Fuzzy inference system (FIS) extensions based on the lattice theory

IEEE Transactions on Fuzzy Systems

Volumn 22, Issue 3, 2014, Pages 531-546

  Kaburlasos, Vassilis G ^a   Kehagias, Athanasios ^b  

^a Human Machines Interaction (HMI) Laboratory   (Greece)

^b ARISTOTLE UNIVERSITY OF THESSALONIKI   (Greece)

Author keywords

Fuzzy inference system (FIS); fuzzy interval; fuzzy lattice reasoning (FLR); granular computing; inclusion measure; industrial dispensing; intervals' number (IN); lattice computing (LC)

Indexed keywords

GRANULAR COMPUTING; INDUSTRIAL APPLICATIONS; PROBABILITY DISTRIBUTIONS;

FUZZY INFERENCE SYSTEMS; FUZZY INTERVAL; FUZZY LATTICE; INCLUSION MEASURE; INDUSTRIAL DISPENSING; INTERVALS' NUMBER (IN); LATTICE COMPUTING (LC);

FUZZY SYSTEMS;

EID: 84901988060     PISSN: 10636706     EISSN: None     Source Type: Journal    
DOI: 10.1109/TFUZZ.2013.2263807     Document Type: Article

References (85)

1. W. Bandler and L. Kohout, "Fuzzy power sets and fuzzy implication operators," Fuzzy Sets Syst., vol. 4, no. 1, pp. 13-30, 1980.
2. R. Belohlavek, Fuzzy Relational Systems: Foundations and Principles. Heidelberg, Germany: Springer-Verlag, 2002.
3. R. Belohlavek and G. J. Klir, Eds., Concepts and Fuzzy Logic. Cumberland, RI, USA: MIT Press, 2011.
4. G. Birkhoff, Lattice Theory, vol. 25. Providence, RI, USA: Amer. Math. Soc., 1967.
5. R. Boukezzoula, S. Galichet, and A. Bisserier, "A midpoint-radius approach to regression with interval data," Int. J. Approx. Reas., vol. 52, no. 9, pp. 1257-1271, 2011.
6. P. Burillo, N. Frago, and R. Fuentes, "Inclusion grade and fuzzy implication operators," Fuzzy Sets Syst., vol. 114, no. 3, pp. 417-429, 2000.
7. H. Bustince, "Indicator of inclusion grade for interval-valued fuzzy sets. Application to approximate reasoning based on interval-valued fuzzy sets," Int. J. Approx. Reas., vol. 23, no. 3, pp. 137-209, 2000. (Pubitemid 34207603)
8. S.-M. Chen,W.-C. Hsin, S.-W. Yang, and Y.-C. Chang, "Fuzzy interpolative reasoning for sparse fuzzy rule-based systems based on the slopes fuzzy sets," Expert Syst. Appl., vol. 39, no. 15, pp. 11961-11969, 2012.
9. O. Cord́on, "A historical review of evolutionary learning methods for Mamdani-type fuzzy rule-based systems: Designing interpretable genetic fuzzy systems," Int. J. Approx. Reason., vol. 52, no. 6, pp. 894-913, 2011.
10. C. Cornelis and E. Kerre, "Inclusion measures in intuitionistic fuzzy set theory," in Proc. Symbol. Quantitative Approaches Reason. Uncertainty. (Lectures Notes Artificial Intell. Series 2711), T.D. Nielsen and N.L. Zhang, Eds. Berlin, Germany: Springer-Verlag, 2003, pp. 345-356. (Pubitemid 36904917)
11. C. Cornelis, C. Van der Donck, and E. Kerre, "Sinha-dougherty approach to the fuzzification of set inclusion revisited," Fuzzy Sets Syst., vol. 134, no. 2, pp. 283-295, 2003.
12. G. Deschrijver and E. E. Kerre, "On the relationship between some extensions of fuzzy set theory," Fuzzy Sets Syst., vol. 133, no. 2, pp. 227-235, 2003.
13. G. Deschrijver and E. E. Kerre, "On the position of intuitionistic fuzzy set theory in the framework of theories modelling imprecision," Inf. Sci., vol. 177, no. 8, pp. 1860-1866, 2007. (Pubitemid 46176955)
