Skip to main content

2015 | OriginalPaper | Buchkapitel

On Discord Between Expected and Actual Developments in Applications of Fuzzy Logic During Its First Fifty Years

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

Developments of applications of fuzzy logic during the first fifty years of its existence are examined in this paper with the aim of comparing the actual developments with the expected ones in various areas of human affairs. It is shown that in many of the examined areas the actual developments turned out to be very different from the expected ones. In each area, an attempt is made to explain reasons for this surprising discord between reasonable expectations and the actual developments.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Fußnoten
1
For historical details regarding this very brief summary, see the recent book by Belohlavek, Dauben and Klir [1].
 
2
However, this statement makes sense only since the 1990s, when the first systems of fuzzy logic in the narrow emerged through the work of Peter Hájek [4] and other logicians.
 
3
Atkins, P. W.: Physical Chemistry, 3rd Edition, p. 406. Oxford Univ. Press, Oxford (1986).
 
4
Bridgman was an excellent experimental physicist who had been most of his academic career with Harvard University. In 1946, he won the Nobel Prize in Physics for his groundbreaking work on the physics of high pressures. He also wrote extensively on measurement in physics and on various other aspects of philosophy of science.
 
5
In general, a concept is viewed in psychology as a mental representation of a class of real or abstract entities, which is usually called a concept category. In the psychology of concepts, a concept is usually viewed more specifically as a body of knowledge regarding the entities in the associated concept category that is stored in the long-term memory (sometimes called a semantic memory) and employed by default in most of cognitive processes.
 
6
Introduction a la Theorie des Sous-Ensembles: vol. 1 (1973); vol. 2 (1975); vol. 3 (1975); vol. 4 (1977). Masson et Cie Editeurs. Only the first volume was published later in English [48].
 
7
Market situation influenced by a few producers.
 
8
Nash, J. F. Equilibrium points in n-person games. Proc. of the National Academy of Sciences 36, 48-49 (1950).
 
9
Kazem Sadegh-Zadeh was born in Tabriz, Iran in 1942. In the 1960s and 1970s, he studied medicine and philosophy at the German universities of Münster, Berlin, and Göttingen. He has been for many years with the University of Münster, where he worked in the area of analytic philosophy of medicine, and where he is now s professor-emeritus.
 
10
This was actually suggested by the Russian musicologist N. A. Garbuzov in 1948 in his book entitled “Zonal Nature of the Human Aural Perception (in Russian), published by the Academy of Sciences of the USSR in Moscow and Leningrad.
 
11
The famous systematic collection of 24 preludes and 24 fugues, each written in all 12 major and 12 minor keys, which are known under the German name “Das Wohltemperierte Klavier” (The Well-Tempered Clavier), were composed by Johann Sebastian Bach to provide an ultimate practical test that a piano is properly tuned in a well tempered way. After they are all played on the piano to be tested and each composition is perceived as well tuned, then the piano may be certified as perfectly well-tempered.
 
