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The archimedean assumption in fuzzy set theory
 University of California, Berkeley
, 1996
"... 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. 1 ..."
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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. 1
Fuzzy Set Theory in Medicine
, 1997
"... iness is sometimes at conflict with the rigor of formal analysis, as the following example demonstrates. * Address: +49 511 7629712; email: steimann@acm.org 09333657/97/$17.00 1997 Elsevier Science B.V. All rights reserved. PII S09333657(97)000195 F. Steimann / Artificial Intelligence in Med ..."
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Cited by 18 (0 self)
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iness is sometimes at conflict with the rigor of formal analysis, as the following example demonstrates. * Address: +49 511 7629712; email: steimann@acm.org 09333657/97/$17.00 1997 Elsevier Science B.V. All rights reserved. PII S09333657(97)000195 F. Steimann / Artificial Intelligence in Medicine 11 (1997) 1  7 2 If the low blood pressure of a patient increases by a small amount, say 1 mmHg, then, because nothing significant has happened, it will still be considered low. A mean arterial blood pressure of 70 mmHg is certainly low. Therefore, by induction, every blood pressure above 70 mmHg should be low, which is, of course, not true. This old paradox (quoted after [4]) is easily resolved if one accepts that the denotation of the word low is not as sharply defined as would be required for induction to be applicable. Clearly, if 70 m
MeasurementTheoretic Frameworks for Fuzzy Set Theory
, 1997
"... 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 i ..."
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Cited by 18 (10 self)
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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
Editorial: Fuzzy Set Theory in Medicine
"... "Indeed, the complexity of biological systems may force us to alter in radical ways our traditional approaches to the analysis of such systems. Thus, we may have to accept as unavoidable a substantial degree of fuzziness in the description of the behavior of biological systems as well as in ..."
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. Zadeh, 1969 [14], p. 200 Lotfi A. Zadeh himself anticipated very early that medical diagnosis would be the most likely application domain of his theory [14]. Despite his prominent forecast, work on fuzzy set theory in medicine has largely remained that of individuals and is still considered informal and
REPRESENTABILITY IN INTERVALVALUED FUZZY SET THEORY
, 2007
"... Intervalvalued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0, 1]valued membership degrees are replaced by intervals in [0, 1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended settin ..."
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Cited by 4 (1 self)
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Intervalvalued fuzzy set theory is an increasingly popular extension of fuzzy set theory where traditional [0, 1]valued membership degrees are replaced by intervals in [0, 1] that approximate the (unknown) membership degrees. To construct suitable graded logical connectives in this extended
Fuzzy set theory and topos theory
 Bull. Can. Math Soc
, 1986
"... ABSTRACT. The relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant categor ..."
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ABSTRACT. The relation between the categories of Fuzzy Sets and that of Sheaves is explored and the precise connection between them is explicated. In particular, it is shown that if the notion of fuzzy sets is further fuzzified by making equality (as well as membership) fuzzy, the resultant
CLOSURE OPERATORS IN FUZZY SET THEORY
, 1998
"... In accordance with Tarski point of view, in this chapter the theory of closure operators is proposed as a unifying tool for fuzzy logics. Indeed, let F be the set of formulas of a given language. Then an abstract fuzzy logic is defined by a fuzzy semantics (i.e. a class of valuations of the formula ..."
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In accordance with Tarski point of view, in this chapter the theory of closure operators is proposed as a unifying tool for fuzzy logics. Indeed, let F be the set of formulas of a given language. Then an abstract fuzzy logic is defined by a fuzzy semantics (i.e. a class of valuations
Indexed identity and fuzzy set theory
, 1999
"... We introduce the concept of indexed identity, where the usual notion of identity is a particular case. Our mathematical framework allows us a generalized method for ‘indexing ’ predicates, which corresponds to ‘fuzzification ’ of properties, in an intuitive sense. It can be established a relationshi ..."
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relationship between this indexed mathematics and fuzzy mathematics. We show some few examples that illustrate our ideas. 1
THE FUZZY SET THEORY FOR ANALYSING THERMAL COMFORT (°)
"... Researchers involved in studying problems concerning the builtup environment face an objective complexity, of easy instrumental evaluation, and a subjective complexity which is psychophysiological concerning human beings with different individual reactions to the same exposure conditions. We are d ..."
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. Considering the thermohygrometrical aspect within the environmental comfort evaluation, this paper looks into the possibility to apply the fuzzy set theory to deal with subjective data, which are imprecise and nonabsolute in themselves. In fact, the fuzzy set theory allows use of linguistic variables
Intuitionistic Fuzzy Set Theory in Medical Imaging
"... Abstract—Medical imaging has been an active area of research where abnormalities are detected non invasively. But dealing with medical images is a challenging task. Due to the complexity in the images, many of the structures are hardly visible; various soft computing techniques are applied by differ ..."
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by different researchers to process medical images. In order to carry out this task, intuitive ways have been found out to interpret and describe the inherent ambiguity and vagueness in the medical images in terms of intuitionistic fuzzy set theory. The efficiency of the use of intuitionistic fuzzy set theory
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