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On the Possibility of Using Complex Values in Fuzzy Logic For Representing Inconsistencies
, 1996
"... In science and engineering, there are "paradoxical" cases when we have some arguments in favor of some statement A (so, the degree to which A is known to be true is positive (nonzero)), and we also have some arguments in favor of its negation :A, and we do not have enough information t ..."
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In science and engineering, there are "paradoxical" cases when we have some arguments in favor of some statement A (so, the degree to which A is known to be true is positive (nonzero)), and we also have some arguments in favor of its negation :A, and we do not have enough information to tell which of these two statements is correct. Traditional fuzzy logic, in which "truth values" are described by numbers from the interval [0; 1], easily describes such "paradoxical" situations: the degree a to which the statement A is true and the degree 1 \Gamma a to which its negation :A is true can be both positive. In this case, if we use traditional fuzzy &\Gammaoperations (min or product), the "truth value" a&(1 \Gamma a) of the statement A&:A is positive, indicating that there is some degree of inconsistency in the initial beliefs.
Which Truth Values in Fuzzy Logics Are Definable?
, 2001
"... In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0; 1]. There are only denumerable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this pap ..."
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In fuzzy logic, every word or phrase describing uncertainty is represented by a real number from the interval [0; 1]. There are only denumerable many words and phrases, and continuum many real numbers; thus, not every real number corresponds to some commonsense degree of uncertainty. In this paper, for several fuzzy logic, we describe which numbers are describing such degrees, i.e., in mathematical terms, which real numbers are definable in the corresponding fuzzy logic. 1 1
IntervalValued Fuzzy Control in Space Exploration
"... Abstract  This paper is a short overview of our NASAsupported research into the possibility of using intervalbased intelligent control techniques for space exploration. Intervalvalues fuzzy sets were introduced by L. Zadeh, J. A. Goguen, and especially by I. B. Türkşen; they were actively used ..."
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Abstract  This paper is a short overview of our NASAsupported research into the possibility of using intervalbased intelligent control techniques for space exploration. Intervalvalues fuzzy sets were introduced by L. Zadeh, J. A. Goguen, and especially by I. B. Türkşen; they were actively used in expert systems by L. Kohout. Before we proceed to explain how to use them in fuzzy control, let us first explain why we need to use them. I. Why intervals? Reasons Ia{c: Intervals naturally appear Ia. Traditional fuzzy control techniques start with the expert’s degree of belief that are represented by numbers from the interval [0; 1]. This use of numbers may be natural when we describe physical quantities, for which there exists a true value that can be, in principle, measured with greater and greater accuracy. However, for degrees of belief, numbers may not be the most adequate representation. Indeed, how are the existing knowledge elicitation techniques determine these numbers? One of the possible techniques is to ask an expert to estimate his or her degree of belief by a number on a scale, say, from 0 to 10. Then, when an expert estimates this degree of belief by choosing, say, 6, we take 6=10 = 0:6 as the numerical expression of the expert’s degree of belief. At first glance, this may sound like a reasonable assignment, but in reality, the fact that an expert has chosen 6 does not necessarily mean that the expert’s degree of belief is exactly equal to 0.6; it rather means that this degree of belief is closer to 0.6 than to the other values between which we have asked the expert to choose (i.e.,
Intelligent Control in Space Exploration: Interval Computations are Needed
"... Abstract — This paper is a short overview of our NASAsupported research into the necessity of using intervalbased intelligent control techniques for space exploration. This is a reasonably new application area for interval computations, and we hope that the overviewed results and problems will be ..."
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Abstract — This paper is a short overview of our NASAsupported research into the necessity of using intervalbased intelligent control techniques for space exploration. This is a reasonably new application area for interval computations, and we hope that the overviewed results and problems will be of some interest to the numerical computations community. This paper is a short version of our detailed report presented to NASA. I. Intelligent Control is Necessary for Space Exploration Control is necessary for space missions. For a space mission to be successful, it is vitally important to have a good control strategy for all possible situations. For example: • For a Space Shuttle, it is necessary to guarantee the success and smoothness of docking, the smoothness and fuel efficiency of trajectory control, etc. • For an automated planet mission, e.g., for a rover mission to Mars, it is important to control the spaceship’s trajectory, and after that, to control the rover so that it would be operable for the longest possible period of time. It is often difficult or impossible to apply methods of traditional control theory. In many complicated control situations, in particular, in many control situations related to space flights, methods of traditional control theory are difficult or even impossible to apply. The main reason for that difficulty is as follows: • For traditional control, we must know (more or less precisely) the properties of the controlled system.