Literatur
1.
Zurück zum Zitat Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2015) Belohlavek, R., Dauben, J.W., Klir, G.J.: Fuzzy Logic and Mathematics: A Historical Perspective. Oxford University Press, New York (2015)
3.
Zurück zum Zitat Zadeh, L.A.: Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs: a précis. Multiple-Valued Logic 1(1), 1–13 (1996)MATHMathSciNet Zadeh, L.A.: Fuzzy logic and the calculi of fuzzy rules and fuzzy graphs: a précis. Multiple-Valued Logic 1(1), 1–13 (1996)MATHMathSciNet
4.
Zurück zum Zitat Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)CrossRefMATH Hájek, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Publishers, Dordrecht (1998)CrossRefMATH
5.
Zurück zum Zitat Yager, R.R., Ovchinnikov, S., Tong, R.M., Nguyen, H.T. (eds.): Fuzzy Sets and Applications: Selected Papers by Zadeh, L.A. Wiley, New York (1987) Yager, R.R., Ovchinnikov, S., Tong, R.M., Nguyen, H.T. (eds.): Fuzzy Sets and Applications: Selected Papers by Zadeh, L.A. Wiley, New York (1987)
6.
Zurück zum Zitat Klir, G.J., Yuan, B. (eds.): Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Zadeh, L.A. World Scientific, Singapore (1996) Klir, G.J., Yuan, B. (eds.): Fuzzy Sets, Fuzzy Logic, and Fuzzy Systems: Selected Papers by Zadeh, L.A. World Scientific, Singapore (1996)
7.
8.
Zurück zum Zitat Zadeh, L.A.: From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circuits Syst.—I. Fundam. Theor. Appl. 45(1), 105–119 (1999) Zadeh, L.A.: From computing with numbers to computing with words—from manipulation of measurements to manipulation of perceptions. IEEE Trans. Circuits Syst.—I. Fundam. Theor. Appl. 45(1), 105–119 (1999)
10.
Zurück zum Zitat Zadeh, L.A.: Generalized theory of uncertainty (GTU)—principal concepts and ideas. Comput. Stat. Data Anal. 51(1), 15–46 (2006)CrossRefMATHMathSciNet Zadeh, L.A.: Generalized theory of uncertainty (GTU)—principal concepts and ideas. Comput. Stat. Data Anal. 51(1), 15–46 (2006)CrossRefMATHMathSciNet
12.
Zurück zum Zitat Goguen, J.A.: The logic of inexact concepts. Synthese 19, 325–373 (1968–69) Goguen, J.A.: The logic of inexact concepts. Synthese 19, 325–373 (1968–69)
13.
Zurück zum Zitat Rescher, N.: Many-Valued Logic. McGraw-Hill, New York (1969)MATH Rescher, N.: Many-Valued Logic. McGraw-Hill, New York (1969)MATH
14.
Zurück zum Zitat Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press, Baldock (2001)MATH Gottwald, S.: A Treatise on Many-Valued Logics. Research Studies Press, Baldock (2001)MATH
16.
Zurück zum Zitat Zadeh, L.A.: Biological applications of the theory of fuzzy sets and systems. In: Proctor, L.D. (ed.) Biocybernetics of the Central Nervous System, pp. 199–212. Little, Brown and Company, Boston (1969) Zadeh, L.A.: Biological applications of the theory of fuzzy sets and systems. In: Proctor, L.D. (ed.) Biocybernetics of the Central Nervous System, pp. 199–212. Little, Brown and Company, Boston (1969)
17.
Zurück zum Zitat Zadeh, L.A.: Fuzzy sets and systems. In: Fox, J. (ed.) System Theory, pp. 29–39. Polytechnic Press, New York (1965) Zadeh, L.A.: Fuzzy sets and systems. In: Fox, J. (ed.) System Theory, pp. 29–39. Polytechnic Press, New York (1965)
18.
19.
20.
Zurück zum Zitat Kickert, W.J.M.: Fuzzy Theories on Decision-Making: A Critical Review. Martinus Nijhoff, Leiden (1978)MATH Kickert, W.J.M.: Fuzzy Theories on Decision-Making: A Critical Review. Martinus Nijhoff, Leiden (1978)MATH
21.
Zurück zum Zitat Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)CrossRefMATH Bezdek, J.C.: Pattern Recognition with Fuzzy Objective Function Algorithms. Plenum Press, New York (1981)CrossRefMATH
22.
Zurück zum Zitat Zadeh, L.A.: A rationale for fuzzy control. J. Dyn. Syst. Meas. Contr. (Trans. of ASME, Series G) 94(1), 3–4 (1972) Zadeh, L.A.: A rationale for fuzzy control. J. Dyn. Syst. Meas. Contr. (Trans. of ASME, Series G) 94(1), 3–4 (1972)
