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Computations with Imprecise Parameters in Engineering Design: Background and Theory
 ASME JOURNAL OF MECHANISMS, TRANSMISSIONS, AND AUTOMATION IN DESIGN
, 1989
"... A technique to perform design calculations on imprecise representations of parameters has been developed and is presented. The level of imprecision in the description of design elements is typically high in the preliminary phase of engineering design. This imprecision is represented using the fuzzy ..."
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Cited by 56 (18 self)
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A technique to perform design calculations on imprecise representations of parameters has been developed and is presented. The level of imprecision in the description of design elements is typically high in the preliminary phase of engineering design. This imprecision is represented using the fuzzy calculus. Calculations can be performed using this method, to produce (imprecise) performance parameters from imprecise (input) design parameters. The Fuzzy Weighted Average technique is used to perform these calculations. A new metric, called the γlevel measure, is introduced to determine the relative coupling between imprecise inputs and outputs. The background and theory supporting this approach are presented, along with one example.
Imprecision in Engineering Design
 ASME JOURNAL OF MECHANICAL DESIGN
, 1995
"... Methods for incorporating imprecision in engineering design decisionmaking are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The ..."
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Cited by 47 (6 self)
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Methods for incorporating imprecision in engineering design decisionmaking are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate setbased concurrent design.
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 37 (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 realtime techniques for calculating with imprecise parameters. These techniques utilize interval mathematics and the notion of αcuts from the fuzzy calculus. The extremes or anomalies of the techniques are also investigated, particularly the evaluation of singular or multivalued functions. It will be shown that realistic engineering functions can be used in imprecision calculations, with reasonable computational performance.
FORMALISMS FOR NEGOTIATION IN ENGINEERING DESIGN
, 1996
"... Engineering projects often undergo several design iterations before being completed. Information received from other groups working on a project (analysis, manufacturing, marketing, sales) will often necessitate changes in a design. The interaction between different groups associated with a design p ..."
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Cited by 24 (5 self)
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Engineering projects often undergo several design iterations before being completed. Information received from other groups working on a project (analysis, manufacturing, marketing, sales) will often necessitate changes in a design. The interaction between different groups associated with a design project often takes the form of informal “negotiation. ” This form of interaction commonly arises when engineering information is imprecise. The Method of Imprecision (MoI) is a formal method for the representation and manipulation of preliminary and imprecise design information. It provides a mechanism for the formalization of these informal negotiations. The nature and scope of informal negotiation in engineering is explored and discussed, and application of the MoI is illustrated with an example.
Implementing the Method of Imprecision: An Engineering Design Example
 In Proceedings of the Third IEEE International Conference on Fuzzy Systems (FUZZIEEE '94
, 1994
"... The Imprecise Design Tool (IDT) presented in this paper implements the method of imprecision, which incorporates the designer's uncertainty in choice into design calculations, using a mathematics derived from fuzzy sets. IDT is intended to be a computational tool for preliminary engineering des ..."
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Cited by 18 (10 self)
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The Imprecise Design Tool (IDT) presented in this paper implements the method of imprecision, which incorporates the designer's uncertainty in choice into design calculations, using a mathematics derived from fuzzy sets. IDT is intended to be a computational tool for preliminary engineering design.
The Empirical Variance of a Set of Fuzzy Intervals
 IEEE Int. Conf on Fuzzy Systems, Reno (Nevada
"... Abstract — The profile method gives a tool to perform fuzzy interval computation under a condition of local monotony of considered functions. This is a plain extension of interval analysis to fuzzy intervals, viewed as pairs of fuzzy bounds. This method yields exact results without applying interval ..."
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Cited by 15 (4 self)
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Abstract — The profile method gives a tool to perform fuzzy interval computation under a condition of local monotony of considered functions. This is a plain extension of interval analysis to fuzzy intervals, viewed as pairs of fuzzy bounds. This method yields exact results without applying interval analysis to αcuts. After a refresher on the notion of profile and its use in fuzzy interval analysis, we adapt the profile method to the computation of the empirical variance of a tuple of fuzzy intervals. To this end, we first reconsider results obtained by Ferson et al. on computation of the empirical variance of a set of intervals. Finally we apply our results to the definition of the variance of a single fuzzy interval,viewed as a family of its αcuts, and compare this definition to previous ones. I.
Including Imprecision in Engineering Design Calculations
 In Design Theory and Methodology – DTM ’94, volume DE68
, 1994
"... The Imprecise Design Tool (IDT) presented in this paper is a working computer implementation of the method of imprecision, a formal theory that represents preferences among design alternatives. An aircraft engine design example indicates how the IDT may be applied to support engineering design decis ..."
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Cited by 10 (6 self)
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The Imprecise Design Tool (IDT) presented in this paper is a working computer implementation of the method of imprecision, a formal theory that represents preferences among design alternatives. An aircraft engine design example indicates how the IDT may be applied to support engineering design decisions, using the Engine Development Cost Estimator provided by General Electric Aircraft Engines, Cincinnati, Ohio.
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 9 (3 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 tocuts, 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.
Optimization Methods for Calculating Design Imprecision
 In Advances in Design Automation
, 1995
"... The preliminary design process is characterized by imprecision: the vagueness of an incomplete design description. The Method of Imprecision uses the mathematics of fuzzy sets to explicitly represent and manipulate imprecise preliminary design information, enabling the designer to explore the space ..."
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Cited by 8 (6 self)
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The preliminary design process is characterized by imprecision: the vagueness of an incomplete design description. The Method of Imprecision uses the mathematics of fuzzy sets to explicitly represent and manipulate imprecise preliminary design information, enabling the designer to explore the space of alternative designs in the context of the designer and customer's preferences among alternatives. This paper introduces new methods to perform Method of Imprecision calculations for general nonmonotonic design evaluation functions that address the practical necessity to minimize the number of function evaluations. These methods utilize optimization and experiment design.