| Title of paper:
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Fundamental justification of intuitionistic fuzzy logic and of interval-valued fuzzy methods
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| Author(s):
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| Misha Koshelev
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| Massachusetts Institute of Technology (MIT), 3 Ames Street Box #57, Cambridge, MA 02138, USA
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| Vladik Kreinovich
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| Department of Computer Science University of Texas at El Paso, El Paso, TX 79968
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| Bhuvan Rachamreddy
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| Department of Computer Science University of Texas at El Paso, El Paso, TX 79968
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| Haris Yasemis
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| Department of Computer Science University of Texas at El Paso, El Paso, TX 79968
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| Krassimir Atanassov
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| CLBME - Bulgarian Academy of Sciences, Sofia-1113, P.O.Box 12, Bulgaria
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| Presented at:
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2nd ICIFS, Sofia, 3—4 Oct. 1998
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| Published in:
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"Notes on Intuitionistic Fuzzy Sets", Volume 4 (1998) Number 2, pages 42—46
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| Download:
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 PDF (2789 Kb, File info)
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| Abstract:
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Traditional fuzzy logic uses a real number d(S) from the interval [0,1] to represent a person's degree of certainty in a statement S. There exist different methods of eliciting these degrees; most of these methods are based on the assumption that a person is able, for every two statements, to choose a statement with the larger degree of certainty. In real life, people are not always capable of a meaningful choice; as a result, instead of numerical values, we get intervals.
For example, in intuitionistic fuzzy logic, the degree of confidence is described by two numbers: d+(S) represents the degree of certainty in S, while d−(S) represents the degree of certainty in its negation ¬S. This can be expressed as an interval d(S) = [d+(S), 1 − d−(S)] of possible values of degree of certainty.
In this paper, we show that there is a fundamental reason for this inability, and thus, the use of interval-valued degrees of belief in intuitionistic fuzzy logic is justified.
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| References:
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