markz@ssc.UUCP (Mark Zenier) (05/29/90)
In the past two weeks there have been several articles in the general media (Fortune, Business Week, Newsweek) on how the U.S. has yet again dropped the ball on an important technology - Fuzzy Logic. Can anyone recommend an applications oriented introduction to the field? markz@ssc.uucp
wdr@wang.com (William Ricker) (05/29/90)
markz@ssc.UUCP (Mark Zenier) writes: >Can anyone recommend an applications oriented introduction to the >field? [ - Fuzzy Logic.] Lofti Zadeh, founder of the field, endorsed Kurt Schmucker's tutorial by writing a glowing preface. It is easily the most readable introduction that would be useful. (Yes, this is the same Kurt Schmucker who did the OOPS for MAC book. I believe the book in question was his thesis.) The title was something like "Natural Language, Fuzzy Logic, & Computer Security". Check Books in Print or your local library card catalogue for exact reference. -- /bill ricker/ wdr@wang.com a/k/a wricker@northeastern.edu *** Warning: This account not authorized to express opinions ***
jim@se-sd.SanDiego.NCR.COM (Jim Ruehlin) (05/30/90)
In article <766@ssc.UUCP> markz@ssc.UUCP (Mark Zenier) writes: >In the past two weeks there have been several articles in the general media >(Fortune, Business Week, Newsweek) on how the U.S. has yet again dropped >the ball on an important technology - Fuzzy Logic. >Can anyone recommend an applications oriented introduction to the >field? Speaking of fuzzy logic, can anyone post pros/cons to this technique? I've heard that it's a good way to represent "partial ownership" of elements of a set. I've also heard that it's nothing more than probability theory (the rebuttal to this is that it's really more like "possibility theory"). The best explication of it I heard may be that it's a "user friendly" probability theory. However, if you look at the math at first it's hard to see why! Comments?? - Jim Ruehlin
wdr@wang.com (William Ricker) (05/31/90)
jim@se-sd.SanDiego.NCR.COM (Jim Ruehlin) writes: >Speaking of fuzzy logic, can anyone post pros/cons to this technique? >I've heard that it's a good way to represent "partial ownership" of >elements of a set. That is exactly what Fuzzy Sets represent. Fuzzy Logic is to Fuzzy Sets as Logic is to Set Theory in general. > I've also heard that it's nothing more than probability >theory (the rebuttal to this is that it's really more like "possibility >theory"). People also try to confuse it with compounded independant probabilties or Baysian probabilities; these are potential models for fuzzy arithmetics, but not usually the ideal ones. I like the phrase "possibility theory", but I'm not sure it is any more intuitive than "fuzzy set". >The best explication of it I heard may be that it's a "user friendly" >probability theory. However, if you look at the math at first it's hard >to see why! When Fuzzy Sets membership and Fuzzy Logic statements are translated into Liguistic Variables, then you have a "user friendly" theory. However, the fact that "really like bald" and "like really bald" don't commute does pose problems to some users; as does an age-gap in the connotation of (the fuzzy modifier function associated with) "like". See the Kurt Schmucker book I cited in my other article on this topic, for which I now supply a full bibliographic entry: Schmucker, Kurt J. /Fuzzy sets, natural language computations, and risk analysis./ Computer Science Press, 1983. 0-914894-38-?. My corporate library has it catalogued as QA 248.S345.1983 [Lib.Cong]; I credit their on-line cat for the bib. here (and blame it for the missing check digit on the ISBN -- which probably fell off the end due to the old Pub# for CSP, which has a new shorter number now). I recently picked up a used book on Fuzzy Logic & Expert Systems, but haven't read it yet, so I can't review it. I haven't tried to do anything fuzzy yet, as the project I bought Schmucker for died prematurely, but have considered implementing fuzzy sets in either Prolog or Smalltalk as extensions of the existing Set implementations. Prolog also has the nice feature of providing reasonable DCG (definite clause grammar) support, which should ease translation to & from liguistic variables. Perhaps I can remember to find the books at home and check their bibliographies for you-all. [[Support a 2nd Person Plural pronoun as well as a 3rd Person singular neutral-but-human!:-] /bill/ -- /bill ricker/ wdr@wang.com a/k/a wricker@northeastern.edu *** Warning: This account not authorized to express opinions ***
cjoslyn@bingvaxu.cc.binghamton.edu (Cliff Joslyn) (05/31/90)