24.
Zurück zum Zitat Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7(1), 1–13 (1975)CrossRefMATH Mamdani, E.H., Assilian, S.: An experiment in linguistic synthesis with a fuzzy logic controller. Int. J. Man Mach. Stud. 7(1), 1–13 (1975)CrossRefMATH
25.
Zurück zum Zitat Mamdani, E.H.: Twenty years of fuzzy control: experiences gained and lessons learnt. In: Proceedings of the Second IEEE International Conference on Fuzzy Systems, pp. 339–344. IEEE, Piscataway, NJ (1993) Mamdani, E.H.: Twenty years of fuzzy control: experiences gained and lessons learnt. In: Proceedings of the Second IEEE International Conference on Fuzzy Systems, pp. 339–344. IEEE, Piscataway, NJ (1993)
26.
Zurück zum Zitat Holmblad, L.P., Østergaard, J.-J.: Control of a cement kiln by fuzzy logic. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 389–399. North-Holland, Amsterdam (1982) Holmblad, L.P., Østergaard, J.-J.: Control of a cement kiln by fuzzy logic. In: Gupta, M.M., Sanchez, E. (eds.) Fuzzy Information and Decision Processes, pp. 389–399. North-Holland, Amsterdam (1982)
27.
Zurück zum Zitat Yasunobu, S., Miyamoto, S.: Automatic train operation system by predictive fuzzy control. In: Sugeno, M. (ed.) Industrial Applications of Fuzzy Control, pp. 1–18. North Holland, Amsterdam (1985) Yasunobu, S., Miyamoto, S.: Automatic train operation system by predictive fuzzy control. In: Sugeno, M. (ed.) Industrial Applications of Fuzzy Control, pp. 1–18. North Holland, Amsterdam (1985)
28.
Zurück zum Zitat McNeill, D., Freiberger, P.: Fuzzy Logic. Simon & Schuster, New York (1993) McNeill, D., Freiberger, P.: Fuzzy Logic. Simon & Schuster, New York (1993)
29.
Zurück zum Zitat Woolf, P.J., Wang, Y.: A fuzzy logic approach to analyzing gene expression data. Physiol. Genomics 3(1), 9–15 (2000) Woolf, P.J., Wang, Y.: A fuzzy logic approach to analyzing gene expression data. Physiol. Genomics 3(1), 9–15 (2000)
30.
Zurück zum Zitat Sadegh-Zadeh, K.: Fuzzy genoms. Artif. Intell. Med. 18(1), 1–28 (2000)CrossRef Sadegh-Zadeh, K.: Fuzzy genoms. Artif. Intell. Med. 18(1), 1–28 (2000)CrossRef
31.
Zurück zum Zitat Xu, D., Keller, J.M., Popescu, M., Bondugula, R.: Applications of Fuzzy Logic in Bioinformatics. Imperial College Press, London (2008) Xu, D., Keller, J.M., Popescu, M., Bondugula, R.: Applications of Fuzzy Logic in Bioinformatics. Imperial College Press, London (2008)
32.
Zurück zum Zitat Zabrodsky, H., Paleg, S., Avnir, D.: Continuous symmetry measures. J. Am. Chem. Soc. 114(20), 7843–7851 (1992)CrossRef Zabrodsky, H., Paleg, S., Avnir, D.: Continuous symmetry measures. J. Am. Chem. Soc. 114(20), 7843–7851 (1992)CrossRef
33.
Zurück zum Zitat Rouvray, D.H. (ed.): Fuzzy Logic in Chemistry. Academic Press, San Diego (1997) Rouvray, D.H. (ed.): Fuzzy Logic in Chemistry. Academic Press, San Diego (1997)
34.
Zurück zum Zitat Bridgman, P.W.: How much rigor is possible in physics? In: Henkin, L., Suppes, P., Tarski, A. (eds.) The Axiomatic Method, pp. 225–237. North Holland, Amsterdam (1959) Bridgman, P.W.: How much rigor is possible in physics? In: Henkin, L., Suppes, P., Tarski, A. (eds.) The Axiomatic Method, pp. 225–237. North Holland, Amsterdam (1959)
35.
Zurück zum Zitat Mari, L.: Beyond the representational viewpoint: a new formalization of measurement. Measurement 27(2), 71–84 (2000)CrossRef Mari, L.: Beyond the representational viewpoint: a new formalization of measurement. Measurement 27(2), 71–84 (2000)CrossRef
36.
Zurück zum Zitat Chiara, M.D., Giuntini, R., Greechie, R.: Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics. Kluwer, Dordrecht (2004)CrossRef Chiara, M.D., Giuntini, R., Greechie, R.: Reasoning in Quantum Theory: Sharp and Unsharp Quantum Logics. Kluwer, Dordrecht (2004)CrossRef
37.
