Application of Fuzzy Theory to Relation Diagram


Nagasawa, Shin'ya   (1990, ASQC)   Asia University, Tokyo, Japan

Annual Quality Congress, San Francisco, CA    Vol. 44    No. 0
QICID: 9513    May 1990    pp. 573-578
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Article Abstract

The Relation Diagram Method, one of the "Seven Management Tools for QC," is employed to solve a intricate problem by means of arrangement of cause and effect relationships of a problem. In applying the Relation Diagram Method to complex relationship among many elements of causes and/or results in the problem to be solved, it is often desirable and sometimes essential to create hierarchies. However, the process of rearranging elements in a hierarchy is not dealt with in the existing Relation Diagram Method.

In order to deal with such a relationship practically and systematically, the author proposes to create a hierarchy and rearrange the elements in a relation diagram by the Fuzzy Structural Modeling (FSM) method, which is developed on the basis of the fuzzy sets theory.

The main purpose of applying the Fuzzy Structural Modeling method to relation diagrams is to describe and illustrate a formal procedure for constructing a graphic representation of the hierarchical rearrangement, given the necessary information concerning the relationship between each element in the diagram. The procedure permits automatic development of a graphical structure portraying the hierarchy. The entries in the fuzzy reachability matrix are given values in the interval [0,1 ] by virtue of a fuzzy binary relation.

In order to demonstrate how the proposed method works, a practical example is given in which the structure of the relation diagram has been successfully identified.


Quality control methodology,Union of Japanese Scientists & Engineers (JUSE)

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