In article <anhgux.67z@wang.com> wdr@wang.com (William Ricker) writes: >jim@se-sd.SanDiego.NCR.COM (Jim Ruehlin) writes: >> I've also heard that it's nothing more than probability >>theory (the rebuttal to this is that it's really more like "possibility >>theory"). >People also try to confuse it with compounded independant probabilties >or Baysian probabilities; these are potential models for fuzzy arithmetics, >but not usually the ideal ones. I like the phrase "possibility theory", >but I'm not sure it is any more intuitive than "fuzzy set". The Fuzzy world has a lot of correlates to the Classical world. Possibility Theory is a strict correlate to Probability Theory [Dubois and Prade 1988, Klir 1984]. While Zadeh [1978] identifies possibility distribution on a universe with a fuzzy set on that universe, possibility theory does not require fuzzy set theory [Shafer 1976]. The comment that fuzzy sets and possibility theory are nothing more than probability theory is rebutted directly by Klir [1989]. This view might be related to the fact that Shafer's Belief and Plausibility measures are derived from a probability measure on the power set of the power set of the universe, and that possibility measures are a class of plausibility measures. Possibility measures are also a class of non-additive fuzzy measures. Fuzzy measures do not necessarily have anything to do with fuzzy sets (alas). Possibility calculus is based on max-min algebra, not +/* algebra. And possibility distributions are normalized with a maximum of 1, not a sum to 1. This is in a sense a "local" property of one element of the distribution, not a "global" property of the whole distribution: a single element of a possibility distribution can be varied without varying any others. Thus possibility theory is useful where the universe of discourse is unknown, unbounded, or changing: introduction of a new "possibility" or changing an old one does not require rescaling of all existing distributions. Some simple semantic considerations argue for the concept of possibility distinct from that of probability. Following from Gaines and Kohout [1976], if we identify a positive possibility with a positive probability, then we are committed to a concept of possibility in which any possible event is "eventual": over a large finite time our uncertainty about the event occuring will become arbitrarily small. But we usually work with a concept of possibility which does not entail this. Certainly all probable event are possible, but the converse is not true. Also, we subjectively construct our uncertainty assesments in a local way, without rescaling all other options each time a new thought comes to mind. Possibility distributions are used to model situations where uncertainty is characterized by vagueness or non-specificity, as opposed to a decision among a set of distinct choices [Klir 1989]. A possibilistic process is a direct generalization of a non-deterministic process. A stochastic process is not. There is now a possibilistic information theory, where the U-uncertainty is a unique correlate to the Shannon entropy [Higashi and Klir 1982, Klir and Mariano 1987] and a direct generalization of the Hartley entropy. Klir has recently proposed [1990] a Principle of Uncertainty Invariance through which transformations from stochastic to possibilistic systems and vice versa can be made without loss of information. Also, since the max-min calculus is substantially more computationally efficient than +/*, possibilistic models are frequently more tractable then stochastic ones. If people have a further interest, I can email or post a copy of my dissertation prospectus on "Possibilistic State Machines" or an extensive annotated bibliography. Dubois D and Prade H: (1989) _Possibility Theory_ Gaines, Brian and Kohout: (1976) "The Logic of Automata", Int. J. Gen. Sys., v. 2:4, 191-208 Higashi, Masahiko and Klir, George: (1982) "Measures of Uncertainty and Information Based on Possibility Distributions", Int. J. Gen. Sys., v. 9 Klir, George: (1984) "Possibilistic Information Theory", Cybernetics and Systems Research, v. 2, ed. R. Trappl ------------: (1989) "Is There More to Uncertainty Than Some Probability Theorists Would Have Us Believe?", Int. J. Gen. Sys. v. 15, 347-378 ------------: (1990) "A Principle of Uncertainty Invariance", J. Approximate Reasoning, v. 17:2 Klir, George, and Mariano: (1987) "On the Uniqueness of Possibilitic Measures of Uncertainty and Information", Fuzzy Sets and Systems, v. 24, 197-219 Shafer, Glen: (1976) _A Mathematical Theory of Evidence_ Zadeh, Lofti: (1978) "Fuzzy Sets as the Basis for a Theory of Possibility", Fuzzy Sets and Systems, v. 1, 3-28 O-------------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large, cjoslyn@bingvaxu.cc.binghamton.edu | Systems Science, SUNY Binghamton, Box 1070, Binghamton NY 13901, USA V All the world is biscuit shaped. . . -- O-------------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large, cjoslyn@bingvaxu.cc.binghamton.edu | Systems Science, SUNY Binghamton, Box 1070, Binghamton NY 13901, USA V All the world is biscuit shaped. . .