14. E. Esmi, P. Sussner, M. E. Valle, F. Sakuray, and L. Barros, "Fuzzy associative memories based on subsethood and similarity measures with applications to speaker identification," in Proc. Hybrid Artif. Intell. Syst., 2012, vol. II, pp. 479-490.
15. J. Fan,W. Xie, and J. Pei, "Subsethood measure: New definitions," Fuzzy Sets Syst., vol. 106, no. 2, pp. 201-209, 1999.
16. L. Foulloy and S. Galichet, "Fuzzy controlwith fuzzy inputs," IEEE Trans. Fuzzy Syst., vol. 11, no. 4, pp. 437-449, Aug. 2003.
17. B. Ganter andR.Wille, Formal Concept Analysis. Heidelberg, Germany: Springer-Verlag, 1999.
18. J. A. Goguen, "L-fuzzy sets," J. Mathemat. Anal. Appl., vol. 18, no. 1, pp. 145-174, 1967.
19. M. Grabisch, "Belief functions on lattices," Int. J. Intell. Syst., vol. 24, no. 1, pp. 76-95, 2009.
20. M. Grana, "Lattice computing in hybrid intelligent systems," in Proc. 12th Intl. Conf. Hybrid Intell. Syst., Dec. 2012, pp. 1-5.
21. M. Grana (Ed.), Special issue on: Lattice computing and natural computing," Neurocomput., vol. 72, no. 10-12, pp. 2065-2066, 2009.
22. M. Grana and A. I. Gonzalez-Acuna, "Learning parsimonious dendritic classifiers," Neurocomput., vol. 109, pp. 3-8, 2013.
23. P. Grzegorzewski, "On possible and necessary inclusion of intuitionistic fuzzy sets," Inf. Sci., vol. 181, no. 2, pp. 342-350, 2011.
24. S. Guillaume, "Designing fuzzy inference systems from data: An interpretability-oriented review," IEEE Trans. Fuzzy Syst., vol. 9, no. 3, pp. 426-443, Jun. 2001. (Pubitemid 32636660)
25. H. J. A. M. Heijmans and R.Keshet, "Inf-semilattice approach to self-dual morphology," J. Mathemat. Imag. Vis., vol. 17, no. 1, pp. 55-80, 2002. (Pubitemid 35350588)
26. Z. Huang and Q. Shen, "Fuzzy interpolation and extrapolation: A practical approach," IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 13-28, Feb. 2008. (Pubitemid 351359125)
27. C.-M. Hwang, M.-S. Yang, and W.-L. Hung, "On similarity, inclusion measure and entropy between type-2 fuzzy sets," Int. J. Uncert. Fuzz. Knowl. Based Syst., vol. 20, no. 3, pp. 433-449, 2012.
28. J. Jiḿenez, S. Montes, B. Seselja, and A. Tepavcevíc, "Lattice-valued approach to closed sets under fuzzy relations: Theory and applications," Comput. Mathemat. Appl., vol. 62, no. 10, pp. 3729-3740, 2011.
29. V. G. Kaburlasos, Adaptive Resonance Theory With Supervised Learning and Large Database Applications. Ph.D. dissertation, Dept. Electr. Eng., Univ. Nevada, Reno, NV, USA, 1992.
30. V. G. Kaburlasos, "FINs: Lattice theoretic tools for improving prediction of sugar production from populations of measurements," IEEE Trans., Syst., Man Cybern. B, vol. 34, no. 2, pp. 1017-1030, Apr. 2004.
31. V. G. Kaburlasos, Towards a Unified Modeling and Knowledge-Representation Based on Lattice Theory (Series Studies in Computational Intelligence, vol. 27). Heidelberg, Germany: Springer-Verlag, 2006.
32. V. G. Kaburlasos, "Special issue on: Information engineering applications based on lattices," Inf. Sci., vol. 181, no. 10, pp. 1771-1773, 2011.
