## Engineering Design Calculations with Fuzzy Parameters. Fuzzy Sets and Systems (1992)

Citations: | 37 - 13 self |

### BibTeX

@MISC{Wood92engineeringdesign,

author = {Kristin L. Wood and Kevin N. Otto and Erik K. Antonsson},

title = {Engineering Design Calculations with Fuzzy Parameters. Fuzzy Sets and Systems},

year = {1992}

}

### Years of Citing Articles

### OpenURL

### Abstract

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.

### Citations

597 |
Fuzzy Sets and Systems: Theory and Application
- Dubois, Prade
- 1980
(Show Context)
Citation Context ...ted averages. In [7], Dong and Wong also review the non-linear programming technique developed by Baas and Kwakernaak [2], an analytical procedure for L-R membership functions due to Dubois and Prade =-=[8]-=-, an investigation of fuzzy number algebraic properties by Mizumoto and Tanaka [13], and an investigation of fuzzy algebra in terms of interval operations by Nakamura [15]. These techniques and invest... |

578 |
Methods and Applications of Interval Analysis
- Moore
- 1979
(Show Context)
Citation Context ...ta [12, 23] describe an analytical method of calculating a fuzzy output (application of Zadeh’s extension principle) from imprecise inputs. This method is based on α-cuts [12] and interval arithmetic =-=[14]-=-. Although the method is straight-forward in its approach, the manipulation of symbols and the solution of expressions that include high order polynomials, both in the numerator and denominator (for e... |

563 |
Theory of Probability
- Jeffreys
- 1948
(Show Context)
Citation Context ...trol or choice over. A manufacturing tolerance is an example of such an uncertainty. Stochastic uncertainties are usually represented and manipulated using the probability calculus (Cox [5], Jeffreys =-=[11]-=-). Design imprecision, on the other hand, concerns the choice of design parameter values used to describe an artifact or process. For example, in the preliminary design of equipment for processing sol... |

397 |
Possibility Theory : An Approach to Computerized Processing of Uncertainty
- Dubois, Prade
- 1988
(Show Context)
Citation Context ...2] propose a method for analytical arithmetic with fuzzy numbers. They introduce the properties of fuzzy numbers, along with an α-cut formulation of the operations on number sets. In [9] and again in =-=[10]-=-, Dubois and Prade review the correctedness of using α-cut calculations. This has been shown in earlier work by Negoit¸ă and Ralescu [16], and as well by Nguyen [17] for 2 variable problems, and in [1... |

163 |
Introduction to Fuzzy Arithmetic: Theory and Applications
- Kaufmann, Gupta
- 1985
(Show Context)
Citation Context ...nts for implementing the methodology, including equation parsing, symbolic manipulation, and so on, is beyond the scope of this document. 2.2 Computation of the Extension Principle Kaufmann and Gupta =-=[12, 23]-=- describe an analytical method of calculating a fuzzy output (application of Zadeh’s extension principle) from imprecise inputs. This method is based on α-cuts [12] and interval arithmetic [14]. Altho... |

119 |
The algebra of probable inference
- Cox
- 1961
(Show Context)
Citation Context ... no direct control or choice over. A manufacturing tolerance is an example of such an uncertainty. Stochastic uncertainties are usually represented and manipulated using the probability calculus (Cox =-=[5]-=-, Jeffreys [11]). Design imprecision, on the other hand, concerns the choice of design parameter values used to describe an artifact or process. For example, in the preliminary design of equipment for... |

56 |
Fuzzy weighted averages and implementation of the extension principle, Fuzzy Sets and Systems 21
- Dong, Wong
- 1987
(Show Context)
Citation Context ...y discrete and analytical methods exist for carrying out extended operations with fuzzy sets (or fuzzy numbers). The Fuzzy Weighted Average (FWA) algorithm, as presented by W.M. Dong and F.S. Wong in =-=[7]-=-, outlines a simple and efficient algorithm that is useful for carrying out engineering design calculations. We extend this algorithm below for generalized real functions of fuzzy variables, referring... |

55 | Computations with Imprecise Parameters in Engineering Design: Background and Theory," Engineering Design Research Laboratory Report 88-01, California I stitute of Technology - Wood, Antonsson |

