Skip to main content

Part of the book series: Studies in Fuzziness and Soft Computing ((STUDFUZZ,volume 293))

Abstract

Let X be a classical set of objects, called the universe, whose generic elements are denoted x.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Aguilo, I., Suner, J., Torrens, J.: A characterization of residual implications derived from left-continuous uninorms. Information Sciences 180, 3992–4005 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aliev, R.A.: Fuzzy knowledge based Intelligent Robots. Radio i svyaz, Moscow (1995) (in Russian)

    Google Scholar 

  3. Aliev, R.A., Aliev, R.R.: Soft Computing and its Application. World Scientific, New Jersey (2001)

    Book  Google Scholar 

  4. Aliev, R.A., Aliev, F.T., Babaev, M.D.: Fuzzy process control and knowledge engineering. Verlag TUV Rheinland, Koln (1991)

    MATH  Google Scholar 

  5. Aliev, R.A., Aliev, R.R.: Soft Computing, vol. I, II, III. ASOA Press, Baku (1997-1998) (in Russian)

    Google Scholar 

  6. Aliev, R.A., Bonfig, K.W., Aliev, F.T.: Messen, Steuern und Regeln mit Fuzzy-Logik. Franzis-Verlag, München (1993)

    Google Scholar 

  7. Aliev, R.A., Fazlollahi, B., Aliev, R.R.: Soft Computing and its Application in Business and Economics. Springer, Heidelberg (2004)

    Book  Google Scholar 

  8. Aliev, R.A., Mamedova, G.A., Aliev, R.R.: Fuzzy Sets Theory and its application. Tabriz University Press, Tabriz (1993)

    Google Scholar 

  9. Aliev, R.A., Mamedova, G.A., Tserkovny, A.E.: Fuzzy control systems. Energoatomizdat, Moscow (1991)

    Google Scholar 

  10. Aliev, R.A., Pedrycz, W.: Fundamentals of a fuzzy-logic-based generalized theory of stability. IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetic 39(4), 971–988 (2009)

    Article  Google Scholar 

  11. Aliev, R.A., Pedrycz, W., Fazlollahi, B., Huseynov, O.H., Alizadeh, A.V., Guirimov, B.G.: Fuzzy logic-based generalized decision theory with imperfect information. Information Sciences 189, 18–42 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  12. Aliev, R.A., Tserkovny, A.: The knowledge representation in intelligent robots based on fuzzy sets. Soviet Math. Doklady 37, 541–544 (1988)

    MathSciNet  MATH  Google Scholar 

  13. Aliev, R.A., Tserkovny, A.E.: A systemic approach to fuzzy logic formalization for approximate reasoning. Information Sciences 181, 1045–1059 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  14. Azadeh, I., Fam, I.M., Khoshnoud, M., Nikafrouz, M.: Design and implementation of a fuzzy expert system for performance assessment of an integrated health, safety, environment (HSE) and ergonomics system: The case of a gas refinery. Information Sciences 178(22), 4280–4300 (2008)

    Article  Google Scholar 

  15. Baldwin, J.F., Pilsworth, B.W.: A model of fuzzy reasoning through multivalued logic and set theory. Int. J. Man-Machines Studies 11, 351–380 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  16. Ban, A.I., Gal, S.G.: Defects of Properties in Mathematics. Quantitative Characterizations. Series on Concrete and Applicable Mathematics, vol. 5. World Scientific, Singapore (2002)

    MATH  Google Scholar 

  17. Bandemer, H., Gottwald, S.: Fuzzy sets, Fuzzy logic, Fuzzy methods with applications. John Wiley and Sons, England (1995)

    MATH  Google Scholar 

  18. Bandemer, H., Nather, W.: Fuzzy data analysis. Kluwer Academic Publishers, Boston (1992)

    Book  MATH  Google Scholar 

  19. Bandler, W., Kohout, L.: Fuzzy power sets and fuzzy implications operators. Fuzzy Sets and Systems 1, 13–30 (1980)

    Article  MathSciNet  Google Scholar 

  20. Bandler, W., Kohout, L.J.: Fuzzy relational products as a tool for analysis of complex artificial and natural systems. In: Wang, P.P., Chang, S.K. (eds.) Fuzzy Sets; Theory and Applications to Policy Analysis and Information Systems, p. 311. Plenum Press, New York (1980)