33. V. G. Kaburlasos and A. Kehagias, "Novel fuzzy inference system (FIS) analysis and design based on lattice theory-Part I: Working principles," Int. J. General Syst., vol. 35, no. 1, pp. 45-67, 2006. (Pubitemid 46508740)
34. V. G. Kaburlasos and A. Kehagias, "Novel fuzzy inference system (FIS) analysis and design based on lattice theory," IEEE Trans. Fuzzy Syst., vol. 15, no. 2, pp. 243-260, Apr. 2007. (Pubitemid 46563425)
35. V. G. Kaburlasos and T. Pachidis, "A lattice-computing ensemble for reasoning based on formal fusion of disparate data types, and an industrial dispensing application," Inf. Fus., doi: 10.1016/j.inffus.2011.04.003.
36. V. G. Kaburlasos and S. E. Papadakis, "Granular self-organizing map (gr-SOM) for structure identification," Neural Netw., vol. 19, no. 5, pp. 623-643, 2006. (Pubitemid 44026583)
37. V. G. Kaburlasos and V. Petridis, "Fuzzy lattice neurocomputing (FLN): A novel connectionist scheme for versatile learning and decision making by clustering," Int. J. Comput. Appl., vol. 4, no. 3, pp. 31-43, 1997.
38. V. G. Kaburlasos and V. Petridis, "Fuzzy lattice neurocomputing (FLN) models," Neural Netw., vol. 13, no. 10, pp. 1145-1169, 2000.
39. V. G. Kaburlasos and V. Petridis, "Learning and decision-making in the framework of fuzzy lattices," in Proc. Learn. Paradigms Soft Comput. (Studies in Fuzziness and Soft Computing Series 84), L.C. Jain and J. Kacprzyk, Eds. Heidelberg, Germany: Physica-Verlag, 2002, pp. 55-96.
40. V. G. Kaburlasos and G. X. Ritter (Eds.), Computational Intelligence Based on Lattice Theory (Series Studies in Computational Intelligence, vol. 67). Heidelberg, Germany: Springer-Verlag, 2007.
41. V. G. Kaburlasos, I. N. Athanasiadis, and P. A. Mitkas, "Fuzzy lattice reasoning (FLR) classifier and its application for ambient ozone estimation," Int. J. Approx. Reas., vol. 45, no. 1, pp. 152-188, 2007. (Pubitemid 46629128)
42. V. G. Kaburlasos, S. E. Papadakis, and A. Amanatiadis, "Binary image 2D shape learning and recognition based on lattice-computing (LC) techniques," J. Mathemat. Imag. Vis., vol. 42, no. 2-3, pp. 118-133, 2012.
43. V. G. Kaburlasos, S. E. Papadakis, and G. A. Papakostas, "Lattice computing extension of the FAM neural classifier for human facial expression recognition," IEEE Trans. Neural Netw. Learn. Syst., doi.: 10.1109/TNNLS.2012.2237038.
44. N. N. Karnik and J. M. Mendel, "Introduction to type-2 fuzzy logic systems," in Proc. IEEE Intl. Conf. Fuzzy Syst. IEEE World Congr. Comput. Intell., May 1998, vol. 2, pp. 915-920.
45. A. Kehagias, "Some remarks on the lattice of fuzzy intervals," Inf. Sci., vol. 181, no. 10, pp. 1863-1873, 2011.
46. A. Kehagias and M. Konstantinidou, "L-fuzzy valued inclusion measure, l-fuzzy similarity and l-fuzzy distance," Fuzzy Sets Syst., vol. 136, no. 3, pp. 313-332, 2003.
47. G. J. Klir and B. Yuan, Fuzzy Sets and Fuzzy Logic: Theory and Applications. Upper Saddle River, NJ, USA: Prentice Hall, 1995.
48. L. T. Ḱoczy and K. Hirota, "Interpolative reasoning with insufficient evidence in sparse fuzzy rule bases," Inf. Sci., vol. 71, no. 1-2, pp. 169-201, 1993.
