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Measurement-Theoretic Justification of Connectives in Fuzzy Set Theory (1995)
| Citations: | 7 - 0 self |
BibTeX
@MISC{Bilgic95measurement-theoreticjustification,
author = {Taner Bilgic and I.B. Türksen},
title = {Measurement-Theoretic Justification of Connectives in Fuzzy Set Theory},
year = {1995}
}
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Abstract
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 which addition and multiplication are meaningful and critically discussed. These conditions must either be accepted on normative grounds or must be empirically verified before the modeling process in order to see which operations are meaningful. It is emphasized that the Archimedean axiom and the existence of natural bounds are crucial in arriving at ratio and absolute scale representations. Keywords: Membership functions, measurement theory, operators, relations. 1 Introduction and Preview When Zadeh [45] introduced the concept of a fuzzy set he suggested to use the functions min and max to model set theoretic intersection an...
Keyphrases
fuzzy set theory measurement-theoretic justification measurement theoretic setting membership function fuzzy set theoretic intersection various proposal cardinal scale archimedean axiom measurement theory function min normative ground absolute scale representation natural bound continuous triangular norm modeling process
