Weighted wedge defuzzification for conceptual system design evaluation

• US 6,763,337 B1
• Filed: 03/03/2000
• Issued: 07/13/2004
• Est. Priority Date: 03/05/1999
• Status: Expired due to Fees

• Current Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Original Assignee: Lockheed Martin Corporation (Martin Marietta Corporation)
• Inventors: Verma, Dinesh, Smith, Caroline
• Primary Examiner(s): Starks, Jr., Wilbert L.
• Assistant Examiner(s): BOOKER, KELVIN
• Application Number:
  US09/518,213
• Time in Patent Office: 1,593 Days
• Field of Search: 706/8, 706/9, 706/1, 706/2
• US Class Current: 706/9
• CPC Class Codes: G05B 13/0275 using fuzzy logic only
• CPC Class Codes: G06N 20/00 Machine learning
• CPC Class Codes: G06N 7/02 using fuzzy logic computing arrangements based on biological models G06N3/00; computing arrangements using knowledge-based models G06N5/00

Abstract

A method, and a system applying the method, for an exact and computationally efficient solution for defuzzification uses linear and non-linear weighted wedge approaches. Fuzzy numbers are used to represent parameters in a number of applications, including design dependent parameters (DDPs) for a project in particular. A defuzzification technique is used within the domain of fuzzy logic, fuzzy set theory, and multi-valued logic to overcome the problem of the lack of absolute ordering of a fuzzy number representation. The requirement profile for the DDP (the fuzzy representation of customer requirements) is compared to the anticipation profile for the DDP (the fuzzy representation of expected performance) in three dimensions. In two dimensions, the area of overlap between the DDP requirement profile and the DDP anticipation profile represents how well the customer requirements have been met. In three dimensions, the area of overlap is projected onto a wedge to obtain a volume of overlap, in order to give higher preference to higher DDP values than lower DDP values in the area of overlap, for a more accurate analysis. The wedge can also be made non-linear in shape, to provide added sensitivity analysis to desired results.

Claims

1. A method for determining compliance for a feasible design dependent parameter (DDP) between an anticipated DDP fuzzy profile and a required DDP fuzzy profile, comprising:

creating a weighted wedge by projecting an image of a surface common to the anticipated DDP fuzzy profile and the required DDP fuzzy profile at an angle from said surface; and

finding an overlap volume of said weighted wedge between a projection of the anticipated DDP fuzzy profile onto said image and a projection of the required DDP fuzzy profile onto said image and

wherein said volume of said anticipated DDP fuzzy profile is precisely measured using the formula

2. The method according to claim 1, wherein said angle is calculated in a manner to make said overlap volume greater if any one of the anticipated DDP fuzzy profile and the required DDP fuzzy profile have projections with higher respective preference levels.

3. The method according to claim 1, further compromising:

generating a feasibility index for said DDP by dividing said overlap volume by a volume obtained from said projection of the anticipated DDP fuzz profile.

4. The method according to claim 1, wherein said common surface is a linear projection plane.

5. The method according to claim 1, wherein said common surface is a non-linear projection plane designed to provide relatively greater differences between one or more of said overlap volumes at higher respective preference levels for any one of the anticipated DDP fuzzy profiles and the required DDP fuzzy profiles.

6. The method according to claim 1, further comprising:

determining a feasible design space for a design concept by finding one or more DDPs for said concept;

determining one or more feasible DDPs for said design space, comprising applying said creating step and said finding step one or more times, and

rating and ranking feasible design concepts by consolidating relative priorities of said one or more feasible DDPs.

7. The method according to claim 6, wherein said feasible design space determining step comprises:

determining a fuzzy quality function deployment (QFD) parameter comprising said DDPs.

8. The method according to claim 6, wherein said feasible design space determining step comprises any one of:

determining an Improvement Potential and Necessity (IPN) measure providing insight into an extent of improvement desirable and necessary for each said DDP; and

determining a Tolerance of Fuzziness (TOF) measure providing insight into how much fuzziness can be tolerated by each said DDP.

9. The method according to claim 6 wherein said determining one or more feasible DDPs step comprises:

generating one or more feasibility indices for said one or more feasible DDPs by dividing overlap volumes thereof by volumes obtained from projections of anticipated DDP fuzzy profiles thereof, and wherein said rating and ranking step comprises;

consolidating relative priorities of said one or more feasible DDPs with said one or more feasibility indices.

10. The method according to claim 1, wherein the finding step comprises:

calculating said overlap volume of said weighted wedge ${\left[\frac{A^2<br><br>x^3}{6}+\frac{{\mathrm{ABx}}^2}{2}+\frac{B^2<br><br>x}{2}\right]}_{x=x_L}^{x_U}$

where A and B respectively represent gradients of either said anticipated DDP fuzzy profile or said required DDP fuzzy profile,

wherein x_L, represents a lower integral limit for said variable x, and wherein x_U represents an upper integral limit for said variable x.

