Junzo Watada

Fuzzy Portfolio Model for Decision Making in Investment

Financial engineering is one of the most important fields, today. Soft-computing methodologies are widely employed in financial engineering. Many problems of decision-making in investment have mainly been studied from optimizing points of view. As the investment is much influenced by the disturbance of a social and economical circumstances, optimization approach is not always the best. It is because problems used to be ill-structured under such influences. Therefore, a satisfaction approach is much better than an optimization one. In this discussion, we employ the aspiration level on the base of past experiences and knowledge possessed by a decision maker to treat a problem. That is, the aspiration level of the decision maker should be considered to solve a problem from the perspective of satisfaction strategy. It is more natural that the vague aspiration level of a decision maker is denoted as a fuzzy number.

Fuzzy robust regression analysis

Since a fuzzy linear regression model was proposed in 1987, its possibilistic model was employed to analyze data. From viewpoints of fuzzy linear regression, data are understood to express the possibilities of a latent system. When data have error or data are very irregular, the obtained regression model has an unnaturally wide possibility range. We propose a fuzzy robust linear regression which is not influenced by data with error. The model is built as rigid a model as possible to minimize the total error between the model and the data. The robustness of the proposed model is shown using numerical examples.<<ETX>>

Fuzzy principal component analysis for fuzzy data

A fuzzy concept is employed to construct a principal component model which can deal with fuzziness, vagueness or possibility, which is called fuzzy principal component analysis for fuzzy data. The fuzzy principal component analysis analyzes the possibility of fuzzy data. The fuzzy principal component analysis for fuzzy data has three formulations according the portions which the possibilities included in fuzzy data are embodied: (1) an eigenvalue, (2) an eigenvector and (3) both eigenvalue and eigenvector. In this paper, we discuss only the first formulation that an eigenvalue is employed to deal with fuzziness of data. The principal component analysis for fuzzy data is employed in this paper to analyze the features of information technology industry. In this analysis, the financial ratio is employed as an index. We evaluate the possibility of a company activity in the information technology industry.

Building a Type II Fuzzy Qualitative Regression Model

The qualitative regression analysis models quantitatively change in the qualitative object variables by using qualitative values of multivariate data (membership degree or type I fuzzy set), which are given by subjective recognitions and judgments. From fuzzy set-theoretical points of view, uncertainty also exists when associated with the membership function of a type I fuzzy set. It will have much impact on the fuzziness of the qualitative objective external criterion. This paper is trying to model the qualitative change of external criterion’s fuzziness by applying type II fuzzy set (we will use type II fuzzy set as well as type II fuzzy data in this paper). Here, qualitative values are assumed to be fuzzy degree of membership in qualitative categories and qualitative change in the objective external criterion is given as the fuzziness of the output.

HIERARCHICAL DECISION MAKING IN STRATEGIC INVESTMENT BY A BOLTZMANN MACHINE

A conventional portfolio selection problem, which is based on a mean-variance model, is difficult to solve by using mathematical programming techniques. This difficulty is caused by the fact that the corresponding mathematical programming problems are large-dimensional one, since almost all variance-covariances of return rates are, typically, not zeros. In this paper, we propose an efficient method for solving a portfolio selection problem, a method which uses a Boltzmann machine. In a real-life problem, it is also important to find the optimal combination of a small number of invested securities out of many securities in a market, because of a limited amount of funds to invest into securities. So we also propose a portfolio selection method to obtain the invest ratio of limited number of securities out of huge number of securities using a multi-stage application of the Boltzmann machine.

Enhanced back-propagation learning and its application to business evaluation

The error backpropagation learning algorithm of layered neural networks have several weak points including: terminating at a local optimal solution and requiring its learning for many hours. In this paper, an enhanced method for learning algorithm is proposed in order to shorten the learning time less than the conventional method. Employing the method in a 4-bits parity check problem, its effectiveness is shown. Finally, as an application of the enhanced learning algorithm of the neural network to a real problem, the neural model of business evaluation based on financial indices was built and its learning time was shorten up to 64% less than the conventional one.<<ETX>>

Trend of fuzzy multivariant analysis in management engineering

In 1965 L.A. Zadeh presented a fuzzy set. After then, fuzzy clustering method was proposed in early stage. L.A. Zadeh presented the concept of similarity for a fuzzy set in 1981. Ruspini proposed a clustering method based on fuzzy decomposition. Dunn and Bezdek wrote a clustering based on IDODATA algorithm in terms of fuzzy concept. Many methods for fuzzy multivariate analysis were presented . For example, there are several approaches to multivariant analysis such as dynamic programming, M. Sugenos measure, similarity concepts and clustering. M. Roubens and M.P. Windham discussed about the validity of clustering. Regarding hierarchical clustering, N. Osumi et al discussed it using fuzzy concepts. J. Watada et al proposed a heuristic hierarchical clustering which is employing similarity concepts of L.A. Zadehs. There are many papers which discuss fuzzy clustering. In 1979 H. Tanaka et al proposed fuzzy linear regression model. This development broke through fuzzy multivariate analysis because no methods are proposed except clustering and hierarchical clustering till then. There are also various applications of fuzzy multicariant analyses. Furthermore, various data analyses were proposed based on the fuzzy linear regression model. For example, J. Watada et al developed Fuzzy time-series analysis and I. Hayashi developed GMDH method. This paper summarizes the 40 year history of Fuzzy Multivariate Methods.

The thought and model of linguistic regression

Generally it is important for human experts to express their ideas and thoughts. Human words are basically employed in these expressions. So we employ fuzzy regression analysis to handle human words and find the latent structures under these human words and build a linguistic regression model.

Enhanced learning in neural networks and its application to financial statement analysis

It is discussed that layered neural networks have several weak points in the learning algorithm of error back-propagation such as terminating at a local optimal solution and requiring its learning for many hours. In this paper an enhanced method for learning algorithm is proposed in order to shorten the learning time more than a conventional method. Employing the method in a 4 bits parity check problem, its effectiveness is shown. At the end, as the application of the enhanced learning algorithm of the neural network to the real problem, the neural model for the financial statement analysis based on financial indices is discussed and its effectiveness is shown.<<ETX>>

Analysis of software reliability by fuzzy regression model

Outlines a method of analysis that can be used to enhance the quality of software and reduce the cost of its development. The method is based on, and was applied to the analysis of, factors that influence software quality in the programming environment. Empirical data on software development are analyzed to show how such attributes of program development as human relations and the organization influence the quality of software. A fuzzy regression model was built to estimate the number of bugs in a software project.