    Google Scholar 

  21. Bandler, W., Kohout, L.J.: Semantics of fuzzy implication operators and relational products. International Journal of Man-Machine Studies 12(1), 89–116 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  22. Bandler, W., Kohout, L.J.: The identification of hierarchies in symptoms and patients through computation of fuzzy relational products. In: Parslow, R.D. (ed.) BCS 1981: Information Technology for the Eighties, P. 191. Heyden & Sons (1980)

    Google Scholar 

  23. Bandler, W., Kohout, L.J.: The four modes of inference in fuzzy expert systems. In: Trappl, R. (ed.) Cybernetics and Systems Research 2, pp. 581–586. North Holland, Amsterdam (1984)

    Google Scholar 

  24. Bede, B., Gal, S.G.: Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets and Systems 151, 581–599 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  25. Beg, I.: Fuzzy multivalued functions. Centre for Advanced Studies in Mathematics, and Department of Mathematics, Lahore University of Management Sciences (LUMS), 54792-Lahore, Pakistan (2012), http://wenku.baidu.com/view/71a84c136c175f0e7cd1372d.html

  26. Belohlavek, R., Sigmund, E., Zacpal, J.: Evaluation of IPAQ questionnaires supported by formal concept analysis. Information Science 181(10), 1774–1786 (2011)

    Article  MathSciNet  Google Scholar 

  27. Bloch, I.: Lattices of fuzzy sets and bipolar fuzzy sets, and mathematical morphology. Information Sciences 181(10), 2002–2015 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  28. Bobillo, F., Straccia, U.: Reasoning with the finitely many-valued Łukasiewicz fuzzy Description Logic SROIQ. Information Sciences 181(4), 758–778 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  29. Buckley, J.J., Eslami, E.: Fuzzy plane geometry I: Points and lines. Fuzzy Sets and Systems 86(2), 179–187 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  30. Bustince, H., Barrenechea, E., Fernandez, J., Pagola, M., Montero, J., Guerra, C.: Contrast of a fuzzy relation. Information Sciences 180, 1326–1344 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  31. Chajda, I., Halas, R., Rosenberg, I.G.: On the role of logical connectives for primality and functional completeness of algebras of logics. Information Sciences 180(8), 1345–1353 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  32. Chen, T.: Optimistic and pessimistic decision making with dissonance reduction using interval valued fuzzy sets. Information Sciences 181(3), 479–502 (2010)

    Article  Google Scholar 

  33. Davvaz, B., Zhan, J., Shum, K.P.: Generalized fuzzy Hv-submodules endowed with interval valued membership functions. Information Sciences 178, Nature Inspired Problem-Solving 1, 3147–3159 (2008)

    MathSciNet  Google Scholar 

  34. Diamond, P., Kloeden, P.: Metric spaces of fuzzy sets. Theory and applications. World Scientific, Singapoure (1994)

    MATH  Google Scholar 

  35. Dian, J.: A meaning based information theory - inform logical space: Basic concepts and convergence of information sequences. Information Sciences 180: Special Issue on Modelling Uncertainty 15, 984–994 (2010)

    MathSciNet  Google Scholar 

  36. Fan, Z.-P., Feng, B.: A multiple attributes decision making method using individual and collaborative attribute data in a fuzzy environment. Information Sciences 179, 3603–3618 (2009)

    Article  MathSciNet  Google Scholar 

  37. Fedrizzi, M., Fuller, R.: Stability in Possibilistic Linear Programming Problems with Continuous Fuzzy Number Parameters. Fuzzy Sets and Systems 47, 187–191 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  38. Fukami, S., Mizumoto, M., Tanaka, K.: Some considerations of fuzzy conditional inference. Fuzzy Sets and Systems 4, 243–273 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  39. Fuller, R., Zimmermann, H.J.: On Zadeh’s compositional rule of inference. In: Lowen, R., Roubens, M. (eds.) Fuzzy Logic: State of the Art, Theory and Decision Library, Series D, pp. 193–200. Kluwer Academic Publishers, Dordrecht (1993)

    Google Scholar 

  40. Gerhke, M., Walker, C.L., Walker, E.A.: Normal forms and truth tables for fuzzy logics. Fuzzy Sets and Systems 138, 25–51 (2003)

    Article  MathSciNet  Google Scholar 

  41. Grabisch, M., Marichal, J., Mesiar, R., Pap, E.: Aggregation functions: Construction methods, conjunctive, disjunctive and mixed classes. Information Sciences 181, 23 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  42. Grzegorzewski, P.: On possible and necessary inclusion of intuitionistic fuzzy sets. Information Sciences 181, 342 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  43. Hajek, P.: Fuzzy Logic from the Logical Point of View. In: Bartosek, M., Staudek, J., Wiedermann, J. (eds.) SOFSEM 1995. LNCS, vol. 1012, pp. 31–49. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  44. Hajek, P.: Metamathematics of Fuzzy Logic. Trends in Logic. Kluwer Academic Publishers (1998)