Zurück zum Zitat Nordlund, U.: Formalizing geological knowledge—with an example of modeling stratigraphy using fuzzy logic. J. Sediment. Res. 66(4), 689–712 (1996) Nordlund, U.: Formalizing geological knowledge—with an example of modeling stratigraphy using fuzzy logic. J. Sediment. Res. 66(4), 689–712 (1996)
38.
Zurück zum Zitat Demicco, R.V., Klir, G.J. (eds.): Fuzzy Logic in Geology. Academic Press, San Diego (2004) Demicco, R.V., Klir, G.J. (eds.): Fuzzy Logic in Geology. Academic Press, San Diego (2004)
40.
Zurück zum Zitat Rosch, E.H.: Natural categories. Cogn. Psychol. 4(3), 328–350 (1973)CrossRef Rosch, E.H.: Natural categories. Cogn. Psychol. 4(3), 328–350 (1973)CrossRef
41.
Zurück zum Zitat Rosch, E.H.: On the internal structure of perceptual and semantic categories. In: Moore, T.M. (ed.) Cognitive Development and the Acquisition of Language, pp. 111–144. Academic Press, New York (1973)CrossRef Rosch, E.H.: On the internal structure of perceptual and semantic categories. In: Moore, T.M. (ed.) Cognitive Development and the Acquisition of Language, pp. 111–144. Academic Press, New York (1973)CrossRef
42.
Zurück zum Zitat Tversky, A.: Features of similarity. Psychol. Rev. 84(4), 327–352 (1977)CrossRef Tversky, A.: Features of similarity. Psychol. Rev. 84(4), 327–352 (1977)CrossRef
43.
Zurück zum Zitat Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981)CrossRef Osherson, D.N., Smith, E.E.: On the adequacy of prototype theory as a theory of concepts. Cognition 9, 35–58 (1981)CrossRef
44.
Zurück zum Zitat Belohlavek, R., Klir, G.J., Lewis, H.W., Way, E.: On the capability of fuzzy set theory to represent concepts. Int. J. Gen. Syst. 31(6), 569–585 (2002)CrossRefMATHMathSciNet Belohlavek, R., Klir, G.J., Lewis, H.W., Way, E.: On the capability of fuzzy set theory to represent concepts. Int. J. Gen. Syst. 31(6), 569–585 (2002)CrossRefMATHMathSciNet
45.
Zurück zum Zitat Belohlavek, R., Klir, G.J., Lewis, H.W., Way, E.: Concepts and fuzzy sets: misunderstandings, misconceptions, and oversights. Int. J. Approximate Reasoning 51(1), 23–34 (2009)CrossRef Belohlavek, R., Klir, G.J., Lewis, H.W., Way, E.: Concepts and fuzzy sets: misunderstandings, misconceptions, and oversights. Int. J. Approximate Reasoning 51(1), 23–34 (2009)CrossRef
46.
Zurück zum Zitat Belohlavek, R., Klir, G.J. (eds.): Concepts and Fuzzy Logic. MIT Press, Cambridge (2011)MATH Belohlavek, R., Klir, G.J. (eds.): Concepts and Fuzzy Logic. MIT Press, Cambridge (2011)MATH
48.
Zurück zum Zitat Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets, vol. 1. Academic Press, New York (1975)MATH Kaufmann, A.: Introduction to the Theory of Fuzzy Subsets, vol. 1. Academic Press, New York (1975)MATH
49.
Zurück zum Zitat Ponsard, C.: An application of fuzzy subset theory to the analysis of the consumer’s spatial preferences. Fuzzy Sets Syst. 5(3), 235–244 (1981)CrossRefMATHMathSciNet Ponsard, C.: An application of fuzzy subset theory to the analysis of the consumer’s spatial preferences. Fuzzy Sets Syst. 5(3), 235–244 (1981)CrossRefMATHMathSciNet
50.
Zurück zum Zitat Ponsard, C., Fustier, B. (eds.): Fuzzy Economics and Spatial Analysis. Institut de Mathématiques Economiques et Librairie de l’Université, Dijon (1986)MATH Ponsard, C., Fustier, B. (eds.): Fuzzy Economics and Spatial Analysis. Institut de Mathématiques Economiques et Librairie de l’Université, Dijon (1986)MATH
52.
Zurück zum Zitat Zimmermann, H.-J.: Fuzzy Set Theory and Its Applications. Kluwer, Boston (1985)CrossRef Zimmermann, H.-J.: Fuzzy Set Theory and Its Applications. Kluwer, Boston (1985)CrossRef
53.
Zurück zum Zitat Billot, A.: Economic Theory of Fuzzy Equilibriums: An Axiomatic Analysis. Springer, Berlin (1992)CrossRefMATH Billot, A.: Economic Theory of Fuzzy Equilibriums: An Axiomatic Analysis. Springer, Berlin (1992)CrossRefMATH
55.