groh@fsucs.cs.fsu.edu (Jim Groh) (06/01/90)
In article <766@ssc.UUCP>, markz@ssc.UUCP (Mark Zenier) writes: >In the past two weeks there have been several articles in the general media >(Fortune, Business Week, Newsweek) on how the U.S. has yet again dropped >the ball on an important technology - Fuzzy Logic. > >Can anyone recommend an applications oriented introduction to the >field? > >markz@ssc.uucp Although not particularly application oriented the book _Fuzzy_Mathematical_Techniques_with_Applications by Abraham Kandel isbn # 0-201-11752-5, Addison Wesley Publishing Co. 1986 is an excellant starting point. In addition its bibliography is worth the price of the book. (disclaimer: Although Dr. Kandel is the chairman of my department I have read the book and it is very good) -- + Jim Groh + Worlds Oldest Gradual Student + + Florida State Univ. + "Where does he get those wonderful toys?" + + groh@sig.cs.fsu.edu + -- The Joker -- + + voice 904-644-8721 + reduced to 4 lines, don't want to be rude +
cjoslyn@bingvaxu.CC.BINGHAMTON.EDU (Cliff Joslyn) (06/04/90)
References to the fuzzy literature, FYI and edification. These are, of course, highly slanted towards my work and interests. However, I believe that the references to introductory and general works are representative. For beginners I'd reccommend Negoita 1981, Dubois + Prade 1980, Kandel 1986, Kandel + Lee 1979, and Klir + Folger 1987. O-------------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large, cjoslyn@bingvaxu.cc.binghamton.edu | Systems Science, SUNY Binghamton, Box 1070, Binghamton NY 13901, USA V All the world is biscuit shaped. . . Journals: /Fuzzy Sets and Systems/ /J. of Approximate Reasoning/ Aubin, JP: "Fuzzy Games", in: /Systems and Control Encyclopedia/, pp. 1913-1917 Baldwin, JF: (1985) "Fuzzy Sets and Expert Systems", /Information Sciences/, v. 36 Bezdek, James C: ed. (1987) /Analysis of Fuzzy Information: Mathematics + Logic/, v. 1 of 3, CRC Press, Boca Raton Black, M: (1937) "Vagueness: An Exercise in Logical Analysis", /Philosophy of Science/, v. 4, pp. 427-455 Probably the best discussion of the meaning of vagueness and its importance in science and philosophy. Solid introduction of most fuzzy systems concepts. Bobylev, VN: (1990) "Possibilistic Argument for Irreversibility", /Fuzzy Sets + Systems/, v. 34, pp. 73-80 Buckley, JJ: (1986) "A Fuzzy Expert System", /Fuzzy Sets and Systems/, v. 20 Buckley, JJ, and Tucker, Douglas: (1987) "Extended Fuzzy Relations: Application to Fuzzy Exp. Sys", /Int. J. Approximate Reasoning/, v. 1, Butnariu, D: (1988) "Autonomous Evolutive Systems w/Ambiguous States", in: /Fuzzy Logic in Knowledge-Based Sys./, ed. MM Gupta et. al., pp. 229-246, North-Holland, Amsterdam Cao, Hong Xing: (1987) "Fuzzy Verification of Weather Forecasts + Climate Sim.", in: /Analysis of Fuzzy Information/, v. III, ed. James Bezdek, CRC Press, Boca Raton Comparison of fuzzy vs. other methods for evaluating the success of predictions of weather forecast models. Cavallo, Roger E, and Klir, George: (1982) "Reconstruction of Possibilistic