A Category-Theoretic Approach to Systems in a Fuzzy World

The last 30 years have seen the growth of a new branch of mathematics called Category Theory which provides a general perspective on many different branches of mathematics. Many workers (see Lawvere, 1972) have argued that it is category theory, rather than Set Theory, that provides the proper setting for the study of the Foundations of Mathematics.

[1]  M. Schützenberger.  On a Theorem of R. Jungen , 1962 .

[2]  Michael Athans,et al.  Optimal Control , 1966 .

[3]  J. Goguen.  L-fuzzy sets , 1967 .

[4]  Michael A. Arbib,et al.  Topics in Mathematical System Theory , 1969 .

[5]  S. Maclane,et al.  Categories for the Working Mathematician , 1971 .

[6]  J. Goguen.  Minimal realization of machines in closed categories , 1972 .

[7]  Roger C. Schank,et al.  Computer Models of Thought and Language , 1974 .

[8]  Michael A. Arbib,et al.  Foundations of system theory: Decomposable systems , 1974, Autom..

[9]  Joseph A. Goguen,et al.  Concept Representation in Natural and Artificial Languages: Axioms, Extensions and Applications for Fuzzy Sets , 1974, Int. J. Man Mach. Stud..

[10]  Hartmut Ehrig,et al.  Universal theory of automata - a categorial approach , 1974, Teubner Studienbücher.

[11]  Hartmut Ehrig,et al.  Structure Theory of Automata , 1974 .

[12]  R. Thom.  Stabilité structurelle et morphogenèse , 1974 .

[13]  E. S. Bainbridge.  Adressed machines and duality , 1974, Category Theory Applied to Computation and Control.

[14]  M. Arbib,et al.  MACHINES IN A CATEGORY: AN EXPOSITORY INTRODUCTION* , 1974 .

[15]  Louis Padulo.  System theory , 1974 .

[16]  M. Arbib,et al.  Fuzzy machines in a category , 1975, Bulletin of the Australian Mathematical Society.

[17]  M. Arbib,et al.  Arrows, Structures, and Functors: The Categorical Imperative , 1975 .

[18]  Ernest Gene Manes,et al.  Category Theory Applied to Computation and Control , 1975, Lecture Notes in Computer Science.

[19]  Hartmut Ehrig,et al.  Universal Theory of Automata , 1976 .