Possibilistic expert systems and process control utilizing fuzzy logic

• US 7,389,281 B2
• Filed: 04/06/2004
• Issued: 06/17/2008
• Est. Priority Date: 06/25/1998
• Status: Expired due to Fees

• Current Assignee: Postlinear Management Incorporated
• Original Assignee: Postlinear Management Incorporated
• Inventors: Strobel Stewart, Lorna Ruth, Hendriks, legal representative, Daams, Johanna Maria
• Primary Examiner(s): Vincent; David
• Assistant Examiner(s): BUSS, BENJAMIN J
• Application Number:
  US10/817,883
• Publication Number:
  US 20050075995A1
• Time in Patent Office: 1,533 Days
• Field of Search: 706/47, 706/52, 706/900
• US Class Current: 706/52
• CPC Class Codes: G06N 5/048 Fuzzy inferencing

Abstract

An explicit assumption of continuity is used to generate a fuzzy implication operator, which yields an envelope of possibility for the conclusion. A single fuzzy rule A B entails an infinite set of possible hypothese A′B′ whose degree of consistency with the original rule is a function of the “distance” between A and A′ and the “distance” between B and B′. This distance may be measured geometrically or by set union/intersection. As the distance between A and A′ increases, the possibility distribution B* spreads further outside B somewhat like a bell curve, corresponding to common sense reasoning about a continuous process. The manner in which this spreading occurs is controlled by parameters encoding assumptions about (a) the maximum possible rate of change of B′ with respect to A′ (b) the degree of conservatism or speculativeness desired for the reasoning process (c) the degree to which the process is continuous of chaotic.

Claims

1. In a computer-based risk management system utilizing fuzzy logic, a method for generating an indication of risk, said method comprising:

a) said system receiving an expert defined rule entered by a user into said risk management system mapping at least one rule input A to at least one rule output B;

b) said system receiving a data input A′ and

a data output B′

from said user;

c) comparing said data input A′

with said rule input A to determine a first degree of mismatch d_x between said rule input A and said data input A′

;

d) assigning a function M_P characterizing the way in which an envelope of possibility B_P spreads as a function of the first degree of mismatch d_x between said rule input A and said data input A′

, said envelope of possibility being indicative of possible outputs;

e) using said first degree of mismatch and said function M_P to calculate a second degree of mismatch d_y between said rule output B and a said data output B′

;

f) calculating said envelope of possibility B_P using said function M_P and said data output B′

;

g) calculating an envelope of belief B_B indicating a degree to which said data output B′

is true, using said first degree of mismatch d_x between said rule input A and said data input A′

;

h) said system receiving additional expert input having at least one assertion G required to be proven true;

i) said system receiving an expert defined minimum degree of proof H_min of said assertion G;

j) comparing said envelope of belief B_B and said assertion G to determine an actual degree of proof H for said assertion G;

k) comparing said required minimum degree of proof H_min and said actual degree of proof H to generate a first conclusion about an acceptability of said actual degree of proof H for said assertion G;

l) said system receiving an expert defined minimum degree of ignorance l_min for said assertion G;

m) calculating an actual degree of ignorance l for said assertion G according to a difference between said envelope of belief B_B and said envelope of possibilities B_P;

n) comparing said minimum degree of ignorance l for said assertion G and said actual degree of ignorance l for said assertion G to generate a second conclusion about an acceptability of said degree of ignorance l for said assertion G;

o) said system receiving an expert defined minimum degree of possibility K_min for said assertion G;

p) comparing said envelope of possibilities B_P and said assertion G to calculate an actual degree of possibility K for said assertion G;

q) comparing said actual degree of possibility K and said required minimum degree of possibility K_min to generate a third conclusion about an acceptability of said degree of possibility K for said assertion G;

r) generating said indication of risk by evaluating said conclusions against said assertion G, said indication of risk indicating whether or not said assertion G is good; and

s) said system outputting said indication of risk.

2. The method according to claim 1, wherein a plurality of rules are obtained and said envelope of possibility B_P considers outputs from each of said plurality of rules.

3. The method according to claim 1, wherein said envelope of possibility B_P is established by consideration of outputs of adjacent rules.

4. The method according to claim 3, wherein said envelope of possibility is established through interpolation between one or more of said outputs of adjacent rules.