49. L. T. Ḱoczy and K. Hirota, "Approximate reasoning by linear rule interpolation and general approximation," Int. J. Approx. Reas., vol. 9, no. 3, pp. 197-225, 1993.
50. B. Kosko, "Fuzzy entropy and conditioning," Inf. Sci., vol. 40, no. 2, pp. 165-174, 1986.
51. B. Li, P.-Y. Liu, R.-X. Hu, S.-S. Mi, and J.-P. Fu, "Fuzzy lattice classifier and its application to bearing fault diagnosis," Appl. Soft Comput., vol. 12, no. 6, pp. 1708-1719, 2012.
52. H. Liu, S. Xiong, and C.-a.Wu, "Hyperspherical granular computing classification algorithm based on fuzzy lattices," Mathemat. Comput.Modell., vol. 57, no. 3-4, pp. 661-670, 2013.
53. E. H. Mamdani and S. Assilian, "An experiment in linguistic synthesis with a fuzzy logic controller," Int. J. Man-Mach. Studies, vol. 7, no. 1, pp. 1-13, 1975.
54. J. M. Mendel, "Type-2 fuzzy sets and systems: An overview," IEEE Comput. Intell. Mag., vol. 2, no. 1, pp. 20-29, Feb. 2007.
55. M. Nachtegael, P. Sussner, T. Ḿelange, and E. E. Kerre, "On the role of complete lattices in mathematical morphology: From tool to uncertainty model," Inf. Sci., vol. 181, no. 10, pp. 1971-1988, 2011.
56. S. Nefti, M. Oussalah, and U. Kaymak, "A new fuzzy set merging technique using inclusion-based fuzzy clustering," IEEE Trans. Fuzzy Syst., vol. 16, no. 1, pp. 145-161, Feb. 2008. (Pubitemid 351359136)
57. H. T. Nguyen and E. A. Walker, A First Course in Fuzzy Logic, 2nd ed. London, U.K.: Chapman & Hall, 2000.
58. S. E. Papadakis and V. G. Kaburlasos, "Piecewise-linear approximation of non-linear models based on probabilistically/possibilistically interpreted intervals' numbers (INs)," Inf. Sci., vol. 180, no. 24, pp. 5060-5076, 2010.
59. W. Pedrycz, A. Skowron, andV.Kreinovich (Eds.), Handbook of Granular Computing. Chichester, U.K.: Wiley, 2008.
60. V. Petridis and V. G. Kaburlasos, "Fuzzy lattice neural network (FLNN): A hybrid model for learning," IEEE Trans. Neural Netw., vol. 9, no. 5, pp. 877-890, Sep. 1998. (Pubitemid 128743653)
61. G. X. Ritter and P. Sussner, "An introduction to morphological neural networks," in Proc. 13th IEEE Intl. Conf. Patt. Recognit., Aug. 1996, vol. 4, pp. 709-717.
62. C. Ronse, "Why mathematical morphology needs complete lattices," Signal Process., vol. 21, no. 2, pp. 129-154, 1990.
63. J. Serra, Image Analysis and Mathematical Morphology, Vol. 2: Theoretical Advances. New York, NY, USA: Academic, 1988.
64. B. Seselja and A. Tepavcevíc, "Completion of ordered structures by cuts of fuzzy sets: An overview," Fuzzy Sets Syst., vol. 136, no. 1, pp. 1-19, 2003.
65. B. Seselja and A. Tepavcevíc, "Representing ordered structures by fuzzy sets: An overview," Fuzzy Sets Syst., vol. 136, no. 1, pp. 21-39, 2003.
66. D. Sinha and E. R. Dougherty, "Fuzzification of set inclusion: Theory and applications," Fuzzy Sets Syst., vol. 55, no. 1, pp. 15-42, 1993.
67. P. Sussner and E. L. Esmi, "Morphological perceptrons with competitive learning: Lattice-theoretical framework and constructive learning algorithm," Inf. Sci., vol. 181, no. 10, pp. 1929-1950, 2011.
