新居 学

本研究では.多数の生産者が市場で競合しているような状況での市場選択問題に対して, 強化学習の代表的手法であるQ学習を用いた解析手法を提案する.市場選択問題では, 市場価格は需要と供給(出荷量)との関係で決定されると仮定する.そのため, 市場選択に関する意思決定の結果として市場から得られる利得は.他の生産者による市場選択の結果に依存する.そこで本研究では, まず, このような市場選択問題を, 一種のn人非協力ゲームとして定式化する.次に, Q学習を市場選択問題へ適用する方法を提案する.Q学習は, 市場価格を決定する需要関数が未知の場合でも有効な手法である.最後に, 数値実験により, Q学習の有効性を明らかにする.数値実験では, 他の生産者が前回と全く同じ行動を取ると仮定した場合での最適な市場選択と, Q学習に基づく市場選択との比較を行う.

This paper discusses the learning of multi-layer feedforward neural networks from linguistic knowledge and numerical data. These two kinds of information are simultaneously utilized in the learning of neural networks. We show back-propagation type learning algorithms for pattern, classification problems and function approximation problems. For pattern classification problems, linguistic knowledge is represented by fuzzy if-then rules such as ''If x(1) is small and x(2) is large then Class 1'' and ''If x(3) is large then Class 3.'' These fuzzy if-then rules are used in the learning of neural networks together with numerical data such as {(x(1), x(2), x(3); class label)} = {(0.1, 0.9, 0.3; Class 1), ..., (0.7, 0.9, 0.8; Class 3)}. For function approximation problems, linguistic knowledge such as ''If x(1) is small and x(2) is large then y is small'' is utilized in the learning of neural networks together with numerical data such as {(x(1), x(2), x(3); y)} = {(0.1, 0.8, 0.2; 0.2), ..., (0.2, 0.3, 0.9; 0.9)}. The learning of neural networks from these two kinds of information is illustrated using computer simulations on several numerical examples. Handling of inconsistency in linguistic knowledge is discussed in this paper. Inconsistency between linguistic knowledge and numerical data is also discussed.

This paper examines the performance of a possibilistic fuzzy classification method where the possibility area of each class is identified by the learning of a multilayer feedforward neural network. The possibility areas of different classes may overlap one another in the pattern space. The overlapping region of the possibility areas of two classes is viewed as the fuzzy boundary between those classes. Thus our method does not always assign ail input pattern to a single class. When an input pattern is on a fuzzy boundary, a set of possible classes is indicated by the trained neural network as the classification result for that pattern. In this paper, we first illustrate our possibilistic fuzzy classification method. Next we examine its performance by computer simulations on real-world test problems. Then we discuss the relation between our method and the reject option. Finally we extend our method to the case where a rejection penalty is explicitly given in classification problems.

This paper proposes a hybrid approach to the design of a compact fuzzy rule-based classification system with a small number of linguistic rules. The proposed approach consists of two procedures: rule extraction from a trained neural network and rule selection by a genetic algorithm. In this paper, we first describe how linguistic rules can be extracted from a multilayer feedforward neural network that has been already trained for a classification problem with many continuous attributes. In our rule extraction procedure, a linguistic input vector corresponding to the antecedent part of a linguistic rule is presented to the trained neural network and the fuzzy output vector from the trained neural network is examined for determining the consequent part and the grade of certainty of that linguistic rule. Next we explain how a genetic algorithm can be utilized for selecting a small number of significant linguistic rules from a large number of extracted rules. Our rule selection problem has two objectives: to minimize the number of selected linguistic rules and to maximize the number of correctly classified patterns by the selected linguistic rules. A multi-objective genetic algorithm is employed for finding a set of nondominated solutions with respect to these two objectives. Finally we illustrate our hybrid approach by computer simulations on real-world test problems.

本研究では, 学習後のニューラルネットワークからファジィIf-Thenルールを獲得するため, ファジィ数の演算に基づく方法を提案する.提案手法では, 多次元パターン識別問題に対して学習された階層型ニューラルネットワークから, 確信度付きのファジィIf-Thenルールが獲得される.例えば「If x_1 is small and x_2 is large then Class 2 with CF=0.9」のようなファジィIf-Thenルールである.ここで, CF=0.9は, このルールの確信度が0.9であることを表している.このようなファジィIf-Thenルールを獲得するため, 提案手法では, まず, 条件部ファジィ集合に対するファジィ数ベクトルが学習後のニューラルネットワークに入力される.次に, ニューラルネットワークからの出力が, ファジィ数の演算に基づき, ファジィ数ベクトルとして得られる.最後に, このファジィ数出力ベクトルを用いて, ファジィIf-Thenルールの結論部とルールの確信度が求められる.本研究では, このような提案手法の有効性を示すため, 2次元パターン識別問題とアヤメの分類問題に対して学習されたニューラルネットワークからファジィIf-Thenルールの抽出を試みた結果についても議論する.