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An Efficient Algorithm to Computing Max-Min Post-inverse Fuzzy Relation for Abductive Reasoning

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Book cover Swarm, Evolutionary, and Memetic Computing (SEMCCO 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7076))

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Abstract

This paper provides an alternative formulation to computing the max-min post-inverse fuzzy relation by minimizing a heuristic (objective) function to satisfy the inherent constraints of the problem. An algorithm for computing the max-min post-inverse fuzzy relation as well as the trace of the algorithm is proposed here. The algorithm exposes its relatively better computational accuracy and higher speed in comparison to the existing technique for post-inverse computation. The betterment of computational accuracy of the max-min post-inverse fuzzy relation leads more accurate result of fuzzy abductive reasoning, because, max-min post-inverse fuzzy relation is required for abductive reasoning.

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References

  1. Arnould, T., Tano, S.: Interval-valued fuzzy backward reasoning. IEEE Trans. Fuzzy Systems 3(4), 425–437 (1995)

    Article  Google Scholar 

  2. Arnould, T., Tano, S.: The inverse problem of the aggregation of fuzzy sets. Int. J. Uncertainity Fuzzyness Knowledge Based System 2(4), 391–415 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  3. Arnould, T., Tano, S., Kato, Y., Miyoshi, T.: Backward chaining with fuzzy “if..then...rules”. In: Proc. of the Second IEEE International Conference on Fuzzy Systems, San Francisco, CA, pp. 548–533 (1993)

    Google Scholar 

  4. Bender, E.A.: Mathematical Methods in Artificial Intelligence. IEEE Computer Society Press Silver Spring, MD (1996)

    MATH  Google Scholar 

  5. Bourke, M.M., Fisher, D.G.: Solution algorithms for fuzzy relational equations with max-product composition. Fuzzy Sets and Systems 94, 61–69 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  6. Cen, J.: Fuzzy matrix partial ordering and generalized inverses. Fuzzy Sets and Systems 105, 453–458 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  7. Cheng-Zhong, L.: Generalized inverses of fuzzy matrix. Approximate Reasoning in Decis. Anal., 57–60 (1982)

    Google Scholar 

  8. Czogala, E., Drewniak, J., Pedrycz, W.: Fuzzy relation equations on a finite set. Fuzzy Sets and Systems 12, 89–101 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  9. Di Nola, A., Sessa, S.: On the set of solutions of composite fuzzy relation equations. Fuzzy Sets and Systems 9, 275–285 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  10. Drewniak, J.: Fuzzy relation inequalities. Cybernet. Syst. 88, 677–684 (1988)

    Google Scholar 

  11. Drewniak, J.: Fuzzy relation equations and inequalities. Fuzzy Sets and Systems 14, 237–247 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  12. Gottwald, S.: Generalized solvability criteria for fuzzy equations. Fuzzy Sets and Systems 17, 285–296 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  13. Gottwald, S., Pedrycz, W.: Solvability of fuzzy relational equations and manipulation of fuzzy data. Fuzzy Sets and Systems 18, 45–65 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  14. Higashi, M., Klir, G.J.: Resolution of finite fuzzy relation equations. Fuzzy Sets and Systems 13, 65–82 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Kim, K.H., Roush, F.W.: Generalized fuzzy matrices. Fuzzy Sets and Systems 4, 293–315 (1980)

    Article  MathSciNet  MATH  Google Scholar 

  16. Klir, G.J., Folger, T.A.: Fuzzy Sets, Uncertainity, and Information, ch. 1. Prentice-Hall, Englewood Cliffs (1988)

    MATH  Google Scholar 

  17. Konar, A.: Computational Intelligence: Principles, Techniques and Applications. Springer, Heidelberg (2005)

    Book  MATH  Google Scholar 

  18. Kosko, B.: Fuzzy Engineering. Prentice-Hall, Englewood Cliffs (1997)

    MATH  Google Scholar 

  19. Leotamonphong, J., Fang, S.-C.: An efficient solution procedure for fuzzy relational equations with max-product composition. IEEE Trans. Fuzzy Systems 7(4), 441–445 (1999)

    Article  Google Scholar 

  20. Lettieri, A., Liguori, F.: Characterization of some fuzzy relation equations provided with one solution in a finite set. Fuzzy Sets and Systems 13, 83–94 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  21. Li, X., Ruan, D.: Novel neural algorithms based on fuzzy δ -rules for solving fuzzy relational equations, part III. Fuzzy Sets and Systems 109, 355–362 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  22. Luoh, L., Wang, W.-J., Liaw, Y.-K.: Matrix-pattern-based computer algorithm for solving fuzzy relational equations. IEEE Trans. on Fuzzy Systems 11(1) (February 2003)

    Google Scholar 

  23. Miyakoshi, M., Shimbo, M.: Solutions of composite fuzzy relational equations with triangular norms. Fuzzy Sets and Systems 16, 53–63 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  24. Pappis, C.P.: Multi-input multi-output fuzzy systems and the inverse problem. European J. of Operational Research 28, 228–230 (1987)