68. P. Sussner and C. R. Medeiros, "An introduction to morphological associative memories in complete lattices and inf-semilattices," in Proc.World Congress Comput. Intell. (WCCI) 2012, FUZZ-IEEE Program, Brisbane, Australia, Jun. 2012, pp. 1-8.
69. P. Sussner and M. E. Valle, "Gray-scale morphological associative memories," IEEE Trans. Neural Netw., vol. 17, no. 3, pp. 559-570, May 2006.
70. P. Sussner and M. E. Valle, "Implicative fuzzy associative memories," IEEE Trans. Fuzzy Syst., vol. 14, no. 6, pp. 793-807, Dec. 2006. (Pubitemid 46432459)
71. P. Sussner, M. Nachtegael, T. Ḿelange, G. Deschrijver, E. Esmi, and E. Kerre, "Interval-valued and intuitionistic fuzzy mathematical morphologies as special cases of l-fuzzy mathematical morphology," J. Math. Imag. Vis., vol. 43, no. 1, pp. 50-71, 2012.
72. T. Takagi and M. Sugeno, "Fuzzy identification of systems and its applications to modeling and control," IEEE Trans. Syst. Man Cybern., vol. SMC-15, no. 1, pp. 116-132, Jan./Feb. 1985.
73. M. E.Valle and P. Sussner, "Ageneral framework for fuzzy morphological associative memories," Fuzzy Sets Syst., vol. 159, no. 7, pp. 747-768, 2008.
74. M. E. Valle and P. Sussner, "Storage and recall capabilities of fuzzy morphological associative memories with adjunction-based learning," Neural Netw., vol. 24, no. 1, pp. 75-90, 2011.
75. M. E. Valle and P. Sussner, "Quantale-based autoassociative memories with an application to the storage of color images," Patt. Recognit. Lett., doi.: 10.1016/j.patrec.2013.03.034.
76. M. E. Valle and D. M. G. Vicente, "Sparsely connected autoassociative lattice memories with an application for the reconstruction of color images," J. Math. Imag. Vis., vol. 44, no. 3, pp. 195-222, 2012.
77. H.Wu and J. M. Mendel, "Uncertainty bounds and their use in the design of interval type-2 fuzzy logic systems," IEEE Trans. Fuzzy Syst., vol. 10, no. 5, pp. 622-639, Oct. 2002. (Pubitemid 35274824)
78. Y. Xu, J. Liu, X. Zhong, and S. Chen, "Lattice-valued matrix game with mixed strategies for intelligent decision suport," Knowl. Based Syst., vol. 32, pp. 56-64, 2012.
79. Y. Xu, D. Ruan, K. Qin, and J. Liu, Lattice-Valued Logic (Series Studies in Fuzziness and Soft Computing, vol. 132).Heidelberg, Germany: Springer-Verlag, 2003.
80. V. R. Young, "Fuzzy subsethood," Fuzzy Sets Syst., vol. 77, no. 3, pp. 371-384, 1996. (Pubitemid 126667353)
81. L. A. Zadeh, "Fuzzy sets," Inf. Control, vol. 8, no. 3, pp. 338-353, 1965.
82. L. A. Zadeh, "Outline of a new approach to the analysis of complex systems and decision processes," IEEE Trans. Syst. Man Cybern., vol. SMC-3, no. 1, pp. 28-44, Jan. 1973.
83. L. A. Zadeh, "The concept of a linguistic variable and its application to approximate reasoning-I," Inf. Sci., vol. 8, no. 3, pp. 199-249, 1975.
84. H. Zhang, M. Dong, W. Zhang, and X. Song, "Inclusion measure and similarity measure of intuitionistic and interval-valued fuzzy sets," in Proc. Intl. Conf. Intell. Syst. Knowl. Eng. (ISKE 2007). T.Li,Y.Xu,and D. Ruan, Eds. Oxford, U.K.: Atlantis, 2007.
85. L. Zhou, "On local inclusion degree of intuitionistic fuzzy sets," in Proc. Rough Sets Knowl. Technol., 2011, pp. 440-446.