Fuzzy Sets in Engineering Design

1999 ◽  
pp. 57-117 ◽  
Author(s):  
Erik K. Antonsson ◽  
Hans-Jürgen Sebastian
Keyword(s):  
Fuzzy Sets ◽  
Engineering Design

Imprecision in Engineering Design

1995 ◽  
Vol 117 (B) ◽  
pp. 25-32 ◽  
Author(s):  
E. K. Antonsson ◽  
K. N. Otto
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Engineering Design ◽  
Cost Estimation ◽  
Formal Method ◽  
Concurrent Design ◽  
Design Decision ◽  
Design Cost ◽  
Formal Information

Methods for incorporating imprecision in engineering design decision-making 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 set-based concurrent design.

Fuzzy Set Based Models in Design Optimization

1988 ◽  
Author(s):  
A. R. Diaz
Keyword(s):  
Multiobjective Optimization ◽  
Design Optimization ◽  
Fuzzy Sets ◽  
Engineering Design ◽  
Goal Programming ◽  
Fuzzy Set ◽  
Optimization Problem ◽  
Traditional Methods ◽  
Multiobjective Problems

Abstract A formulation for multiobjective optimization for engineering design based on fuzzy sets is presented. Models for the optimization problem and operations to introduce model variations are described formally. Under a reasonable set of rules it is shown that solutions to fuzzy multiobjective problems are weakly efficient and can reproduce solutions obtained by traditional methods such as compromise and goal programming. Results are easily implemented in computations.

A Fuzzy Sets Approach to Computational Tools for Preliminary Engineering Design

1987 ◽  
Author(s):  
K. L. Wood ◽  
E. K. Antonsson
Keyword(s):  
Fuzzy Sets ◽  
Engineering Design ◽  
Data Driven ◽  
Preliminary Design ◽  
Engineering Structures ◽  
Design Decisions ◽  
Computational Tools ◽  
Alternative Technologies ◽  
Imprecise Parameters ◽  
Preliminary Phase

Abstract The primary goal of this research is to provide computational tools, or aids, to engineering designers, particularly for the preliminary phase of design. Such aids will be particularly useful in choosing between alternative technologies. Design choices of this nature are perhaps the most critical, and likely to be the most costly if in error. Our approach has been to aid preliminary design decisions with analysis tools developed for computations on imprecise parameters. Contemporary computers and algorithms are not well suited for manipulating imprecise descriptions of objects. To provide these basic tools, we are applying the mathematics of fuzzy sets. This approach (along with “data-driven programming”) appears to be well suited to our problem and has been applied to similar problems in analyzing civil engineering structures and failures.

Comparing Fuzzy and Probability Calculus for Representing Imprecision in Preliminary Engineering Design

1989 ◽  
Author(s):  
K. L. Wood ◽  
E. K. Antonsson ◽  
J. L. Beck
Keyword(s):  
Fuzzy Sets ◽  
Engineering Design ◽  
Stochastic Uncertainty ◽  
Probability Calculus ◽  
Fuzzy Calculus ◽  
Design Calculations

Abstract A technique to perform design calculations on imprecise representations of parameters using the calculus of fuzzy sets has been previously developed [17]. An analogous approach to representing and manipulating uncertainty in choosing among alternatives (imprecision) using probability calculus is presented and compared with the fuzzy calculus technique. We find that the fuzzy calculus is well suited to representing and manipulating the imprecision aspect of uncertainty, and probability is best used to represent stochastic uncertainty.

Imprecision in Engineering Design

1995 ◽  
Vol 117 (B) ◽  
pp. 25-32 ◽  
Author(s):  
E. K. Antonsson ◽  
K. N. Otto
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Engineering Design ◽  
Cost Estimation ◽  
Formal Method ◽  
Concurrent Design ◽  
Design Decision ◽  
Design Cost ◽  
Formal Information

Methods for incorporating imprecision in engineering design decision-making 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 set-based concurrent design.

Aggregation Functions for Engineering Design Trade-Offs

1995 ◽  
Author(s):  
Michael J. Scott ◽  
Erik K. Antonsson
Keyword(s):  
Fuzzy Sets ◽  
Engineering Design ◽  
Formal Theory ◽  
Preliminary Design ◽  
Design Information ◽  
Trade Offs ◽  
Aggregation Functions ◽  
Design Alternatives

Abstract The Method of Imprecision (MoI) is a formal theory for the manipulation of preliminary design information that represents preferences among design alternatives with the mathematics of fuzzy sets. Using the MoI, different design tradeoff strategies can be applied. To date, two aggregation functions have been developed for the MoI, one representing a compensating strategy and one a non-compensating strategy. Other research on aggregation functions on fuzzy sets has focused on two classes of functions that are not suitable for engineering design. The general restrictions on design-appropriate aggregation functions are discussed, and a family of functions ranging from the non-compensating min to the compensating product of powers is presented. An application to preliminary engineering design is given.

A First Class of Computational Tools for Preliminary Engineering Design

1988 ◽  
Author(s):  
K. L. Wood ◽  
E. K. Antonsson
Keyword(s):  
Fuzzy Sets ◽  
Engineering Design ◽  
Preliminary Design ◽  
Functional Requirement ◽  
Computational Tool ◽  
Computational Tools ◽  
Input Parameters ◽  
Implementation Scheme ◽  
Design Calculations ◽  
Fuzzy Parameters

Abstract Preliminary engineering design intrinsically consists of imprecise descriptions of the input parameters. We present new conceptual and algorithmic procedures for dealing with such imprecise descriptions. Specifically, a two-part method is outlined for performing design calculations on these “fuzzy” parameters, as well as determining a measure for the parameters’ coupling. By interpreting the input set of variables for preliminary design in terms of fuzzy sets, we demonstrate how the engineer may associate his subjective meaning with the input parameters and the output functional requirement, leading to the foundation of our approach. An example of the method highlights the primary issues and the implementation scheme as a computational tool.

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