Qualitative fuzzy system structures

The authors attempt to establish a measurement-theoretic foundation for fuzzy sets. A qualitative relational system called the fuzzy system structure is introduced. This forms the basis for examining the ordering and properties of a fuzzy system. More specifically, an empirical relation is used to c...

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Bibliographic Details
Main Authors: Wong, S.K.M., Yao, Y.Y., Bollmann-Sdorra, P.
Format: Conference Proceeding
Language:English
Subjects:
Computer science
Fuzzy set theory
Fuzzy sets
Fuzzy systems
Lakes
Sufficient conditions
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Summary:The authors attempt to establish a measurement-theoretic foundation for fuzzy sets. A qualitative relational system called the fuzzy system structure is introduced. This forms the basis for examining the ordering and properties of a fuzzy system. More specifically, an empirical relation is used to characterize the relationship between two objects with respect to a fuzzy set. Another empirical relation is used to characterize the relationship between two fuzzy sets with respect to an object x. These two primitive relations together characterize a qualitative fuzzy system, by which the necessary and sufficient conditions that justify the use of the min-max numerical system are identified.< >
DOI:10.1109/FUZZY.1993.327554