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86
Engineering Design Calculations with Fuzzy Parameters. Fuzzy Sets and Systems
, 1992
"... Uncertainty in engineering analysis usually pertains to stochastic uncertainty, i.e.,variance in product or process parameters characterized by probability (uncertainty in truth). Methods for calculating under stochastic uncertainty are well documented. It has been proposed by the authors that other ..."
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Cited by 43 (13 self)
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Uncertainty in engineering analysis usually pertains to stochastic uncertainty, i.e.,variance in product or process parameters characterized by probability (uncertainty in truth). Methods for calculating under stochastic uncertainty are well documented. It has been proposed by the authors that other forms of uncertainty exist in engineering design. Imprecision, or the concept of uncertainty in choice, is one such form. This paper considers real-time techniques for calculating with imprecise parameters. These techniques utilize interval mathematics and the notion of α-cuts from the fuzzy calculus. The extremes or anomalies of the techniques are also investigated, particularly the evaluation of singular or multi-valued functions. It will be shown that realistic engineering functions can be used in imprecision calculations, with reasonable computational performance.
Probabilistic Arithmetic
, 1989
"... This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The long-term goal is to ..."
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Cited by 27 (0 self)
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This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The long-term goal is to be able to handle random problems (such as the determination of the distribution of the roots of random algebraic equations) using algorithms which have been developed for the deterministic case. To this end, in this thesis we survey a number of previously proposed methods for calculating convolutions and representing probability distributions and examine their defects. We develop some new results for some of these methods (the Laguerre transform and the histogram method), but ultimately find them unsuitable. We find that the details on how the ordinary convolution equations are calculated are
FUZZY SETS: HISTORY AND BASIC NOTIONS
"... This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh&a ..."
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Cited by 18 (0 self)
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This paper is an introduction to fuzzy set theory. It has several purposes. First, it tries to explain the emergence of fuzzy sets from an historical perspective. Looking back to the history of sciences, it seems that fuzzy sets were bound to appear at some point in the 20th century. Indeed, Zadeh's works have cristalized and popularized a concern that has appeared in the first half of the century, mainly in philosophical circles. Another purpose of the paper is to scan the basic definitions in the field, that are required for a proper reading of the rest of the volume, as well as the other volumes of the Handbooks of Fuzzy Sets Series. This Chapter also contains a discussion on operational semantics of the generally too abstract notion of membership function. Lastly, a survey of variants of fuzzy sets and related matters is provided.
A Qualitative Simulation Approach for Fuzzy Dynamical Models. A CM Transactions on Modelling and Computer Simulation 4(4
, 1994
"... This article deal with simulation of approximate models of dynamic systems. We propose an approach that is appropriate when the uncertainty intrinsic in some models cannot be reduced by traditional identification techniques, due to the impossibility of gathering experimental data about the system it ..."
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Cited by 16 (1 self)
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This article deal with simulation of approximate models of dynamic systems. We propose an approach that is appropriate when the uncertainty intrinsic in some models cannot be reduced by traditional identification techniques, due to the impossibility of gathering experimental data about the system itself. The article presents a methodology for qualitative modeling and simulation of approximately known systems. The proposed solution is based on the Fuzzy Sets theory, extending the power of traditional numerical-logical methods. We have implemented a fuzzy simulator that integrates a fuzzy, qualitative approach and traditional, quantitative methods.
Gradual Numbers and their Application to Fuzzy Interval Analysis
, 2008
"... We introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual num ..."
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Cited by 16 (4 self)
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We introduce a new way of looking at fuzzy intervals. Instead of considering them as fuzzy sets, we see them as crisp sets of entities we call gradual (real) numbers. They are a gradual extension of real numbers, not of intervals. Such a concept is apparently missing in fuzzy set theory. Gradual numbers basically have the same algebraic properties as real numbers, but they are functions. A fuzzy interval is then viewed as a pair of fuzzy thresholds, which are monotonic gradual real numbers. This view enable interval analysis to be directly extended to fuzzy intervals, without resorting to-cuts, in agreement with Zadeh’s extension principle. Several results show that interval analysis methods can be directly adapted to fuzzy interval computation where end points of intervals are changed into left and right fuzzy bounds. Our approach is illustrated on two known problems: computing fuzzy weighted averages, and determining fuzzy floats and latest starting times in activity network scheduling.
Is The Success Of Fuzzy Logic Really Paradoxical? Or: Towards The . . .
- INTERNATIONAL JOURNAL OF INTELLIGENT SYSTEMS
, 1994
"... The formal concept of logical equivalence in fuzzy logic, while theoretically sound, seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions. Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all sub- ..."
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Cited by 16 (10 self)
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The formal concept of logical equivalence in fuzzy logic, while theoretically sound, seems impractical. The misinterpretation of this concept has led to some pessimistic conclusions. Motivated by practical interpretation of truth values for fuzzy propositions, we take the class (lattice) of all sub-intervals of the unit interval [0,1] as the truth value space for fuzzy logic, subsuming the traditional class of numerical truth values from [0,1]. The associated concept of logical equivalence is stronger than the traditional one. Technically, we are dealing with much smaller set of pairs of equivalent formulas, so that we are able to check equivalence algorithmically. The checking is done by showing that our strong equivalence notion coincides with the equivalence in logic programming.
On Hardware Support For Interval Computations And For Soft Computing: Theorems
, 1994
"... This paper provides a rationale for providing hardware supported functions of more than two variables for processing incomplete knowledge and fuzzy knowledge. The result is in contrast to Kolmogorov's theorem in numerical (non-fuzzy) case. ..."
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Cited by 9 (5 self)
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This paper provides a rationale for providing hardware supported functions of more than two variables for processing incomplete knowledge and fuzzy knowledge. The result is in contrast to Kolmogorov's theorem in numerical (non-fuzzy) case.
On the use of the Choquet integral with fuzzy numbers in Multiple Criteria Decision Aiding
- EUSFLAT- LFA 2005
, 2005
"... This paper presents a multiple criteria decision aiding approach in order to build a ranking on a set of alternatives. The partial evaluations of the alternatives on the points of view can be fuzzy numbers. The aggregation is performed through the use of a fuzzy extension of the Choquet integral. We ..."
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Cited by 9 (0 self)
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This paper presents a multiple criteria decision aiding approach in order to build a ranking on a set of alternatives. The partial evaluations of the alternatives on the points of view can be fuzzy numbers. The aggregation is performed through the use of a fuzzy extension of the Choquet integral. We detail how to assess the parameters of the aggregator by using alternatives which are well-known to the decision maker, and which originate from his domain of expertise.
COMBINATION OF ROUGH AND FUZZY SETS BASED ON α-LEVEL SETS
, 1997
"... A fuzzy set can be represented by a family of crisp sets using its α-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set a ..."
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Cited by 9 (1 self)
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A fuzzy set can be represented by a family of crisp sets using its α-level sets, whereas a rough set can be represented by three crisp sets. Based on such representations, this paper examines some fundamental issues involved in the combination of rough-set and fuzzy-set models. The rough-fuzzy-set and fuzzy-rough-set models are analyzed, with emphasis on their structures in terms of crisp sets. A rough fuzzy set is a pair of fuzzy sets resulting from the approximation of a fuzzy set in a crisp approximation space, and a fuzzy rough set is a pair of fuzzy sets resulting from the approximation of a crisp set in a fuzzy approximation space. The approximation of a fuzzy set in a fuzzy approximation space leads to a more general framework. The results may be interpreted in three different ways.
