Correction Theory and Algorithm for Fuzzy Reachability Matrix Model

Abstract

Fuzzey Flexible Interpretive Structural Modeling (FISM/Fuzzy) is a fuzzy version of Flexible Interpretive Structural Modeling (FISM). The fuzzy transitive embedding is a problem of how to efficiently fill the fuzzy reachability matrix.To perform the fuzzy transitive embedding logicaly and effectively, a fuzzy partially filled reachability matrix (FPR-matrix) is proposed. While an FISM/fuzzy structural model is being developed, or after it has been developed, the developer may want to make changes in it. Procedure for changing a structural model with computer assistance is called "correction". Correction is key to FISM/fuzzy. This is becase developing a structural model is inherently a trial-and-error process.In this paper a correction theory and algorithm for FRR-matrix is proposed. Use of the algorithm makes it possible to do a flexible and an efficient modeling for complex and fuzzy systems.