Tetsuji Okuda

On Fuzzy-Mathematical Programming

In problems of system analysis, it is customary to treat imprecision by the use of probability theory. It is becoming increasingly clear, however, that in the case of many real world problems involving large scale systems such as economic systems, social systems, mass service systems, etc., the major source of imprecision should more properly be labeled ‘fuzziness’ rather than ‘randomness.’ By fuzziness, we mean the type of imprecision which is associated with the lack of sharp transition from membership to nonmembership, as in tall men, small numbers, likely events, etc. In this paper our main concern is with the application of the theory of fuzzy sets to decision problems involving fuzzy goals and strategies, etc., as defined by R. E. Bellman and L. A. Zadeh [1]. However, in our approach, the emphasis is on mathematical programming and the use of the concept of a level set to extend some of the classical results to problems involving fuzzy constraints and objective functions.

A formulation of fuzzy decision problems with fuzzy information using probability measures of fuzzy events

For decision problems in the real world, states of nature, information, and actions should be viewed as fuzzy events. The application of the fuzzy sets theory and the statistical decision theory to the decision problems in fuzzy events leads to a specific formulation of fuzzy decision problems and the definitions of entropy, worth of information, and quantity of information. Some results which are analogous to those in the statistical decision theory are given in this paper.

DECISION-MAKING AND ITS GOAL IN A FUZZY ENVIRONMENT

Publisher Summary There are many problems in a fuzzy environment where it is necessary to decide a present estimated goal. Therefore, it becomes necessary to formulate decision problems in such a sense that an estimated goal can be decided. This chapter defines N-decision problems from that point of view and discusses the properties of optimal decision and goal with a view to solve N-decision problems. It discusses some properties of 1-decision problems and shows that 1-decision problems can be reduced to simply 0-decision problems. As it seems that almost real world problems involving economic systems and public systems satisfy a pseudo complement in the domain under consideration, almost N-decision problems can be solved by the method for solving 0-decision problems. 0-decision problems may be regarded as optimization problems of logical functions. The chapter discusses the properties of optimization problems including logical functions.

On decision-making in fuzzy environment Fuzzy information and decision making

SUMMARY In some systems where human aspects have to be included, such as management systems, the problems of decision-making in a fuzzy environment have recently attracted special interest in a sense that it is becoming incre:isingly clear that many real-world problems have more to do with fuzziness, rather than randomness, for the major source of imprecision In this paper, a fuzzified bayes formula for decision-making is proposed, and the fuzzy observation system is discussed in order to make clear some properties of the fuzzy information. On the basis of the above discussion, a global decision approach is proposed.

An Analysis of Expected Utility based on Fuzzy Interval Data

In this paper, we investigate an analysis of expected utility based on fuzzy interval data. We establish a data processing method that can treat fuzzy interval data. Unfortunately, the method that direct usage of membership functions of fuzzy interval data has the problems of the efficiency when we carry out a calculation. To solve such problems, we propose a practical method that uses the midpoints of membership functions as the representative values.