あいまい理論によるシステムの構造モデル
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概要
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In studying complex problems, in developing plans, in managing organizations, in working with systems and in various other kinds of human endeavor, it is often desirable and sometimes essential to synthesize hierachies. The process of arranging elements in a hierachy is usually dealt with intuitively. On the other hand, the concept of fuzzy sets gives an important mathematical clue for an approach to studies of such systems with no sharp boundaries. On the basis of fuzzy sets theory, we propose a method for structuring hierachy for the several problems mentioned above, that is Fuzzy Structural Modeling (FSM) method. An important requirement for structural modeling of complex systems is that the necessary data is acquired and organized into a form which a structural model can be developed. A fuzzy reachability matrix is one such form. The main purpose of this method is to describe and illustrate a formal procedure for constructing the graphic presentation of the hierachical arrangement, given the necessary information concerning the relation of each element to each other element. The procedure permits the automatic development of the graphic structure that portrays the hierachy. The entries in the matrix are taken to values on the interval [0,1] by virtue of a fuzzy binary relation. According to the matrix, a fuzzy digraph describes a contextual relation among the elements of the system and can be transformed into an interpretive structural model of the system with respect to the relation. A significant step in the development of the proposed fuzzy structural modeling consists of the relaxation of transitivity, irreflexivity and asymmetry with respect to the construction of subordination matrix. The relaxation extends the flexibility and applicability for the structural modeling of systems. In order to show how the proposed method works, a few examples have been illustrated and the structure for the system has been successfully identified.
- 社団法人日本オペレーションズ・リサーチ学会の論文
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