Kiyoji Asai

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.

Fuzzy solution in fuzzy linear programming problems

Fuzzy linear programming problems are discussed in which both constraints and objective functions are assumed to be fuzzy inequalities. The problem is to obtain a fuzzy solution such that the fuzzy inequalities hold. It is shown how to reduce this problem to the conventional linear programming problem so that it can be easily solved by the ordinary algorithms of linear programming.

A value of information in FLP problems via sensitivity analysis

Abstract A Fuzzy Linear Programming (FLP) Problem is formulated and the value of information is discussed. If the fuzziness of coefficients is decreased by using information about the coefficients, we can expect to obtain a more satisfactory solution than without information. With this view, the prior value of information is discussed. Using the sensitivity analysis technique, a method of allocating the given investigation cost to each fuzzy coefficient is proposed.

Fuzzy discriminant analysis in fuzzy groups

Abstract This paper deals with discriminant problems to classify samples with fuzzy multi-attribute into fuzzy groups. In this problem, the objective is to determine the linear discriminant function that provides the maximum separation of fuzzy groups in a real space. For this purpose, we define the fuzzy variance ratio and employ maximization of the fuzzy variance ratio as a criterion. Furthermore, a partial correlation coefficient in the fuzzy groups is defined to estimate the influence of each attribute itself on the discrimination between fuzzy groups.

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.

Adjointness of fuzzy systems

Abstract This paper deals with two adjoint fuzzy systems based on - and -compositions, which correspond to the normal use of ∀ and ∃ in L-fuzzy logic, respectively. The resolution of composite fuzzy relational inequations for these adjoint fuzzy systems can be skillfully treated by the Gentzen-type sequent calculus as well as by the lattice-theoretical way, owing to the adjointness of - and -compositions.

DISCRIMINANT ANALYSIS BASED ON FUZZY DISTANCE.

Abstract It is frequently discussed in economic, social, managemental, or diagnostic problems to classify objects which are vaguely specified in a fuzzy environment. Objects in a real world have vague attributes. This paper deals with a method of discrimination between fuzzy groups with vaguely defined multi-aspect. Fuzzy distance is defined by using a fuzzy scatter matrix which consists of fuzzy covariances between aspects in fuzzy groups. The fuzzy distance plays an important and central role in this paper. This concept enables us to measure the distance of a sample from each fuzzy group in consideration of scatterness of samples in each fuzzy group.