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This chapter presents a review of various interpretations of the fuzzy membership function together with ways of obtaining a membership function. We emphasize that different interpretations of the membership function call for different elicitation methods. We try to make this distinction clear using techniques from measurement theory. 3.
We present an ontology for representing requirements that supports a generic requirements management process in engineering design domain. The requirement ontology we propose is a part of a more general ontology to capture engineering design knowledge. Objects included in the ontology are parts, features, requirements, and constraints. We define a generic… (More)
Two different but related measurement problems are considered within the fuzzy set theory. The first problem is the membership measurement and the second is property ranking. These two measurement problems are combined and two axiomatizations of fuzzy set theory are obtained. In the first one, the indifference is transitive but in the second one this… (More)
Different languages that are offered to model vague preferences are reviewed and an interval-valued language is proposed to resolve a particular difficulty encountered with other languages. It is shown that interval-valued languagesare well definedfor De Morgan triples constructedby continuoustriangular norms, conorms and a strong negation function. A new… (More)
The problem of representing intersection and union in fuzzy set theory is considered. There are various proposals in the literature to model these concepts. The possibility of using continuous triangular norms and conorms (including min and max) are taken up in a measurement–theoretic setting. The conditions are laid out to arrive at cardinal scales on… (More)
The case-based retrieval is frequently reported as a valuable tool for engineering design. We discuss similarity based retrieval in the engineering design domain when the context is given as a set of constraints. This approach comprises the lowest level with which we support case-based retrieval from our Integrated Knowledge-Base. The characterization of… (More)
The Archimedean axiom in fuzzy set theory is critically discussed. The axiom is brought into perspective within a measurement theoretic framework and then its validity for fuzzy set theory is questioned. The discussion sheds light into what type of vagueness fuzzy set theory models.
A taxonomy of interpretations for fuzzy membership functions is given. Depending on each interpretation, the elicitation method and the theory to apply seems to be different. When different interpretations are cast into a measurementtheoretic framework, the difference becomes clearer. However, this raises questions about the validity of the overall… (More)