11. The method according to claim 1, wherein the DDP is selected from the group consisting of:

reliability;

maintainability;

environmental compliance;

visual quality;

data transfer rate;

audio/visual synchronization;

color capability;

skill level for operation;

skill level for maintenance;

audio quality;

communication initiation time;

maximum group size;

simultaneous groups active;

maximum membership size;

design/production cost;

operating cost;

support cost;

maintenance cost;

safety;

disposability; and

communication security.

12. A system for determining compliance for a feasible design dependent parameter (DDP) between an anticipated DDP fuzzy profile and a required DDP fuzzy profile, comprising:

creating device that creates a weighted wedge by projecting an image of a surface common to the anticipated DDP fuzzy profile and the required DDP fuzzy profile at an angle from said surface; and

an overlap finding device that finds an overlap volume of said weighted wedge between a projection of the anticipated DDP fuzzy profile onto said image and projection of the required DDP fuzzy profile onto said image and

wherein said volume of said anticipated DDP fuzzy profile is precisely measured using the formula

 

V_TOTAL(I,n)=V_L+V_R

wherein $V_R=\frac{1}{6}<br><br>\left\{a_2^2<br><br>\left(x_5^3-x_2^3\right)+3<br><br>a_2<br><br>b_2<br><br>\left(x_5^2-x_2^2\right)+3<br><br>b_2^2<br><br>\left(x_5-x_2\right)\right\}$

and $V_L=\frac{1}{6}<br><br>\left\{a_1^2<br><br>\left(x_2^3-x_1^2\right)+3<br><br>a_1<br><br>b_1<br><br>\left(x_2^2-x_1^2\right)+3<br><br>b_1^2<br><br>\left(x_2-x_1\right)\right\}.$

13. The system according to claim 12, wherein said angle is calculated in a manner to make said overlap volume greater if any one of the anticipated DDP fuzzy profile and the required DDP fuzzy profile have projections with higher respective preference levels.

14. The system according to claim 12, further comprising:

feasibility index generating device that generates a feasibility index for said DDP by dividing said overlap volume by a volume obtained from said projection of the anticipated DDP fuzzy profile.

15. The system according to claim 12, wherein said common surface is a linear projection plane.

16. The system according to claim 12, wherein said common surface is a non-linear projection plane designed to provide relatively greater differences between one or more of said overlap volumes at higher respective preference levels for any one of the anticipated DDP fuzzy profiles and the required DDP fuzzy profiles.

17. The system according to claim 12, further comprising:

first device that determines a feasible design space for a design concept by finding one or more DDPs for said concept;

second device that determines one or more feasible DDPs for said design space, comprising applying said creating step and said finding step one or more times; and

third device that rates and ranks feasible design concepts by consolidating relative priorities of said one or more feasible DDPs.

18. The system according to claim 17, wherein said first device comprises:

device that determines a fuzzy quality function deployment (QFD) parameter comprising said DDPs.

19. The system according to claim 17, wherein said first device comprises any one of:

device that determines an Improvement Potential and Necessity (IPN) measure providing insight into an extent of improvement desirable and necessary for each said DDP; and

device that determines a Tolerance of Fuzziness (TOF) measure providing insight into how much fuzziness can be tolerated by each said DDP.

20. The system according to claim 17, wherein said second device comprises:

device that generates one or more feasibility indices for said one or more feasible DDPs by dividing overlap volumes thereof by volumes obtained from projections of anticipated DDP fuzzy profiles thereof, and wherein said third device comprises;

device that consolidates relative priorities of said one or more feasible DDPs with said one or more feasibility indices.

21. The system according to claim 12, wherein said overlap finding device comprises:

a device that calculates said overlap volume of said weighted wedge as ${\left[\frac{A^2<br><br>x^3}{6}+\frac{{\mathrm{ABx}}^2}{2}+\frac{B^2<br><br>x}{2}\right]}_{x=x_L}^{x_U}$

where A and B respectively represent gradients of either said anticipated DDP fuzzy profile or said required DDP fuzzy profile,

wherein x_L represents a lower integral limit for said variable x, and

wherein x_U represents an upper integral limit for said variable x.

22. The system according to claim 12, wherein the DDP is selected from the group consisting of:

reliability;

maintainability;

environmental compliance;

visual quality;

data transfer rate;

audio/visual synchronization;

color capability;

skill level for operation;

skill level for maintenance;

audio quality;

communication initiation time;

maximum group Size;

simultaneous groups active;

maximum membership size;

design/production cost;

operating cost;

support cost;

maintenance cost;

safety;

disposability; and

communication security.

23. A computer program product for determining compliance for a feasible design dependent parameter (DDP) between an anticipated DDP fuzzy profile and a required DDP fuzzy profile,

wherein said computer program product comprises a computer useable medium having computer program logic stored therein, said computer program logic comprising:

means for enabling a computer to create a weighted wedge by projecting an image of a surface common to the anticipated DDP fuzzy profile and the required DDP fuzzy profile at an angle from said surface; and

means for enabling a computer to find an overlap volume of said weighted wedge between a projection of the anticipated DDP fuzzy profile onto said image and a projection of the required DDP fuzzy profile onto said image and

wherein said volume of said anticipated DDP fuzzy profile is precisely measured using the formula