Behavior Systems", /Fuzzy Sets and Systems/, v. 8 Chanas, : (1989) ""On possibilistic coin-flip"", /Fuzzy Sets and Systems/, NOTE: From John Simms Cheesman, P: "Probabilistic vs. Fuzzy Reasoning", in: /Uncertainty in Artificial Intell./, ed. LN Kanal, JF Lemmer, pp. 85-102, North-Holland, Amsterdam An anti-fuzzy position. Chen, Yung Yaw, and Tsu, Chin Tsao: (1989) "Description of the Dynamical Behavior of Fuzzy Systems", /IEEE Trans. on Sys., Man + Cyb./, v. 19:4, pp. 745-755 Cell-to-cell mapping to describe long-term behavior of fuzzy control system seen as a fuzzy dynamical system. Dal Cin, M: (1975) "Fuzzy-State Automata: Stability and Fault Tolerance", /Int. J. Computer and Info. Sci./, v. 4, pp. 63-80 (1975) "Modification Tolerance of Fuzzy-State Automata", /Int. J. Computer and Infor. Sci/, v. 4, pp. 81-93 De Luca, A, and Termini, S: (1972) "Def. of Nonprob. Ent. in Setting of Fuzzy Set Theory", /Information and Control/, v. 20, pp. 301-312 First definition of fuzzy entropy. Dubois, D: (1987) "Fuzzy Numbers: An Overview", in: /Analysis of Fuzzy Information/, v. 1 of 3, pp. 3-39, CRC Press, Boca Raton Dubois, D, and Prade, H: "Set Theoretic View Of. . .", /Int. J. Gen. Sys./, v. 12:3 Relation between fuzzy sets and measures. "A Class of Fuzzy Measures Based on Triangle Inequalitie", /Int. J. Gen. Sys./, v. 8 On relation between fuzzy sets and measures. (1980) /Fuzzy Sets and Systems: Theory and Applications/, Academic Press, New York First overview textbook of fuzzy theory. Highly recommended. Dubois, D, and Prade, Henri: (1983) "Unfair Coins + Necessity Measures", /Fuzzy Sets + Systmes/, v. 10, pp. 15-20 Towards a possibilistic interpretation of histograms. An interesting but ultimately poor method for probability to possibility conversion. Dubois, D, and Prade, : (1988) /Possibility Theory/, Plenum Press, New York Overview and text on fuzzy theory, possibility theory, and applications. Dutta, Amitava: (1985) "Reasoning with Imprecise Knowledge in Expert Systems", /Information Science/, v. 37 Forbes, : /Logic of Possibility/, NOTE: Suggestion from Klir Gaines, Brian R: (1983) "Precise Past - Fuzzy Future", /Int. J. Man-Machine Studies/, v. 19, pp. 117-134 Gaines, Brian R, and Kohout, Ladislav J: (1976) "Logic of Automata", /Int. J. Gen. Sys./, v. 2:4, pp. 191-208 Logical bases of all automata; Rescher's Probability Logic as the basis of fuzzy, stochastic, and non-deterministic automata; mixed discrete-continuous logical models; relations to modal logic; toplogical and algebraic models. Gaines, Brian R, and Shaw, M.L.: (1985) "Systemic Foundations for Reasoning in Expert Systems", in: /Approximate Reasoning in Exp. Sys./, ed. Gupta, M. et. al., North-Holland, Amsterdam On fuzzy and modal logics. Gaines, Brian R, and Shaw, MLG: (1985) "From Fuzzy Logic to Expert Systems", /Information Science/, v. 36 Good overview of methodology. Goodman, IR: "Fuzzy Sets as Equivalence Classes of Random Sets", in: /Fuzzy Sets and Possibility Theory/, ed. Yager Goodman, IR, and Nguyen, : (1986) /Uncertainty Models for Knowledge-Based Systems/, NOTE: Chapter 3++ Gordon, Jean, and Shortliffe, Edward: (1984) "Dempster-Shafer Theory of Evidence", in: /Rule Based Expert Systems/, ed. BruceBuchanan+E.Shor, Addison Wesley, Reading MA Gupta, MM, and Yamakawa, T: eds. (1988) /Fuzzy Logic in Knowledge-Based Systems/, North-Holland, Amsterdam eds. (1988) /Fuzzy Computing/, North-Holland, Amsterdam Haavind, Robert: ed. /Fuzzy Logic/, in: /PC Computing/, v. 9/89, pp. 147-149 Good survey of some applications of fuzzy control theory. Henkind, Steven J, and Harrison, Malcolm C: (1988) "Analysis of Four Uncertainty Calculi", /IEEE Trans. Man Sys. Cyb./, v. 18:5, pp. 700-714 On Bayesian, Dempster-Shafer, Fuzzy Set, and MYCIN methods of uncertainty management. Higashi, Masahiko, and Klir, George: (1982) "Measures of Unc. and Inf. Based on Poss. Distributions", /Int. J. Gen. Sys./, v. 9 First definition of U-uncertainty, the unique measure of possibilistic information. (1984) "Resolution of Finite Fuzzy Relation Equations", /Fuzzy Sets and Systems/, v. 13 (1984) "Reconstruction Families of Possibilistic Structure Sys.", /Fuzzy Sets and Systems/, v. 12 Hirota, Kaoru, and Kazuhiro, Ozawa: (1989) "Concept of the Fuzzy Flip-Flop", /IEEE Trans. on Sys., Man + Cyb./, v. 19:5, pp. 980-997 Theory and hardware implementations of fuzzy correlates to classical switching circuits. Hirota, Kaoru, and Zama, KO: (1989) "Fuzzy Flip-Flop and Fuzzy Registers", /Fuzzy Sets and Systems/, v. 32, pp. 139-148 Hisdal, E: (1978) "Conditional Possibilities Independence + Noninteraction", /Fuzzy Sets + Systems/, v. 1:4, pp. 283-297 First general treatment of conditional possibility. Hu, Xiang En: "Dynamic Fuzzy Sets", /Fuzzy Mathematics/, v. 5:4, pp. 95-104 Hummel, RA, and Manevitz, LM: (1987) "Combining Bodies of Dependent Information", in: /Proc. 1987 Int. Joint Conf. on AI/, pp. 1015-1017, NOTE: From Klir Joslyn, Cliff: /Artificial Approx. Reasoning: Fuzzy Theory in ExpertSys/, NOTE: For SS 517 Jumarie, Guy: (1983) "Entropy of Fuzzy Events Revisitted", /Cybernetica/, v. 26:2, pp. 99-116 (1987) "New Concepts in Information Theory", /Physica Scripta/, v. 35:2, pp. 220-224 Kandel, A: (1986) /Fuzzy Mathematical Techniques with Applications/, Addison-Wesley Kandel, A, and Lee, A: (1979) /Fuzzy Switching and Automata/, Crane Russak, New York Another very good text on fuzzy systems and processes. Kaufmann, A., and Gupta, M.M.: (1985) /Introduction to Fuzzy Arithmetic/, Reinhold, New York Klir, George: (1984) "Possibilistic Information Theory", in: /Cybernetics and Systems Research/, v. 2, ed. R. Trappl (1989) "Is There More to Uncert. than Some Prob. Theor. Believe", /Int. J. Gen. Sys./, v. 15, pp. 347-378 Presented to the 8th Maximum Entropy Workshop in Cambridge, Spring 1988. Critical arguments on relation between probability and general uncertainty theory. Excellent review of Dempster-Shafer theory. (1990) "Principle of Uncertainty Invariance", /J. Approximate Reasoning/, v. 17:2 Isomorphisms from possibilistic to stochastic systems preserving informational properties. Klir, George, and Behzad, Parviz: (1986) "Gen. Reconstruction Characteristics of Prob.+Poss. Sys.", /Int. J. Man-Machine Studies/, v. 25 Klir, George, and Folger, Tina: (1987) /Fuzzy Sets, Uncertainty, and Information/, Prentice Hall Primary, excellent text on fuzzy systems theory and extended information theory. Klir, George, and Mariano, M: (1987) "On Uniqueness of Poss. Measures of Uncertainty + Inf.", /Fuzzy Sets + Systems/, v. 24, pp. 197-219 Key proofs in possibilistic information theory. Kloeden, PE: (1982) "Fuzzy Dynamic Systems", /Fuzzy Sets and Systems/, v. 7, pp. 275-296 Mathematical development of fuzzy dynamical systems on crisp, complete, locally compat metric space. Fuzzy attainability, trajectories. Kosko, B: /"On fuzzy automata"/ ""On fuzzy vs. Prob"", /Information Sciences/ Kruse, R, and Meyer, KD: (1988) /Statistics with Vague Data/, Kluwer Lee, Newton S., and Grize, Yves L.: (1987) "Quant. Model for Reasoning Under Unc. in Know-Based ES", /Int. J. Intelligent Systems/, v. 2:15 Looney, Carl G: (1988) "Fuzzy Petri Nets for Rule-Based Decisionmaking", /IEEE Trans. on Sys., Man + Cyb./, v. 18:1, pp. 178-183 Negoita, CV: (1989) "Rev: Fuzzy Sets, Uncertainty, + Information by G. Klir", /Kybernetes/, v. 18:1, pp. 73-74 Good analysis of the significance of fuzzy set theory. Negoita, CV, and Ralescu, DA: (1975) /Applications of Fuzzy Sets to Systems Analysis/, Birkhauser, Stuttgart Negotia, CV: (1981) /Fuzzy Systems/, Abacus Press, Tunbridge-Wells Simple, coherent introduction to fuzzy systems theory. Nguyen, HT: (1978) "On Conditional Possibility Distributions", /Fuzzy Sets and Systems/, v. 1:4 Second definition of conditional possibility, contrary to Hisdal. Oh, Sang-Bong, and Kim, W. et. al.: (1990) "Approach to Causal Modeling in Fuzzy Environemnt + Appl", /Fuzzy Sets + Systems/, v. 35, pp. 43-55 Pedrycz, W: (1981) "On Approach to the Analysis of Fuzzy Systmes", /Int. J. of Control/, v. 34, pp. 403-421 Ramer, Arthur: (1989) "Conditional Possibility Measures", /Cybernetics and Systems/, v. 20, pp. 233-247 Later update of definitions of conditional possibility. (1990) "Axioms of Uncertainty Measures: Dependence + Indep.", /Fuzzy Sets + Systems/, v. 35, pp. 185-196 Roberts, DW: (1989) "Analysis of Forest Succession with Fuzzy Graph Theory", /Ecological Modeling/, v. 45, pp. 261-274 Ruspini, Enrique H: (1989) "Semantics of Vague Knowledge", /Rev. Int. de Systemique/, v. 3:4, pp. 387-420 Santos, E: (1968) "Maximin Automata", /Information Control/, v. 13, pp. 363-377 (1972) "On Reductions of Maximin Machines", /J. Math. Anal. Appl./, v. 40, pp. 60-78 Santos, E, and Wee, WG: (1968) "General Formulation of Sequential Machines", /Information Control/, v. 12, pp. 5-10 Shafer, Glen: (1976) /A Mathematical Theory of Evidence/, Princeton U., Princeton On the foundations of extended information theory, in particular extended probabilities, Dempster-Shafer evidential inference, and possibility theory. (1987) "Belief Functions and Possibility Measures", in: /Analysis of Fuzzy Information/, v. 1 of 3, pp. 51-85, CRC Press, Boca Raton Shahinpoor, M: (1982) "Mathematical Modelling of theFuture for Complex Systems", /Mathematical Modelling/, v. 3, pp. 153-160 Sims, John R, and Wang, Zhenyuan: (1990) "Fuzzy Measures and Fuzzy Integrals: An Overview", /Int. J. Gen. Sys./, v. to appear Smithson, Michael: (1988) /Ignorance and Uncertainty: Emerging Paradigms/, Springer-Verlag, New York Modern philosphical treatment, fuzzy. Strat, TM: (1984) "Continuous Belief Functions for Evidential Reasoning", in: /Proc. 1984 Am. Assoc. for AI/, pp. 308-313 Walley, P, and Fine, TL: (1979) "Varieties of Model (Classificatory) and Compar. Prob.", /Synthese/, v. 41, pp. 321-374 On fuzzy chance. Wang, G, and et. al., : (1989) "Dynamic Fuzzy Sets and Fuzzy Processes", in: /Proc. 3rd IFSA Conference/, pp. 276-279 Wang, Paul P, and Chang, SK: eds. (1980) /Fuzzy Sets/, Plenum, New York Wang, Zhenyuan: (1989) /Fuzzy Measure Theory/, NOTE: To be published Wechler, W: (1978) /Concept of Fuzziness in Automata and Language Theory/ Wee, WG, and Fu, KS: (1969) "Formulation of Fuzzy Aut.+Appl. as Model of Learn. Sys.", /IEEE Trans. Sys. Sci. Cyb./, v. 5, pp. 215-223 Whalen, Thomas, and Schott, Brian: (1985) "Alternative Logics for Approximate Reasoning in Exp.Sys", /Int. J. Man-Machine Studies/, v. 22 Wong, GA, and Shen, DWC: "On Learning Behavior of Fuzzy Automata", /Advances in Cyb. and Sys./, v. 2, pp. 885 Yen, John: (1989) "Gertis: Dempster-Shafer App. to Diagnosing Hier. Hyp.", /Comm. ACM/, v. 32:5, pp. 573-585 Zadeh, Lofti A: (1965) "Fuzzy Sets and Systems", in: /Systems Theory/, ed. J. Fox, pp. 29-37, Polytechnic Press, Brooklyn NY (1968) "Probability Measures of Fuzzy Events", /J. Math. Analysis + Applications/, v. 10, pp. 421-427 (1973) "Outline of a New Approach to Analysis of Complex Sys.", /IEEE Trans. on Sys., Man + Cyb./, v. 3 A motivation for using fuzziness in dealing with very complex systems is discussed in detail in terms of linguistic variables. (1975) /Fuzzy Sets + Appl. to Cognitive + Decision Processes/, Academic Press (1978) "Fuzzy Sets as the Basis for a Theory of Possibility", /Fuzzy Sets and Systems/, v. 1, pp. 3-28 Seminal paper on possibility theory. (1982) "Fuzzy Systems Theory: Framework for Anal. of Buer. Sys.", in: /Sys. Meth. in Social Science Res./, ed. RE Cavallo, pp. 25-41, Kluwer-Nijhoff, Boston (1985) "Role of Fuzzy Logic in Management of Unc. in Expert Sys", in: /Approximate Reasoning in Exp. Sys./, ed. MM Gupta et. al., U California, Berkeley (1989) "Knowledge Representation in Fuzzy Logic", /IEEE Trans. on Knowledge+ Data Eng./, v. 1:1, pp. 89-100 Review of fuzzy logic through linguistic variables. Zadeh, Lofti A.: ed. (1987) /Fuzzy Sets and Applications/, ed. Yager et. al., Wiley, New York Zwick, Martin: (1978) "Fuzziness and Catastrophe", in: /Proc. of the Int. Conf. of Cyb.+Soc/, pp. 1237-1241, Tokyo/Kyoto, NOTE: IEEE SMC Japan -- O-------------------------------------------------------------------------> | Cliff Joslyn, Cybernetician at Large, cjoslyn@bingvaxu.cc.binghamton.edu | Systems Science, SUNY Binghamton, Box 1070, Binghamton NY 13901, USA V All the world is biscuit shaped. . .