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Generalized Fuzzy Theory with Two Fuzzy Membership Functions and Application to Medical Expert Systems

P. Venkata Subba Reddy

Abstract


Zadeh defined fuzzy set with membership function A = μA(x ) for the proposition of the type “ x is A”. Fuzzy set with single membership function is not sufficient to deal with uncertain information. The fuzzy set with two fuzzy membership functions will give more evidence to deal with uncertainty. In this paper, fuzzy set is defined by generalized fuzzy set A= { μABelief(x), μDisbelief(x)} with the two fuzzy membership functions based on Belief and Disbelief. The fuzzy inference and the fuzzy reasoning are studied with generalized fuzzy set. The fuzzy conditional inference for “ if … then …” and “if … then … else” are discussed with two fuzzy membership functions, also Fuzzy Certainty Factor is defined with difference between “Belief” and ”Disbelief “ membership functions to made as single fuzzy membership function. An Medical Expert System is discussed as one of the applications of Generalized fuzzy set. In EMYCIN, Belief anf Disbelief are defined with Probability. In this paper, generalized fuzzy sets are discussed for EMYCIN.

Keywords


Fuzzy Logic, Generalized Fuzzy Theory, Fuzzy Membership Functions, Fuzzy Belief, Fuzzy Disbelief, Fuzzy Inference, Fuzzy Reasoning.

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References


Z. Bubnicki, Analysis and Decision Making in Uncertain Systems, Springer Verlag, 2004.

Buchanan.B.G and E.H Sortliffe, Rule-Based Expert System: The MYCIN Experiments of the Stanford Heuristic Programming Project, Readings, Addition-Wesley, M.A,1984.

D. Dubois and H. Prade, “On several representations of an uncertain body of evidence”, In: Fuzzy information and decision processes, M.M.Gupta and E. Sanchez (Eds.), North-Holland, (1982) 167-181.

D. Dubois and H. Prade, Representation and combination of uncertainty with belief functions and possibility measures, Computational Intelligence 4(1988) 244-264.

D. Dubois and H. Prade, Non-Standard Theories of Uncertainty in Knowledge Representation and Reasoning, KR, (1994) 634-645.

D. Dubois, H. Fargier and H. Prade, Comparative uncertainty, belief functions and accepted beliefs, UAI, (1998)113-120.

D. Dubois and H. Prade, On the use of aggregation operations in information fusion processes, Fuzzy sets and Systems, 142(1)(2004)143-161.

Kaufmann and M.M. Gupta, Introduction to Fuzzy Arithmetic: Theory and Applications, New York: Von Nostrand, 1985.

M Mizumoto, F Fukmi and K Tanak, “Some Methods of Fuzzy Reasoning”, in Advances in Fuzzy set Theory and applications, M M Gupta, R R Ragade and R R Ragar(Eds.,), North-Holland, 1976.

REN Ping, “Generalized Fuzzy Sets and Representation of Incomplete Knowledge”, Fuzzy Sets and Systems, 36, (1990)91-96.

N. Rescher, Many-Valued Logic, McGrow-Hill, New York, 1969.

H. Prade , “ A Computational Approach to Approximate and Plausible Reasoning with Applications to Expert Systems”, IEEE Transactions on Pattern Analysis and Machine Intelligence, 7(1985)3-29.

Shafer, G, A Mathematical Theory of Evidence , Princeton, NJ, University Press, 1976.

Shafer, G, and J. Pearl, Readings in Uncertainty Reasoning, Los Altos, CA, Morgan-Kaufmann, 1990.

N.D. Singpurwalla and J.M. Booker, Membership functions and probability measures of fuzzy sets, Journal of the American Statistical Association, 99 (467) (2004) 867-889.

P. Smets, Imperfect Information: Imprecision and Uncertainty, Uncertainty Management in Information Systems, (1996)225-254.

P. Venkata Subba reddy, “Generalized Fuzzy Sets in Various Situations for Incomplete Knowledge, Proceedings FT&T 92, Durham 1992.

P. Venkata subba Reddy, “Fuzzy Modulations for Knowledge Representation and Distributed Automated Fuzzy Reasoning System”, International Journal of Computational Intelligence and Information Security, vol.1, no.2, pp.76-79,2010.

P. Venkata Subba reddy and M. Syam Babu, „Some Methods of Reasoning for Conditional Propositions”, Fuzzy Sets and Systems, vol.52, no.1, pp.1-22,1992.

P. Venkata Subba Reddy , Fuzzy Modeling and Natural Language Processing for Panini‟s Sanskrit Grammar, Journal of Computer Science and Engineering,Vol.1,no. 1,pp.99-101,2010.

P. Venkata Subba Reddy , “FUZZYALGOL: Fuzzy Algorithmic Language for designing Fuzzy Algorithms””, Journal of Computer Science and Engineering, Vol.2, no.2, pp.21-24, 2010.

P. Venkata Subba Reddy , “ Knowledge Representation for Fuzzy Reasoning Systems”, Journal of Computer Science and Engineering, Vol.4, no. 1, pp.29-31, 2010.

P. Venkata Subba Reddy, Fuzzy Medical Reasoning in Distributed Fuzzy Medical Expert Systems, CiiT International Journal of Fuzzy Systems, vol.3, No.2, pp.64-69, feb.2011

R.R. Yager, Uncertainty representation using fuzzy measures, IEEE Trans. on Systems, Man and Cybernetics, Part B. 32(2002)13-20.

J. Yen and R. Langari, Fuzzy Logic: Intelligence, Control and Information, Prentice Hall, 1st edition, 1998.

L. A Zadeh, “Calculus of Fuzzy Restrictions”, In Fuzzy Sets and their Applications to Cognitive and Decision Processes, L. A. Zadeh, King-Sun FU, Kokichi Tanaka and Masamich Shimura (Eds.), Academic Press, New York, (1975)1-40.

L.A. Zadeh, Fuzzy sets, In Control 8, 338-353, 1965.

L.A Zadeh , “ The role of fuzzy logic in the management if uncertainty in Medical Expert systems” Fuzzy sets and systems, 11, (1983),1983.

L.A. Zadeh, Probability measures of fuzzy events, Jour. Math. Analysis and Appl. 23(1968) 421-427.


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