16-17 May 2019 • Sofia, Bulgaria

Submission: 1 February 2019 • Notification: 1 March 2019 • Final Version: 1 April 2019

# Issue:Fundamental justification of intuitionistic fuzzy logic and of interval-valued fuzzy methods

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Title of paper: Fundamental justification of intuitionistic fuzzy logic and of interval-valued fuzzy methods
Author(s):
 Misha Koshelev Massachusetts Institute of Technology (MIT), 3 Ames Street Box #57, Cambridge, MA 02138, USA Vladik Kreinovich Department of Computer Science University of Texas at El Paso, El Paso, TX 79968 Bhuvan Rachamreddy Department of Computer Science University of Texas at El Paso, El Paso, TX 79968 Haris Yasemis Department of Computer Science University of Texas at El Paso, El Paso, TX 79968 Krassimir Atanassov CLBME - Bulgarian Academy of Sciences, Sofia-1113, P.O.Box 12, Bulgaria
Presented at: 2nd ICIFS, Sofia, 3—4 Oct. 1998
Published in: Conference proceedings, "Notes on IFS", Volume 4 (1998) Number 2, pages 42—46
Abstract: 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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