fills the role of interval normalization. The modified interval global weights reflect a decision maker's uncertain judgments as intervals without redundancy.

Analytic hierarchy process (AHP) is proposed to give priority weights with respect to many items. The priority weights are obtained from the comparison matrix whose elements are given by a decision maker as crisp numbers. We assume that the item's weights are intervals, because a comparison matrix based on human intuition must be inconsistent. Three models depending on the objective functions are proposed in this paper. In each model, the interval weights are determined so as to include the given comparisons. This concept is similar to the upper approximation in interval regression analysis.

本研究では,DEAにおける区間効率値の改善方法を提案する.従来のDEAは,当該事業体に対して仮想出力の仮想入力に対する比の相対的な最大値を効率値として,事業体にとって有利な重み付けを行い評価する手法であるといえる.それに対して,真の効率値が存在する区間として区間効率値を求める手法が提案されている.区間効率値は,有利な立場からの評価である上限と不利な立場からの評価である下限により定められ,上限は従来のDEAによる効率値と一致する.下限は,従来のDEAでは最大効率値を求めるのに対して,最小効率値を求める最適化問題により求められる.改善対象となるDMUは,区間効率値の上限が1ではないDMU,すなわち有利な立場から評価しても効率的であると判断されないDMUとする.本研究では,区間効率値に基づき,従来のDEAの考え方と同様である区間効率値の上限を1に改善し,そのうち下限ができるだけ大きくなるような改善方法を提案している.区間効率値の下限は与えられる出力値に偏りがあるとき小さくなるので,下限を考慮して改善を行うと,DMUの与えられた各項目の入力値を配慮して,それらがバランスのよい出力値となるように改善することができる.出力値のみに着目して,与えられた出力値を減らすことなくDMUを改善する方法を示すが,入力値のみに着目する方法,入出力値を同時に考慮する方法についても同様に考えることができる.

In this paper, multi-source possibilistic information is represented by a set of possibilistic constraints to characterize decision variables from different information aspects. Possibilistic linear programming is used to integrate multi-source possibilistic information into the upper and the lower possibility distributions of decision vector.

本研究では, 意思決定者の評価を反映したウェイト制約を用いたDEAを定式化を提案している.AHPなどで取り扱われる項目の重要度は和が1となる確率測度であるとみなすことができる.この確率測度として得られる重要度をDEAウェイトに対応させるため, 分析対象であるDMUの入出力データに基づきデータの正規化を行う.DEAでの, 項目の重要度は, ウェイトとデータの積により表現されていると考えることができる.正規化したデータを用いて求められるウェイトとデータの積は, そのウェイトに等しくなるので, ウェイトは確率測度を用いて表される項目の重要度と自然に対応する.また, 求められる効率値は, もとのデータを用いた場合と等しい.この正規化により, DEAにおいて得られる入力に対する最適ウェイトの和は1, 出力に対する最適ウェイトの和は効率値となる.多人数の意思決定者を仮定し, 意思決定者ごとにAHPを用いて求められる重要度を確率測度とみなすと, 容易に区間重要度を求めることができ, DEAでのウェイト制約として導入できる.さらに, 意思決定者から得られる情報に部分的無知量が含まれるとき, 重要度を半可動確率質量(基本確率)とみなすと, デンプスター・シェーファー理論を用いて, 無知量を取り扱うことができる.