    Article  Google Scholar 

  25. Pappis, C.P., Adamopoulos, G.I.: A computer algorithm for the solution of the inverse problem of fuzzy systems. Fuzzy Sets and Systems 39, 279–290 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  26. Pappis, C.P., Sugeno, M.: Fuzzy relational equation and the inverse problem. Fuzzy Sets and Systems 15(1), 79–90 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  27. Pedrycz, W.: Inverse problem in fuzzy relational equations. Fuzzy Sests and Systems 36, 277–291 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  28. Pedrycz, W.: Fuzzy Set Calculus. In: Ruspini, E.H., Bonissone, P.P., Pedrycz, W. (eds.) Handbook of Fuzzy Computation. IOP Publishing, Bristol (1998)

    Google Scholar 

  29. Pedrycz, W.: Fuzzy relational equations with generalized connectives and their applications. Fuzzy Sets and Systems 10, 185–201 (1983)

    Article  MathSciNet  MATH  Google Scholar 

  30. Perfilieva, I., Tonis, A.: Compatibility of systems of fuzzy relation equations. Int. J. General Systems 29(4), 511–528 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  31. Prevot, M.: Algorithm for the solution of fuzzy relations. Fuzzy Sets and Systems 5, 319–322 (1981)

    Article  MathSciNet  MATH  Google Scholar 

  32. Rich, E., Knight, K.: Artificial Intelligence. McGraw-Hill, New York (1991)

    Google Scholar 

  33. Ross, T.J.: Fuzzy Logic with Engg. Applications. McGraw-Hill, New York (1995)

    Google Scholar 

  34. Saha, P.: Abductive Reasoning with Inverse fuzzy discrete Relations, Ph. D. Dissertation, Jadavpur University, India (2002)

    Google Scholar 

  35. Saha, P., Konar, A.: A heuristic algorithm for computing the max-min inverse fuzzy relation. Int. J. of Approximate Reasoning 30, 131–147 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  36. Sanchez, E.: Resolution of composite fuzzy relation equations. Inf. Control 30, 38–48 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  37. Sanchez, E.: Solution of fuzzy equations with extended operations. Fuzzy Sets and Systems 12, 237–247 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  38. Sessa, S.: Some results in the setting of fuzzy relation equation theory. Fuzzy Sets and Systems 14, 281–297 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  39. Togai, M.: Application of fuzzy inverse relation to synthesis of a fuzzy controller for dynamic systems. In: Proc. 23rd Conf. on Decision and Control, Las Vegs, NV (December 1984)

    Google Scholar 

  40. Wang, S., Fang, S.-C., Nuttle, H.L.W.: Solution set of interval valued fuzzy relational equation. Fuzzy Optim. Decision Making 2(1), 41–60 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  41. Wu, Y.-K., Guu, S.-M.: An efficient procedure for solving a fuzzy relational equation with Max-Archimedean t-norm composition. IEEE Trans. on Fuzzy Systems 16(1) (February 2008)

    Google Scholar 

  42. Yeh, C.-T.: On the minimal solutions of max-min fuzzy relational equations. Fuzzy Sets and Systems 159(1) (January 2008)

    Google Scholar 

  43. Zadeh, L.A.: Knowledge representation in fuzzy logic. IEEE Trans. Knowledge Data Engg. (1988)

    Google Scholar 

  44. Zimmerman, H.J.: Fuzzy Set Theory and its Applications. Kluwer Academic Publishers, Dordrecht (1996)

    Book  Google Scholar 

  45. Chakraborty, S., Konar, A., Jain, L.C.: An Efficient Algorithm to Computing Max-Min Inverse Fuzzy Relation for Abductive Reasoning. IEEE Trans. Sys. Man Cybernet (A) 40(1) (January 2010)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Artificial Intelligence Laboratory, Dept. of Electronics and Tele-Communication Engineering, Jadavpur University, Calcutta, 32, India

    Sumantra Chakraborty & Amit Konar

  2. Department of IT, Jaya Engg. College, Chennai, India

    Ramadoss Janarthanan

Authors
  1. Sumantra Chakraborty
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  2. Amit Konar
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  3. Ramadoss Janarthanan
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Editor information

Editors and Affiliations

  1. Department of Electrical Engineering, IIT Delhi, India

    Bijaya Ketan Panigrahi

  2. School of Electrical and Electronic Engineering, Nanyang Technological University, 639798, Singapore

    Ponnuthurai Nagaratnam Suganthan

  3. Department of Electronics and Telecommunications, Jadavpur University, 700032, Kolkata, India

    Swagatam Das

  4. ANITS, Visakhapatnam, India

    Suresh Chandra Satapathy

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Chakraborty, S., Konar, A., Janarthanan, R. (2011). An Efficient Algorithm to Computing Max-Min Post-inverse Fuzzy Relation for Abductive Reasoning. In: Panigrahi, B.K., Suganthan, P.N., Das, S., Satapathy, S.C. (eds) Swarm, Evolutionary, and Memetic Computing. SEMCCO 2011. Lecture Notes in Computer Science, vol 7076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27172-4_61

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  • DOI: https://doi.org/10.1007/978-3-642-27172-4_61

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-27171-7

  • Online ISBN: 978-3-642-27172-4

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