Gödel含意を導入した様相制約条件計画問題と種々のファジィ数理計画問題

抄録

The modality constrained programming (MCP) problem is previously proposed as the base model for unifying various fuzzy mathematical programming (FMP) problems. The relationships between MCP problems and six kinds of FMP problems have been discussed. However, some FMP problems, such as robust programming problem, FMP problem using fuzzy max, etc., did not have the relationships to MCP problems.
In this paper, introducing the Gödel implication into modality measures, a fuzzy relation between elements is extended to eight kinds of relations between possibility distributions. MCP problems are reformulated using these eight kinds of relations. The relationships between reformulated MCP problems and four kinds of FMP problems, i. e., robust programming problem, FMP problem using fuzzy max, FMP problem proposed by Luhandjula and modality goal programming problem, are investigated. Itis emphasized that most of FMP problems are interpreted in the framework of MCP problems and formulated based on the modal concept.