ago, and eliminating terms involving the higher derivatives.

15.10 A typical fuzzy control rule might be

IF input is Small and rate is Large then control is

Negative;

In this rule input, rate, and control are ¬‚oating-point numbers; Small, Large,

and Negative are members of discrete fuzzy sets, linguistic variables, to

which membership functions are attached.

15.11 The notation is very compact; fuzzi¬cation and defuzzi¬cation are auto-

matic. However, the notation is quite in¬‚exible, and does not permit

making the discrete fuzzy sets available for use in later rules or for

program output.

15.12 Focused rules usually permit a fuzzy reasoning system to be built with a much

smaller number of rules than required by unfocused rules following the typical

fuzzy control rule pattern. Such rules also usually produce more reliable

outputs. The only disadvantage is that the programmer has to think a lot

harder; it is dif¬cult to construct such rules by data mining techniques.

15.13 Since many if not most computer programs use the standard array of

Boolean numerical comparison operators, it is not surprising that the

programs using fuzzy numbers require the fuzzy version of the common

Boolean numerical comparison operators.

15.14 Data-driven sequential-rule-¬ring programs retain all data in memory, in

case they are needed during backtracking. This means that if continuously

bringing in data on-line, available memory will be exhausted in a ¬nite

length of time.

15.15 Data-driven parallel-rule-¬ring programs do not retain deleted data or data

that has been later modi¬ed in memory; since there is no backtracking, old

TEAM LinG - Live, Informative, Non-cost and Genuine !

397

ANSWERS

data are not again needed. The result is that real-time on-line programs can

run inde¬nitely without over¬‚owing memory.

15.16 The major steps in a real-time on-line program are data acquisition; data

screening; data processing; output validity checks; and program output.

15.17 After development off-line using a fuzzy expert system shell, the program

can be recoded using a procedural language, possibly replacing fuzzy

logic with interval logic.

15.18 The ¬rst stage is to acquire data on disk so that the program can be written

and debugged off-line. If the program is to be closed-loop, a way of simu-

lating the process should be found so that the dynamics of a program run

can be checked. Processes may be simulated by a digital computer

program, an analog computer, or some other process model that will

accept the expert system output and produce a response that can be input

to the expert system.

TEAM LinG - Live, Informative, Non-cost and Genuine !

TEAM LinG - Live, Informative, Non-cost and Genuine !

REFERENCES

Anderson JR (1993). Rules of the Mind. Lawrence Erlbaum, Mahwah, New Jersey.

Baldwin JF, Martin TP, Pilsworth BW (1995). Fril”Fuzzy and Evidential Reasoning in

Arti¬cial Intelligence. Research Studies Press, Taunton, Somerset, England.

Brownston L, Farrell R, Martin N (1985). Programming Expert Systems in OPS5. Addison-

Wesley, Reading, Massachusetts.

Buchanan BG, Shortliffe EH, eds (1984). Rule-Based Expert Systems. Addison-Wesley,

Reading, Massachusetts.

Buckley JJ, Siler W (1998a). Echocardiogram analysis using fuzzy numbers and relations.

Fuzzy Sets and Systems 26: 373 “ 380.

Buckley JJ, Siler W (1998b). A new t-norm. Fuzzy Sets and Systems 100: 283 “ 290.

Buckley JJ, Siler W (1999). L-1 fuzzy logic. Fuzzy Sets and Systems 107: 309 “ 322.

Combs WE, Andrews JE (1998). Combinatorial rule explosion eliminated by a fuzzy rule

con¬guration. IEEE Trans. Fuzzy Systems 6(1): 1 “ 11.

Cox E (1999). The Fuzzy Systems Handbook: A Practitioner™s Guide to Building, Using and

Maintaining Fuzzy Systems. Morgan Kaufmann, Los Altos, California.

Cox E (2000). Fuzzy Logic for Business and Industry. Charles River Media, Boston.

de Silva CW (1995). Intelligent Control: Fuzzy Logic Applications. CRC Press, Boca Raton,

Florida.

Dempster AP (1967). Upper and lower probabilities induced by a multivalued mapping.

Annals Mathematical Statistics 38: 325“ 339.

Dubois D, Prade H (1988). Possibility Theory: An Approach to Computerized Processing of

Uncertainty. Plenum Press, New York.

Elkan D (XXX). The paradoxical success of fuzzy logic.