    Google Scholar 

  45. Hu, Q., Yu, D., Guo, M.: Fuzzy preference based rough sets. Information Sciences 180: Special Issue on Intelligent Distributed Information Systems 15, 2003–2022 (2010)

    MathSciNet  Google Scholar 

  46. Buckley, J.J., Feuring, T.: Fuzzy differential equations. Fuzzy Sets and Systems 151, 581–599 (2005)

    Article  MathSciNet  Google Scholar 

  47. Jantzen, J.: Array approach to fuzzy logic. Fuzzy Sets and Systems 70, 359–370 (1995)

    Article  Google Scholar 

  48. Jayaram, B., Mesiar, R.: I-Fuzzy equivalence relations and I-fuzzy partitions. Information Sciences 179, 1278–1297 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  49. Jenei, S.: Continuity in Zadeh’s compositional rule of inference. Fuzzy Sets and Systems 104, 333–339 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  50. Kallala, M., Kohout, L.J.: The use of fuzzy implication operators in clinical evaluation of neurological movement disorders. In: International Symposium on Fuzzy Information Processing in Artificial Intelligence and Operational Research, Christchurch College, Cambridge University (1984)

    Google Scholar 

  51. Kallala, M., Kohout, L.J.: A 2-stage method for automatic handwriting classification by means of norms and fuzzy relational inference. In: Proc. of NAFIPS 1986 (NAFIPS Congress), New Orleans (1986)

    Google Scholar 

  52. Kalina, M.: Derivatives of fuzzy functions and fuzzy derivatives. Tatra Mountains Mathematical Publications 12, 27–34 (1997)

    MathSciNet  MATH  Google Scholar 

  53. Kandel, A., Last, M.: Special issue on advances in Fuzzy logic. Information Sciences 177, 329–331 (2007)

    Article  MathSciNet  Google Scholar 

  54. Kaufman, A.: Introduction to theory of fuzzy sets, vol. 1. Academic Press, Orlando (1973)

    Google Scholar 

  55. Kehagias, A.: Some remarks on the lattice of fuzzy intervals. Information Sciences 181(10), 1863–1873 (2010)

    Article  MathSciNet  Google Scholar 

  56. Kiszka, J.B., Kochanska, M.E., Sliwinska, D.S.: The influence of some fuzzy implication operators on the accuracy of a fuzzy model. Fuzzy Sets and Systems 15, (Part1) 111–128, (Part2) 223–240 (1985)

    Google Scholar 

  57. Klir, G.J., Yuan, B.: Fuzzy sets and fuzzy logic. Theory and Applications. PRT Prentice Hall, NJ (1995)

    MATH  Google Scholar 

  58. Klir, G.J., Clair, U.S., Yuan, B.: Fuzzy Set Theory. Foundations and Applications. PTR Prentice Hall, NJ (1997)

    MATH  Google Scholar 

  59. Kohout, L.J. (ed.): Perspectives on Intelligent Systems: A Framework for Analysis and Design. Abacus Press, Cambridge (1986)

    Google Scholar 

  60. Kolesarova, A., Mesiar, R.: Lipschitzian De Morgan triplets of fuzzy connectives. Information Sciences 180, 3488–3496 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  61. Lai, J., Xu, Y.: Linguistic truth-valued lattice-valued propositional logic system lP(X) based on linguistic truth-valued lattice implication algebra. Information Sciences 180: Special Issue on Intelligent Distributed Information Systems, 1990–2002 (2010)

    Google Scholar 

  62. Lakshmikantham, V., Mohapatra, R.: Theory of fuzzy differential equations and inclusions. Taylor & Francis, London (2003)

    Book  MATH  Google Scholar 

  63. Levy, P.: From social computing to reflexive collective intelligence: The IEML research program. Information Sciences 180: Special Issue on Collective Intelligence 2, 71 (2010)

    Google Scholar 

  64. Li, C., Yi, J.: Sirms based interval type–2 fuzzy inference systems properties and application. International Journal of Innovative Computing. Information and Control 6(9), 4019–4028 (2010)

