Abstract
Generalized fuzzy rules provide the essential means for computational representation of equational and inequality constraints over fuzzy granular structures. In this chapter, we are concerned with the ways the rules can be acquired from the real world data. We also provide a method for elicitation of knowledge of experts and link this to Zadeh’s Computational Theory of Perceptions. The algorithms for extracting and consistency checking of the rules explore the BK-products of relations. This makes it possible to treat the numerical and linguistic computations in a unified framework with the methods for extrapolation of knowledge and data.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
W. Bandler and L.J. Kohout. Mathematical Relations, their Products and Generalized Morphisms. Tech. report, Man-Machine Systems Laboratory, EES-MMS-REL 77-3, Dept. of Electrical Eng., University of Essex, Colchester, Essex, U.K., 1977. Reprinted as Ch. 2 in: Kohout, L.J. & Bandler, W., Survey of Fuzzy and Crisp Relations, Lect. Notes in Fuzzy Mathematics and Computer Sei., Creighton Univ. Omaha (to appear in 2000).
W. Bandier and L.J. Kohout. Fuzzy relational products and fuzzy implication operators. In International Workshop on Fuzzy Reasoning Theory and Applications, London, September 1978. Queen Mary College, University of London.
W. Bandler and L.J. Kohout. Activity structures and their protection. In R.F. Ericson, editor, Improving the Human Condition: Quality and Stability in Social Systems (Proc. Silver Anniversary 1979 International Meeting of the Society for General Systems Research), pages 239–244, Louisville KY, 1979. Society for General Systems Research, Distributed by Springer Verlag, New York.
W. Bandier and L.J. Kohout. Fuzzy relational products as a tool for analysis and synthesis of the behavior of complex natural and artificial systems. In P.P. Wang and S.K. Chang, editors, Fuzzy Sets: Theory and Applications to Policy Analysis and Information Systems, pages 341–367. Plenum press, New York and London, 1980.
W. Bandier and L.J. Kohout. Semantics of implication operators and fuzzy relational products. Internat. Journal of Man-Machine Studies, 12:89–116, 1980. Reprinted in Mamdani, E.H. and Gaines, B.R. eds. Fuzzy Reasoning and its Applications. Academic Press, London, 1981, pages 219-246.
W. Bandier and L.J. Kohout. On the general theory of relational morphisms. International Journal of General Systems, 13:47–66, 1986.
W. Bandier and L.J. Kohout. A survey of fuzzy relational products in their applicability to medicine and clinical psychology. In L.J. Kohout and W. Bandier, editors, Knowledge Representation in Medicine and Clinical Behavioral Science, pages 107–118. an Abacus Book, Gordon and Breach Publ., London and New York, 1986.
W. Bandier and L.J. Kohout. Fuzzy implication operators. In M.G. Singh, editor, Systems and Control Encyclopedia, pages 1806–1810. Pergamon Press, Oxford, 1987.
W. Bandier and L.J. Kohout. Relations, mathematical. In M.G. Singh, editor, Systems and Control Encyclopedia, pages 4000–4008. Pergamon Press, Oxford, 1987.
W. Bandier and L.J. Kohout. Special properties, closures and interiors of crisp and fuzzy relations. Fuzzy Sets and Systems, 26(3):317–332, 1988.
W. Bandier and L.J. Kohout. On the universality of the triangle superproduct and the square product of relations. Internat. Journal of General Systems, 25(4):399–403, 1997.
W. Bandier, V. Mancini, and L.J. Kohout. Investigating the structures of knowledge and thought. Presented at ICSRIC’88 (4th International Conference on Systems Research, Informatics and Cyber-netics, Baden Baden, Germany, 15-21 August 1988). In: Proceedings thereof.
