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A category-theoretic approach to systems in a fuzzy world

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Bibliography

  • Arbib, M. A. and Manes, E. G.: 1974a, ‘Machines in a Category: An Expository Introduction’, SIAM Review 16, 163–192.

    Google Scholar 

  • Arbib, M. A. and Manes, E. G.: 1974b, ‘Foundations of System Theory: Decomposable Machines’, Automatica 10, 285–302.

    Google Scholar 

  • Arbib, M. A. and Manes, E. G.: 1975, Arrows, Structures, and Functors: The Categorical Imperative, Academic Press, New York.

    Google Scholar 

  • Arbib, M. A. and Manes, E. G.: (to appear), ‘Fuzzy Machines in a Category’.

  • Athans, M. and Falb, P. L.: 1966, Optimal Control, McGraw-Hill.

  • Bainbridge, E. S.: 1975, ‘Addressed Machines and Duality’, in E. G. Manes (ed.), Category Theory Applied to Computation and Control, Lecture Notes in Computer Science 25, 93–98, Springer-Verlag, Heidelberg.

    Google Scholar 

  • Bobrow, L. S. and Arbib, M. A.: 1974, Discrete Mathematics, Saunders, Philadelphia.

    Google Scholar 

  • Ehrig, H., Kiermeier, K.-D., Kreowski, M.-J, and Kühnel, W.: 1974, Universal Theory of Automata: A Categorical Approach, Teubner.

  • Goguen, J. A.: 1967, ‘L-Fuzzy Sets’, J. Math. Anal. Appl. 18, 145–174.

    Google Scholar 

  • Goguen, J. A.: 1969, ‘The Logic of Inexact Concepts’, Synthese 19, 325–373.

    Google Scholar 

  • Goguen, J. A.: 1972, ‘Minimal Realization of Machines in Closed Categories’, Bull. Amer. Math. Soc. 78, 777–783.

    Google Scholar 

  • Goguen, J. A.: 1973, ‘Realization is Universal’, Math. Sys. Th. 6, 359–374.

    Google Scholar 

  • Goguen, J. A.: 1974, ‘Concept Representation in Natural and Artificial Languages: Axioms, Extensions and Applications for Fuzzy Sets’, Int. J. Man-Machine Studies 6, 513–561.

    Google Scholar 

  • Goguen, J. A., Thatcher, J. W., Wagner, E. G., and Wright, J. B.: 1973, ‘A Junction Between Computer Science and Category Theory, I: Basic Concepts and Examples (Part 1)’, IBM Research Report RC 4526, T. J. Watson Research Center.

  • Kalman, R. E., Falb, P. L., and Arbib, M. A.: 1969, Topics in Mathematical System Theory, Mc-Graw Hill.

  • Lawvere, F. W. (ed.): 1972, Toposes, Algebraic Geometry and Logic, Lecture Notes in Mathematics 274, Springer-Verlag.

  • MacLane, S.: 1971, Categories for the Working Mathematician, Springer-Verlag.

  • Manes, E. G.: 1975a, Algebraic Theories, Springer-Verlag.

  • Manes, E. G. (ed.): 1975b, Category Theory Applied to Computation and Control, Proceedings of the First International Symposium, Lecture Notes in Computer Science 25, Springer-Verlag, Heidelberg.

    Google Scholar 

  • Padulo, L. and Arbib, M. A.: 1974, System Theory, Saunders, Philadelphia.

    Google Scholar 

  • Schank, R. C. and Colby, K. M. (eds.): 1973, Computer Models of Thought and Language, W. H. Freeman.

  • Schützenberger, M. P.: 1962, ‘On a Theorem of R. Jungen’, Trans. Amer. Math. Soc. 13, 885–890.

    Google Scholar 

  • Thom, R.: 1972, Stabilité Structurelle et Morphogénèse, W. A. Benjamin, Inc.

  • Zadeh, L.: 1965, ‘Fuzzy Sets’, Inform. Control 8, 338–353.

    Google Scholar 

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The research reported in this paper was supported in part by the National Science Foundation under Grant No. GJ 35759.

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Arbib, M.A., Manes, E.G. A category-theoretic approach to systems in a fuzzy world. Synthese 30, 381–406 (1975). https://doi.org/10.1007/BF00485051

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