53 |
A note on the extension principle for fuzzy set
- Nguyen
(Show Context)
Citation Context ...n number sets. In [9] and again in [10], Dubois and Prade review the correctedness of using α-cut calculations. This has been shown in earlier work by Negoit¸ă and Ralescu [16], and as well by Nguyen =-=[17]-=- for 2 variable problems, and in [18] by Novák. It is presented clearly in a recent work by Buckley and Qu [4]. Dong and Wong [7], as described above, present a computational algorithm for implementin... |

47 |
Introduction to Design
- Asimow
- 1962
(Show Context)
Citation Context ...formance. 1 Introduction 1.1 Uncertainty in Engineering Design Engineering design may be viewed as a goal-directed process, with the generally recognized stages of synthesis, evaluation, and decision =-=[1, 3]-=-. Other authors [19, 21] define engineering design, instead, as a mapping of the functional description of an artifact or process to a form description. While these definitions focus on different aspe... |

46 |
Vertex method for computing functions of fuzzy variables. Fuzzy Sets Syst
- Dong, HC
- 1987
(Show Context)
Citation Context ...ties by Mizumoto and Tanaka [13], and an investigation of fuzzy algebra in terms of interval operations by Nakamura [15]. These techniques and investigations will not be discussed here. Dong and Shah =-=[6]-=- also present a computational algorithm for implementing the extension principle. The application domain for this algorithm emphasizes purely algebraic expressions. They also introduce an algorithm fo... |

39 |
Engineering design, The design council
- Pahl, Beitz
- 1984
(Show Context)
Citation Context ...on 1.1 Uncertainty in Engineering Design Engineering design may be viewed as a goal-directed process, with the generally recognized stages of synthesis, evaluation, and decision [1, 3]. Other authors =-=[19, 21]-=- define engineering design, instead, as a mapping of the functional description of an artifact or process to a form description. While these definitions focus on different aspects of design as a human... |

38 | Rating and ranking of multiple-aspect alternatives using fuzzy sets, Automatica 13
- Baas, Kwakernaak
- 1977
(Show Context)
Citation Context ...plications. This is compounded by the fact that the exact solution to the analytical application of the extension principle can be shown to be equivalent to an unwieldy non-linear programming problem =-=[2]-=-. A discrete numerical approach is therefore necessary to meet the computational requirements for handling many design parameters. This section will discuss a useful numerical technique, the LIA algor... |

37 |
Applications of Fuzzy Sets to Systems Analysis
- Negoiţă, Ralescu
- 1975
(Show Context)
Citation Context ...mulation of the operations on number sets. In [9] and again in [10], Dubois and Prade review the correctedness of using α-cut calculations. This has been shown in earlier work by Negoit¸ă and Ralescu =-=[16]-=-, and as well by Nguyen [17] for 2 variable problems, and in [18] by Novák. It is presented clearly in a recent work by Buckley and Qu [4]. Dong and Wong [7], as described above, present a computation... |

28 |
Computation of rational interval functions
- Skelboe
- 1974
(Show Context)
Citation Context ...e α-cut on dn. 4. If the above condition is true, compare the calculated extrema ξl with P αj from the LIA algorithm such that P αj =[min(p αj ,ξl),max(p αj ,ξl)] for all l. 12Alternatively, Skelboe =-=[20]-=- developed an algorithm for computing interval expressions with internal extrema. Skelboe’s approach, which implements Theorem A.3 and Theorem A.4, relies on a subdivision of the argument intervals of... |

26 |
Fuzzy numbers: an overview, in
- Dubois, Prade
- 1987
(Show Context)
Citation Context ...mann and Gupta [12] propose a method for analytical arithmetic with fuzzy numbers. They introduce the properties of fuzzy numbers, along with an α-cut formulation of the operations on number sets. In =-=[9]-=- and again in [10], Dubois and Prade review the correctedness of using α-cut calculations. This has been shown in earlier work by Negoit¸ă and Ralescu [16], and as well by Nguyen [17] for 2 variable p... |