B. De Baets and E. Kerre. Fuzzy relational compositions. Fuzzy Sets and Systems, 60(1):109–120, 1993.
B. De Baets and E. Kerre. A revision of Bandler-Kohout composition of relations. Mathematica Pannonica, 4:59–78, 1993.
B. Dubrosky, L.J. Kohout, R.M. Walker, E. Kim, and H.P. Wang. Use of fuzzy relations for advanced technology cost modeling and affordability decisions. In 35th AIAA Aerospace Sciences Meeting and Exhibit (Reno, Nevada, January 6-9,1997), pages 1–12, Reno, NV, January 1997. AIAA, the American Institute of Aeronautics and Astronautics. Paper AIAA 97-0079.
P. Hájek. A remark on Bandler-Kohout products of relations. Internat. Journal of General Systems, 25(2): 165–166, 1996.
P. Hájek. Metamathematics of Fuzzy Logics. Kluwer, Dordrecht, 1998.
P. Hájek and L. Godo. Deductive systems of fuzzy logic. In R. Mesiar and B. Riecan, editors, Tatra Mountains, Mathematical Publications (Special Issue: Fuzzy Structures — Current Trends), pages 35–68. Mathematical Institute, Slovak Academy of Sciences, Bratislava, 1997.
L.O. Hall. Some comments on, and an extension to Activity Structures for intelligent systems. Journal of Fuzzy Logic and Intelligent Systems, 3(1):23–28, 1993. A Special Issue in Honor of Wyllis Bandier, edited by L.A. Zadeh et al.
U. Höhle and E.P. Klement. Non-Classical Logics and their Applications to Fuzzy Subsets: A Handbook of Mathematical Foundations of Fuzzy Sets. Kluwer, Boston, 1995.
E. Husserl. Ideas. Collier Macmillan, London, 1962.
B. Juliano and W. Bandier. Tracing Chains-of-Thought: Fuzzy Methods in Cognitive Diagnosis. Physica Verlag. A Springer-Verlag Company, Heidelberg, 1996.
E. Kim and L.J. Kohout. A new tool for comparative evaluation of fuzzy implications, t-norms and co-norms based on generalized morphisms. Fuzzy Sets and Systems, 1999. In press.
E. Kim, L.J. Kohout, B. Dubrosky, and W. Bandier. Use of fuzzy relations for affordability decisions in high technology. In R.A. Adey, G. Rzevski, and A.K. Sunol, editors, Applications of Artificial Intelligence in Engineering XL Computational Mechanics Publications, Southampton, UK — Bilerica, MA, USA, 1996.
E.P. Klement and R. Mesiar. Triangular norms. In R. Mesiar and B. Riecan, editors, Tatra Mountains, Mathematical Publications (Special Issue: Fuzzy Structures — Current Trends), pages 169–194. Mathematical institute Slovak academy of sciences, Bratislava, 1997.
L.J. Kohout. The functional hierarchies of the brain. In G.J. Klir, editor, Applied General Systems Research: Recent Developments and Trends, pages 531–544. Plenum Press, New York, 1978.
L.J. Kohout. Activity structures as a tool for design of technological artifacts. Systems and Cybernetics: An International Journal, 18(1):27–34, 1987.
L.J. Kohout. A Perspective on Intelligent Systems: A Framework for Analysis and Design. Chapman and Hall & Van Nostrand, London & New York, 1990. In 1991, received a prize from The International Institute for Advanced Studies in Systems Research: “The best book of the year in AI Systems”.
L.J. Kohout. Activity Structures: A methodology for design of multi-environment and multi-context knowledge-based systems. In L.J. Kohout, J. Anderson, and W. Bandier, editors, Knowledge-Based Systems for Multiple Environments, chapter 5. Ashgate Publ. (Gower), Aldershot, U.K., 1992.
L.J. Kohout. Dynamic sharing of cognitive structures by means of generalized morphisms. In P.P. Wang, editor, Proc. of the 2nd Joint Conf. on Information Sciences (Sept. 28 — Oct. 1, Wrightsville Beach, NC, USA), pages 597–600. Duke University, 1995.
L.J. Kohout. Generalized morphisms in BL-logics. In Logic Colloquium 1998(The 1998 ASL European Summer Meeting, Prague). Association for Symbolic Logic, August 9-15 1998. (Extended abstract presenting the main mathematical theorems, to appear in the Bulletin of ASL, 1999).