Feigenbaum EA, Buchanan BG (1993). DENDRAL and Meta-DENDRAL: roots of

knowledge systems and expert systems applications. Arti¬cial Intelligence 59:

233“ 240.

Fisher R (1936). The use of multiple measurements in taxonomic problems. Annals of

Eugenics 7 (part 2): 179 “188.

Forgy C, Rete L (1982). A fast algorithm for the many pattern/many object pattern match

problem. Arti¬cial Intelligence 19: 17“ 37.

Haykin S (1994). Neural Networks: A Comprehensive Foundation. Prentice-Hall, Englewood

Cliffs, New Jersey.

Jackson P (1999). Introduction to Expert Systems. Addison-Wesley, Reading, Massachusetts.

Fuzzy Experts Systems: Theory and Practice, by William Siler and James J. Buckley

ISBN 0-471-38859-9 Copyright # 2005 John Wiley & Sons, Inc.

399

TEAM LinG - Live, Informative, Non-cost and Genuine !

400 REFERENCES

Kandel A, ed (1991). Fuzzy Expert Systems. CRC Press, Boca Raton, Florida.

Kasabov NK (1998). Foundations of Neural Networks, Fuzzy Systems and Knowledge

Engineering. MIT Press, Cambridge, Massachusetts.

Kecman V (2001). Learning and Soft Computing: Support Vector Machines, Neural Net-

works, and Fuzzy Logic Systems (Complex Adaptive Systems). MIT Press, Cambridge,

Massachusetts.

Klir GJ, Yuan B (1995). Fuzzy Sets and Fuzzy Logic: Theory and Applications. Prentice-Hall

PTR, Upper Saddle River, New Jersey.

Klir GJ, Yuan B, eds (1996). Fuzzy Sets, Fuzzy Logic and Fuzzy Systems: Selected Papers by

Lot¬ A. Zadeh. World Scienti¬c, Singapore.

Mamdani EH (1976). Advances in the linguistic synthesis of fuzzy controller. International

Journal of Man-Machine Studies 8(6): 669“ 678.

McDermott J (1980). R1: an expert in the computing system domain. In Proceedings of the

National Conference on Arti¬cial Intelligence, 269“ 271.

Minsky M (1975). A framework for representing knowledge. In The Psychology of Computer

Vision, Winston PH, ed, McGraw-Hill, New York.

Mitchell TM (1997). Machine Learning. McGraw-Hill, New York.

Newell A, Simon HA (1972). Human Problem Solving. Prentice-Hall, Englewood Cliffs,

New Jersey.

Pedrycz W (1995). Fuzzy Sets Engineering. CRC Press, Boca Raton, Florida.

Quillian MR (1968). Semantic Memory. In Semantic Information Processing, Minsky M, ed,

227“ 270. MIT Press, Cambridge, Massachusetts.

Ruspini EH (1982). Possibility approaches for advanced information systems. Computer 15:

83“ 91.

Schank RC, Childers PG (1984). The Cognitive Computer: on Language, Learning and

Arti¬cial Intelligence. Pearson Addison-Wesley, New York.

Scott AC, Clayton JE, Gibson EL (1991). A Practical Guide to Knowledge Acquisition.

Addison-Wesley, New York.

Shortliffe EH (1976). Computer-Based Medical Consultations: MYCIN. Elsevier,

New York.

Siler W, Tucker D, Buckley J (1987). A parallel rule ¬ring production system with resolution

of memory con¬‚icts by weak fuzzy monotonicity, applied to the classi¬cation of multiple

objects characterized by multiple uncertain features. International Journal of Man-Machine

Studies 26: 321 “ 332.

Thomas SF (1995). Fuzziness and Probability. ACG Press, Wichita, Kansas.

Weinschenk JJ, Marks II RJ, Combs WE (2003). Layered URC fuzzy systems: a novel link

between fuzzy systems and neural networks. Proceedings of the IEEE International Joint

Conference on Neural Networks, Portland, Oreson: 2995“ 3000.

Zadeh LA (1965). Fuzzy sets. Information and Control 8: 338 “ 353.

Zadeh LA (1972). A fuzzy-set-theoretic interpretation of linguistic hedges. Journal of

Cybernetics 2: 4“ 34.

Zadeh LA (1974). On the analysis of large-scale systems. In “Fuzzy Sets and their Application

to Cognitive and Decision Processes”, Academic Press, New York.

TEAM LinG - Live, Informative, Non-cost and Genuine !

401