    Google Scholar 

  65. Lifschitz, V. (ed.): Formalizing Common Sense, Papers by John McCarthy. Greenwood Publishing Group Inc., NJ (1990)

    Google Scholar 

  66. Long, Z., Liang, X., Yang, L.: Some approximation properties of adaptive fuzzy systems with variable universe of discourse. Information Sciences 180, 2991–3005 (2010)

    Article  MATH  Google Scholar 

  67. Ma, H.: An analysis of the equilibrium of migration models for biogeography-based optimization. Information Sciences 180, 3444–3464 (2010)

    Article  MATH  Google Scholar 

  68. Mamdani, E.H.: Application of fuzzy logic to approximate reasoning using linguistic syntheses. IEEE Transactions on Computers C-26(12), 1182–1191 (1977)

    Google Scholar 

  69. Mas, M., Monserrat, M., Torrens, J.: The law of importation for discrete implications. Information Sciences 179, 4208–4218 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  70. Mas, M., Monserrat, M., Torrens, J., Trillas, E.: A Survey on Fuzzy Implication Functions. IEEE Transactions on Fuzzy Systems 15(6), 1107–1121 (2007)

    Article  Google Scholar 

  71. Mayburov, S.: Fuzzy geometry of phase space and quantization of massive Fields. Journal of Physics A: Mathematical and Theoretical 41, 1–10 (2008)

    Article  MathSciNet  Google Scholar 

  72. Medina, J., Ojeda Aciego, M.: Multi-adjoint t-concept lattices. Information Sciences 180, 712–725 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  73. Mendel, J.M.: On answering the question “Where do I start in order to solve a new problem involving interval type-2 fuzzy sets?”. Information Sciences 179, 3418–3431 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  74. Mizumoto, M., Fukami, S., Tanaka, K.: Some methods of fuzzy reasoning. In: Gupta, R., Yager, R. (eds.) Advances in Fuzzy Set Theory Applications. North-Holland, New York (1979)

    Google Scholar 

  75. Mizumoto, M., Zimmermann, H.-J.: Comparison of fuzzy reasoning methods. Fuzzy Sets and Systems 8, 253–283 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  76. Molai, A.A., Khorram, E.: An algorithm for solving fuzzy relation equations with max-T composition operator. Information Sciences 178, 1293–1308 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  77. Mordeson, J.N., Nair, P.S.: Fuzzy mathematics: an introduction for engineers and Scientists. Physica-Verlag, Heidelberg (2001)

    MATH  Google Scholar 

  78. Mueller, E.: Commonsense Reasoning. Morgan Kaufmann, San Francisco (2006)

    Google Scholar 

  79. Munoz-Hernandez, S., Pablos-Ceruelo, V., Strass, H.: R Fuzzy: Syntax, semantics and implementation details of a simple and expressive fuzzy tool over Prolog. Information Sciences 181(10), 1951–1970 (2011)

    Article  MathSciNet  Google Scholar 

  80. Nachtegael, M., Sussner, P., Melange, T., Kerre, E.E.: On the role of complete lattices in mathematical morphology: From tool to uncertainty model. Information Sciences (2010); corrected proof, available online 15 (in Press)

    Google Scholar 

  81. Nguyen, H.T., Walker, E.A.: A first Course in Fuzzy logic. CRC Press, Boca Raton (1996)

    Google Scholar 

  82. Noguera, C., Esteva, F., Godo, L.: Generalized continuous and left-continuous t-norms arising from algebraic semantics for fuzzy logics. Information Sciences 180, 1354–1372 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  83. Oh, K.W., Bandler, W.: Properties of fuzzy implication operators, Florida State University, Tallahassee, FL, U. S. A. Department of Computer Science, pp. 24–33 (1988)

    Google Scholar 

  84. Ouyang, Y., Wang, Z., Zhang, H.: On fuzzy rough sets based on tolerance relations. Information Sciences 180, 532 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  85. Pavelka, J.: On fuzzy logic I, II, III. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 25(45-52), 119–134, 447–464 (1979)

    MathSciNet  MATH  Google Scholar 

  86. Pei, D.: Unified full implication algorithms of fuzzy reasoning. Information Sciences 178, 520 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  87. Poston, T.: Fuzzy geometry. Ph.D. Thesis, University of Warwick (1971)

    Google Scholar 

  88. Rescher, N.: Many-Valued Logic. McGraw–Hill, NY (1969)

    MATH  Google Scholar 

  89. Roe, J.: Index theory, coarse geometry, and topology of manifolds. In: CBMS: Regional Conf. Ser. in Mathematics. The American Mathematical Society, Rhode Island (1996)