L.J. Kohout. Theory and applications of non-associative products of relations. In T. Childers, editor, The Lógica Yearbook 1997, chapter 16, pages 152–164. Filosofia (Publisher of the Institute of Philosophy, Czech Academy of Sciences), Prague, 1998. (ISBN 80-7007-109-5).
L.J. Kohout. Boolean and fuzzy relations. In P.M. Pardalos and C.A. Floudas, editors, The Encyclopedia of Optimization. Kluwer, Boston, 1999. In press.
L.J. Kohout, J. Anderson, and W. et al. Bandler. Knowledge-Based Systems for Multiple Environments. Ashgate Publ. (Gower), Aider-shot, U.K., 1992. Awarded “Outstanding Scholarly Contribution Award” by the Systems Research Foundation in 1993.
L.J. Kohout and W. Bandler. Fuzzy relational products in knowledge engineering. In V. Novák et al., editor, Fuzzy Approach to Reasoning and Decision Making, pages 51–66. Academia and Kluwer, Prague and Dordrecht, 1992.
L.J. Kohout and W. Bandier. Use of fuzzy relations in knowledge representation, acquisition and processing. In L.A. Zadeh and J. Kacprzyk, editors, Fuzzy Logic for the Management of Uncertainty, pages 415–435. John Wiley, New York, 1992.
L.J. Kohout and B.R. Gaines. Protection as a general systems problem. Internat. Journal of General Systems, 3:1–21, 1976.
L.J. Kohout and M. Kallala. Choice of fuzzy optimal logics for pattern classifiers by means of measure analysis. In Proc. of 7th International Congress on Cybernetics and Systems, Imperial College, London, September 1987.
L.J. Kohout and E. Kim. Granular relational computing with semiotic descriptors using BK-products of fuzzy relations. In P. Wang, Paul, editor, Computing with Words, chapter 4. John Wiley, New York, 1999. In press.
L.J. Kohout and I Stabile. Logic and methodology of galen: Its relevance to contemporary systems science. In G.E. Lasker and R.R. Hough, editors, Advances in Support Systems Research (Proc. of 2nd Internatinal Congress on Systems Research, Informatics and Cybernetics 1989), pages 271–276, 1990. ISBN 0-921836-06-6.
R.D. Maddux. Some varieties containing relation algebras. Transact, of the American Mathematical Society, 272(2):501–526, 1982.
V. Mancini, W. Bandier, and L.J. Kohout. Overview of the urbs project. In P.P. Wang, editor, Proc. of the 2nd Joint Conf. on Information Sciences (Sept. 28 — Oct. 1, Wrightsville Beach, NC, USA), pages 131–133. Duke University, 1995. (In: Invited Session on Fuzzy Relational Modeling as a Tool for Improving Human Sustainable Environment — URBS Project).
L.A. Zadeh. From computation with measurements to computation with perceptions: A paradigm shift. Abstract of a lecture given at BISC, University of California, Berkeley on September 16th, 1999
L.A. Zadeh. Fuzzy Logic = Computing with Words. IEEE Trans. on Fuzzy Systems, 4(2): 103–111, 1996.
L.A. Zadeh. Toward a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic. Fuzzy Sets and Systems, 90(2): 111–127, 1997.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer Science+Business Media New York
About this chapter
Cite this chapter
Kohout, L.J., Kim, E. (2000). Reasoning with Cognitive Structures of Agents I: Acquisition of Rules for Computational Theory of Perceptions by Fuzzy Relational Methods. In: Ruan, D., Kerre, E.E. (eds) Fuzzy If-Then Rules in Computational Intelligence. The Springer International Series in Engineering and Computer Science, vol 553. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4513-2_8
Download citation
DOI: https://doi.org/10.1007/978-1-4615-4513-2_8
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4613-7035-2
Online ISBN: 978-1-4615-4513-2
eBook Packages: Springer Book Archive