5. The method according to claim 3, wherein said envelope of possibility is established through extrapolation between one or more of said outputs of adjacent rules.

6. The method according to claim 1 including providing a set of examples associated with said rule to provide a plurality of possible outputs for said input.

7. The method according to claim 1 wherein said first degree of mismatch d_x is established based on similarity between selected data input A′

and said rule input A.

8. The method according to claim 1 wherein a parameter is applied to limit said data output B′

and thereby modify said envelope of possibility B_P.

9. The method according to claim 1 wherein a subset of said envelope of belief B_B is established by applying a parameter to qualify said rule input A and data input A′

.

10. The method according to claim 1 wherein a subset of said envelope of possibility B_P is established by applying a parameter to qualify said data output B′

.

11. A computer-based risk management system utilizing fuzzy logic for generating an indication of risk, said system comprising a computer readable medium having computer executable instructions for:

a) receiving an expert defined rule entered into said possibilistic system mapping at least one rule input A to at least one rule output B;

b) receiving a data input A′ and

a data output B′

c) comparing said data input A′

with said rule input A to determine a first degree of mismatch d_x between said rule input A and said data input A′

;

d) assigning a function M_P characterizing the way in which an envelope of possibility B_Pspreads as a function of the first degree of mismatch d_x between said rule input A and said data input A′

, said envelope of possibility being indicative of possible outputs;

e) using said first degree of mismatch and said function M_P to calculate a second degree of mismatch d_y between said rule output B and a said data output B′

;

f) calculating said envelope of possibility B_P using said function M_P and said data output B′

;

g) calculating an envelope of belief B_B indicating a degree to which said data output B′

is true, using said first degree of mismatch d_x between said rule input A and said data input A′

;

h) receiving additional expert input having at least one assertion G required to be proven true;

i) receiving an expert defined minimum degree of proof H_min of said assertion G;

j) comparing said envelope of belief B_B and said assertion G to determine an actual degree of proof H for said assertion G;

k) comparing said required minimum degree of proof H_min and said actual degree of proof H to generate a first conclusion about an acceptability of said actual degree of proof H for said assertion G;

l) receiving an expert defined minimum degree of ignorance l_min for said assertion G;

m) calculating an actual degree of ignorance l for said assertion G according to a difference between said envelope of belief B_B and said envelope of possibilities B_P;

n) comparing said minimum degree of ignorance l for said assertion G and said actual degree of ignorance l for said assertion G to generate a second conclusion about an acceptability of said degree of ignorance l for said assertion G;

o) receiving an expert defined minimum degree of possibility K_min for said assertion G;

p) comparing said envelope of possibilities B_P and said assertion G to calculate an actual degree of possibility K for said assertion G;

q) comparing said actual degree of possibility K and said required minimum degree of possibility K_min to generate a third conclusion about an acceptability of said degree of possibility K for said assertion G;

r) generating said indication of risk by evaluating said conclusions against said assertion G, said indication of risk indicating whether or not said assertion G is good; and

s) outputting said indication of risk.

12. The possibilistic expert system according to claim 11, wherein a plurality of rules are obtained and said envelope of possibility B_P considers outputs from each of said plurality of rules.

13. The possibilistic expert system according to claim 11, wherein said envelope of possibility B_P is established by consideration of outputs of adjacent rules.

14. The possibilistic expert system according to claim 13, wherein said envelope of possibility is established through interpolation between one or more of said outputs of adjacent rules.

15. The possibilistic expert system according to claim 13, wherein said envelope of possibility is established through extrapolation between one or more of said outputs of adjacent rules.

16. The possibilistic expert system according to claim 11 including providing a set of examples associated with said rule to provide a plurality of possible outputs for said input.

17. The possibilistic expert system according to claim 11 wherein said first degree of mismatch d_x is established based on similarity between selected data input A′

and said rule input A.

18. The possibilistic expert system according to claim 11 wherein a parameter is applied to limit said data output B′

and thereby modify said envelope of possibility B_P.

19. The possibilistic expert system according to claim 11 wherein a subset of said envelope of belief B_B is established by applying a parameter to qualify said rule input A and data input A′

.

20. The possibilistic expert system according to claim 11 wherein a subset of said envelope of possibility B_P is established by applying a parameter to qualify said data output B′

.