    Google Scholar 

  90. Rosenfeld, A.: The diameter of a fuzzy set. Fuzzy Sets and Systems 13, 241–246 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  91. Rosenfeld, A.: Distances between fuzzy sets. Pattern Recognition Letters 3(4), 229–233 (1985)

    Article  MATH  Google Scholar 

  92. Rosenfeld, A.: Fuzzy rectangles. Pattern Recognition Letters 11(10), 677–679 (1990)

    Article  MATH  Google Scholar 

  93. Rosenfeld, A.: Fuzzy plane geometry: triangles. Pattern Recognition Letters 15, 1261–1264 (1994)

    Article  Google Scholar 

  94. Rosenfeld, A.: Fuzzy geometry: an updated overview. Information Science 110(3-4), 127–133 (1998)

    Article  MathSciNet  Google Scholar 

  95. Rutkowski, L., Cpalka, K.: Flexible Neuro-Fuzzy Systems. IEEE Transactions on Neural Networks 14(3), 554–573 (2003)

    Article  Google Scholar 

  96. Sankar, K.P., Ghosh, A.: Fuzzy geometry in image analysis. Fuzzy Sets and Systems 48, 23–40 (1992)

    Article  MathSciNet  Google Scholar 

  97. Sankar, K.P.: Fuzzy geometry, entropy, and image information. In: Proceedings of the Second Join Technology Workshop on Neural Networks and Fuzzy Logic, vol. 2, pp. 211–232 (1991)

    Google Scholar 

  98. Serruier, M., Dubois, D., Prade, H., Sudkamp, T.: Learning fuzzy rules with their implication operator. Data & Knowledge Engineering 60, 71–89 (2007)

    Article  Google Scholar 

  99. Shieh, B.S.: Infinite fuzzy relation equations with continuous t-norms. Information Sciences 178, 1961–1967 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  100. Simon, H.: Models of Bounded Rationality: Empirically Grounded Economic Reason, vol. 3. MIT Press, Cambridge (1997)

    Google Scholar 

  101. Toulmin, S.: The Uses of Argument. Cambridge University Press, UK (2003)

    Book  Google Scholar 

  102. Tzafestas, S.G., Chen, C.S., Fokuda, T., Harashima, F., Schmidt, G., Sinha, N.K., Tabak, D., Valavanis, K. (eds.): Fuzzy logic applications in engineering science. Microprocessor based and Intelligent Systems Engineering, vol. 29, pp. 11–30. Springer, Netherlands (2006)

    Book  Google Scholar 

  103. Valle, M.E.: Permutation-based finite implicative fuzzy associative memories. Information Sciences 180, 4136–4152 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  104. Valverde Albacete, F.J., Pelaez Moreno, C.: Extending conceptualization modes for generalized Formal Concept Analysis. Information Sciences 181(10), 1888–1909 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  105. Wenstop, F.: Quantitative analysis with linguistic values. Fuzzy Sets and Systems 4(2), 99–115 (1980)

    Article  MATH  Google Scholar 

  106. Werthner, H.: Qualitative Reasoning, Modeling and the Generation of Behavior. Springer (1994)

    Google Scholar 

  107. Wilke, G.: Approximate Geometric Reasoning with Extended Geographic Objects. In: Proceedings of the Workshop on Quality, Scale and Analysis Aspects of City Models, Lund, Sweden, December 3-4 (2009), http://www.isprs.org/proceedings/XXXVIII/2W11/Wilke.pdf

  108. Xie, A., Qin, F.: Solutions to the functional equation I(x, y) = I(x, I(x, y)) for three types of fuzzy implications derived from uninorms. Information Sciences 186(1), 209–221 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  109. Xu, Y., Liu, J., Ruan, D., Li, X.: Determination of [alpha]-resolution in lattice-valued first-order logic LF(X). Information Sciences 181(10), 1836–1862 (2010)

    Article  MathSciNet  Google Scholar 

  110. Yager, R.R.: On measures of specificity. In: Kaynak, O., Zadeh, L.A., Turksen, B., Rudas, I.J. (eds.) Computational Intelligence: Soft Computing and Fuzzy-Neuro Integration with Applications, pp. 94–113. Springer, Berlin (1998)