23 |
Fuzzy Logic and Approximate
- Zadeh
- 1975
(Show Context)
Citation Context ...erences on the performance parameters with peak preferences on the design parameters, a required feature for the transformation. The imprecision transformation is based on Zadeh’s extension principle =-=[27]-=- to calculate the preference of any performance parameter value pj: µ(pj) = { sup {min {µ(d1),...,µ(dN)}|d1,...,dN :pj =fj(d1,...,dN)} 0 if {d1,...,dN |pj =fj(d1,...,dN)}=∅ where d1,...,dN are values ... |

12 |
Synthesis of Schematic Description
- Ulrich, Seering
- 1989
(Show Context)
Citation Context ...on 1.1 Uncertainty in Engineering Design Engineering design may be viewed as a goal-directed process, with the generally recognized stages of synthesis, evaluation, and decision [1, 3]. Other authors =-=[19, 21]-=- define engineering design, instead, as a mapping of the functional description of an artifact or process to a form description. While these definitions focus on different aspects of design as a human... |

11 |
A Method for Representing and Manipulating Uncertainties in Preliminary Engineering Design
- Wood
- 1989
(Show Context)
Citation Context ...neering design uncertainty is comprised of design imprecision (uncertainty in choosing among alternatives) and stochastic uncertainty (usually pertaining to manufacturing and measurement limitations) =-=[23]-=-. Stochastic uncertainty arises from a lack of exact knowledge of a parameter due to some process the designer has no direct control or choice over. A manufacturing tolerance is an example of such an ... |

7 |
A Formal Method for Representing Uncertainties in Engineering Design
- Wood, Otto, et al.
- 1990
(Show Context)
Citation Context ...eferences at each performance parameter’s functional requirement level. This involves trading off conflicting goals and is beyond the scope of this document, but the interested reader should refer to =-=[23, 26]-=-. The design paradigm presented so far assumes the preliminary design process can be carried out in a forward manner. Of course, there will be iteration among the steps presented. Observations in the ... |

5 |
Some properties of fuzzy numbers
- Mizumoto, Tanaka
- 1979
(Show Context)
Citation Context ...ue developed by Baas and Kwakernaak [2], an analytical procedure for L-R membership functions due to Dubois and Prade [8], an investigation of fuzzy number algebraic properties by Mizumoto and Tanaka =-=[13]-=-, and an investigation of fuzzy algebra in terms of interval operations by Nakamura [15]. These techniques and investigations will not be discussed here. Dong and Shah [6] also present a computational... |

4 |
On using α-cuts to evaluate fuzzy equations
- Buckley, Qu
- 1990
(Show Context)
Citation Context ... This has been shown in earlier work by Negoit¸ă and Ralescu [16], and as well by Nguyen [17] for 2 variable problems, and in [18] by Novák. It is presented clearly in a recent work by Buckley and Qu =-=[4]-=-. Dong and Wong [7], as described above, present a computational algorithm for implementing the extension principle. The application domain for this algorithm emphasizes purely algebraic expressions, ... |

4 |
M.From Idea to Working Model
- WILSON, WILSON
- 1970
(Show Context)
Citation Context ...and more-informed decisions. The model implies the designer arrives at candidate solutions by the designer’s own creative inferencing, using, for example, traditional techniques of divergent thinking =-=[1, 22]-=-. Yet these models so determined are not completely described, and the designer cannot determine which candidate offers the best alternative to pursue into the subsequent, expensive detailed-design st... |

3 |
A structural design process: philosophy and methodology
- BECKER
- 1973
(Show Context)
Citation Context ...formance. 1 Introduction 1.1 Uncertainty in Engineering Design Engineering design may be viewed as a goal-directed process, with the generally recognized stages of synthesis, evaluation, and decision =-=[1, 3]-=-. Other authors [19, 21] define engineering design, instead, as a mapping of the functional description of an artifact or process to a form description. While these definitions focus on different aspe... |

2 |
Extension of algebraic calculus on fuzzy numbers using alpha-level sets
- Nakamura
- 1984
(Show Context)
Citation Context ...tions due to Dubois and Prade [8], an investigation of fuzzy number algebraic properties by Mizumoto and Tanaka [13], and an investigation of fuzzy algebra in terms of interval operations by Nakamura =-=[15]-=-. These techniques and investigations will not be discussed here. Dong and Shah [6] also present a computational algorithm for implementing the extension principle. The application domain for this alg... |