Zurück zum Zitat Klir, G.J.: Uncertainty in economics: the heritage of G. L. S. Shackle. Fuzzy Economic Review 7(2), 3–21 (2002) Klir, G.J.: Uncertainty in economics: the heritage of G. L. S. Shackle. Fuzzy Economic Review 7(2), 3–21 (2002)
56.
Zurück zum Zitat Zadeh, L.A.: Fuzzy systems theory: a framework for the analysis of humanistic systems. In: Cavallo, R. (ed.) Systems Methodology in Social Science Research; Recent Developments, pp. 25–41. Kluwer-Nijhoff, Boston (1982)CrossRef Zadeh, L.A.: Fuzzy systems theory: a framework for the analysis of humanistic systems. In: Cavallo, R. (ed.) Systems Methodology in Social Science Research; Recent Developments, pp. 25–41. Kluwer-Nijhoff, Boston (1982)CrossRef
57.
Zurück zum Zitat Smithson, M.: Fuzzy Set Analysis for Behavioral and Social Sciences. Springer, NewYork (1987)CrossRef Smithson, M.: Fuzzy Set Analysis for Behavioral and Social Sciences. Springer, NewYork (1987)CrossRef
58.
Zurück zum Zitat Ragin, C.C.: Fuzzy-Set Social Science. Univ. of Chicago Press, Chicago (2000) Ragin, C.C.: Fuzzy-Set Social Science. Univ. of Chicago Press, Chicago (2000)
59.
Zurück zum Zitat Ragin, C.C.: Redesigning Social Inquiry. Univ. of Chicago Press, Chicago (2008)CrossRef Ragin, C.C.: Redesigning Social Inquiry. Univ. of Chicago Press, Chicago (2008)CrossRef
60.
Zurück zum Zitat Arfi, B.: Linguistic Fuzzy Logic Methods in Social Sciences. Springer, Berlin (2010)CrossRef Arfi, B.: Linguistic Fuzzy Logic Methods in Social Sciences. Springer, Berlin (2010)CrossRef
61.
Zurück zum Zitat Clark, T.D., Larson, J.M., Mordeson, J.N., Potter, J.D., Wierman, M.J.: Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Springer, Berlin (2008)MATH Clark, T.D., Larson, J.M., Mordeson, J.N., Potter, J.D., Wierman, M.J.: Applying Fuzzy Mathematics to Formal Models in Comparative Politics. Springer, Berlin (2008)MATH
62.
Zurück zum Zitat Albin, M.A.: Fuzzy Sets and Their Applications to Medical Diagnosis and Pattern Recognition. Doctoral Dissertation, Univ. of California-Berkeley (1975) Albin, M.A.: Fuzzy Sets and Their Applications to Medical Diagnosis and Pattern Recognition. Doctoral Dissertation, Univ. of California-Berkeley (1975)
63.
Zurück zum Zitat Sanchez, E.: Solution in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Gupta, M.M., Sarids, G.N., Gaines, B.R. (eds.) Fuzzy Automata and Decision Processes, pp. 221–234. North-Holland, New York (1977) Sanchez, E.: Solution in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Gupta, M.M., Sarids, G.N., Gaines, B.R. (eds.) Fuzzy Automata and Decision Processes, pp. 221–234. North-Holland, New York (1977)
64.
Zurück zum Zitat Sanchez, E.: Medical diagnosis and composite fuzzy relations. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 434–444. North-Holland, Amsterdam (1979) Sanchez, E.: Medical diagnosis and composite fuzzy relations. In: Gupta, M.M., Ragade, R.K., Yager, R.R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 434–444. North-Holland, Amsterdam (1979)
65.
Zurück zum Zitat Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30(1), 38–48 (1976)CrossRefMATH Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30(1), 38–48 (1976)CrossRefMATH
66.
Zurück zum Zitat Adlassnig, K.-P.: The section on medical expert and knowledge-based systems at the department of medical computer sciences of University of Vienna Medical School. Artif. Intell. Med. 21(1), 139–146 (2001)CrossRef Adlassnig, K.-P.: The section on medical expert and knowledge-based systems at the department of medical computer sciences of University of Vienna Medical School. Artif. Intell. Med. 21(1), 139–146 (2001)CrossRef
67.
Zurück zum Zitat Zimmermann, H.-J. (ed.): Practical Applications of Fuzzy Technologies. Kluwer, Dordrecht (1999)MATH Zimmermann, H.-J. (ed.): Practical Applications of Fuzzy Technologies. Kluwer, Dordrecht (1999)MATH
68.
Zurück zum Zitat Mordeson, J.N., Malik, D.S., Cheng, S.-C.: Fuzzy Mathematics in Medicine. Spriner, Heidelberg (2000)MATH Mordeson, J.N., Malik, D.S., Cheng, S.-C.: Fuzzy Mathematics in Medicine. Spriner, Heidelberg (2000)MATH
69.
Zurück zum Zitat Rakus-Andersson, E.: Fuzzy and Rough Techniques in Medical Diagnosis and Medication. Springer, Berlin (2007)MATH Rakus-Andersson, E.: Fuzzy and Rough Techniques in Medical Diagnosis and Medication. Springer, Berlin (2007)MATH
70.
Zurück zum Zitat Massa, E., Ortega, N.R.S., De Barros, L.C., Struchiner, C.J.: Fuzzy Logic in Action: Applications in Epidemiology and Beyond. Springer, Berlin (2008)CrossRef Massa, E., Ortega, N.R.S., De Barros, L.C., Struchiner, C.J.: Fuzzy Logic in Action: Applications in Epidemiology and Beyond. Springer, Berlin (2008)CrossRef
71.
Zurück zum Zitat Barro, S., Marín, R. (eds.): Fuzzy Logic in Medicine. Physica-Verlag, Heidelberg (2002) Barro, S., Marín, R. (eds.): Fuzzy Logic in Medicine. Physica-Verlag, Heidelberg (2002)
72.
Zurück zum Zitat Sadegh-Zadeh, K.: Handbook of Analytic Philosophy of Medicine. Springer, Dordrecht (2012) Sadegh-Zadeh, K.: Handbook of Analytic Philosophy of Medicine. Springer, Dordrecht (2012)
73.
Zurück zum Zitat Seising, R., Tabacchi, M.E. (eds.): Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care. Springer, Berlin (2013) Seising, R., Tabacchi, M.E. (eds.): Fuzziness and Medicine: Philosophical Reflections and Application Systems in Health Care. Springer, Berlin (2013)
74.
Zurück zum Zitat Bojadziev, G., Bojadziev, M.: Fuzzy Logic for Business, Finance, and Management. World Scientific, Singapore (1997)MATH Bojadziev, G., Bojadziev, M.: Fuzzy Logic for Business, Finance, and Management. World Scientific, Singapore (1997)MATH
75.
Zurück zum Zitat Ostaszewski, K.: An Investigation into Possible Applications of Fuzzy Methods in Actuarial Science. Society of Actuaries, Schumburg (1993) Ostaszewski, K.: An Investigation into Possible Applications of Fuzzy Methods in Actuarial Science. Society of Actuaries, Schumburg (1993)
76.
Zurück zum Zitat Carlsson, C., Fedrizzi, M., Fullér, R.: Fuzzy Logic in Management. Kluwer, Boston (2004)CrossRefMATH Carlsson, C., Fedrizzi, M., Fullér, R.: Fuzzy Logic in Management. Kluwer, Boston (2004)CrossRefMATH
77.
Zurück zum Zitat Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and Its Applications in Business and Economics. Springer, Berlin (2004)CrossRefMATH Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and Its Applications in Business and Economics. Springer, Berlin (2004)CrossRefMATH
78.
Zurück zum Zitat Gil-Lafuente, A.M.: Fuzzy Logic in Financial Analysis. Springer, Berlin (2005)MATH Gil-Lafuente, A.M.: Fuzzy Logic in Financial Analysis. Springer, Berlin (2005)MATH
79.
Zurück zum Zitat Haluška, J.: The Mathematical Theory of Tone Systems. Marcell Dekker, New York (2004)MATH Haluška, J.: The Mathematical Theory of Tone Systems. Marcell Dekker, New York (2004)MATH
80.
Zurück zum Zitat Goguen, J.A.: Complexity of hierarchically organized systems and the structure of musical experiences. Int. J. Gen. Syst. 3(4), 233–251 (1977)CrossRefMathSciNet Goguen, J.A.: Complexity of hierarchically organized systems and the structure of musical experiences. Int. J. Gen. Syst. 3(4), 233–251 (1977)CrossRefMathSciNet
83.
Zurück zum Zitat León, T., Liern, V.: Mathematics and soft computing in music. In: Seising, R., Sanz, V. (eds.) Soft Computing in Humanities and Social Sciences, pp. 451–465. Springer, Berlin (2012) León, T., Liern, V.: Mathematics and soft computing in music. In: Seising, R., Sanz, V. (eds.) Soft Computing in Humanities and Social Sciences, pp. 451–465. Springer, Berlin (2012)
Metadaten
Titel
On Discord Between Expected and Actual Developments in Applications of Fuzzy Logic During Its First Fifty Years
verfasst von
George J. Klir
Copyright-Jahr
2015
DOI
https://doi.org/10.1007/978-3-319-19683-1_12