    Chapter  Google Scholar 

  111. Yager, R.R.: On global requirements for implication operators in fuzzy modus ponens. Fuzzy Sets and Systems 106, 3–10 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  112. Yager, R.R.: A framework for reasoning with soft information. Information Sciences 180(8), 1390–1406 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  113. Yeh, R.T., Bang, S.Y.: Fuzzy relations, fuzzy graphs, and their applications to clustering analysis. In: Zadeh, L.A., Fu, K.S., Shimura, M.A. (eds.) Fuzzy Sets and Their Applications, pp. 125–149. Academic Press, NY (1975)

    Google Scholar 

  114. Zadeh, L.A.: Fuzzy Sets. Information and Control 8, 338–353 (1965)

    Article  MathSciNet  MATH  Google Scholar 

  115. Zadeh, L.A.: Probability measures of fuzzy events. Journal of Mathematical Analysis and Applications 23(2), 421–427 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  116. Zadeh, L.A.: Fuzzy orderings. Information Sciences 3, 117–200 (1971)

    Google Scholar 

  117. Zadeh, L.A.: Similarity relations and Fuzzy orderings. Information Sciences 3, 177–200 (1971)

    Article  MathSciNet  MATH  Google Scholar 

  118. Zadeh, L.A.: Outline of a new approach to the analysis of complex system and decision processes. IEEE Trans. Systems, Man, and Cybernetics 3, 28–44 (1973)

    Article  MathSciNet  MATH  Google Scholar 

  119. Zadeh, L.A.: The concept of a linguistic variable and its applications in approximate reasoning. Information Sciences 8, 43–80, 301–357; 9, 199–251 (1975)

    Google Scholar 

  120. Zadeh, L.A.: Fuzzy sets and information granularity. In: Gupta, M., Ragade, R., Yager, R. (eds.) Advances in Fuzzy Set Theory and Applications, pp. 3–18. North-Holland Publishing Co., Amsterdam (1979)

    Google Scholar 

  121. Zadeh, L.A.: Possibility theory, soft data analysis. In: Cobb, L., Thrall, R.M. (eds.) Mathematical Frontiers of the Social and Policy Sciences, pp. 69–129. Westview Press, Boulder (1981)

    Google Scholar 

  122. Zadeh, L.A.: Fuzzy logic. IEEE Computer 21(4), 83–93 (1988)

    Article  Google Scholar 

  123. Zadeh, L.A.: Toward a generalized theory of uncertainty — an outline. Information Sciences 172, 1–40 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  124. Zadeh, L.A.: Generalized theory of uncertainty (GTU) – principal concepts and ideas. Computational statistics & Data Analysis 51, 15–46 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  125. Zadeh, L.A.: Is there a need for fuzzy logic? Information Sciences 178, 2751–2779 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  126. Zadeh, L.A.: Fuzzy logic. In: Encyclopedia of Complexity and Systems Science, pp. 3985–4009. Springer, Berlin (2009)

    Google Scholar 

  127. Zadeh, L.A.: Toward extended fuzzy logic. A first step. Fuzzy Sets and Systems 160, 3175–3181 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  128. Zadeh, L.A.: A Note on Z-numbers. Information Sciences 181, 2923–2932 (2010)

    Article  MathSciNet  Google Scholar 

  129. Zhang, J., Yang, X.: Some properties of fuzzy reasoning in propositional fuzzy logic systems. Information Sciences 180, 4661–4671 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  130. Zhang, L., Cai, K.Y.: Optimal fuzzy reasoning and its robustness analysis. Int. J. Intell. Syst. 19, 1033–1049 (2004)

    Article  MATH  Google Scholar 

  131. Zhang, X., Yao, Y., Yu, H.: Rough implication operator based on strong topological rough algebras. Information Sciences 180, 3764–3780 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  132. Zhao, S., Tsang, E.C.C.: On fuzzy approximation operators in attribute reduction with fuzzy rough sets. Information Sciences 178, Including Special Issue: Recent Advances in Granular Computing (2008); Fifth International Conference on Machine Learning and Cybernetics, vol. 15, pp. 3163–3176

    Google Scholar 

  133. Zimmermann, H.J.: Fuzzy Set Theory and its applications. Kluwer Academic Publishers, Norwell (1996)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Rafik Aziz Aliev .

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Aliev, R.A. (2013). Fuzzy Sets and Fuzzy Logic. In: Fundamentals of the Fuzzy Logic-Based Generalized Theory of Decisions. Studies in Fuzziness and Soft Computing, vol 293. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34895-2_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-34895-2_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-34894-5

  • Online ISBN: 978-3-642-34895-2

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics