fuzzy logics of living systems
0.1 Fuzzy logics of living organisms.
Living organisms or biosystems can be represented assuper-complex systems (http://planetmath.org/ComplexSystemsBiology) with dynamicsthat is not reducible to that of their components, such as molecules and atoms. It is anempirically accepted fact that living organisms exhibit a wide degree of ‘biological variability’:genetic/epigenetic and also phenotypic/metabolic within the same species; their behaviorand dynamics thus exhibit a type of ‘fuzziness’ (refs.[2, 3]) that unlike Zadeh’sfuzzy sets characteristic ([7, 8]) is neither random nor always following a (symmetric
) Gaussian distribution.It has been proposed that the operational logics underlyingsuper-complex systems dynamics (http://planetmath.org/FundamentalDiagramsInCategoricalTheoryOfLevels) are many-valued logics (http://planetmath.org/AlgebraicCategoryOfLMnLogicAlgebras) for both geneticand neural networks (refs. [3, 6]).
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References
- 1 Georgescu, G. 2006, N-valued Logics and Łukasiewicz-MoisilAlgebras
, Axiomathes, 16 (1-2): 123-136.
- 2 Baianu, I.C. and M. Marinescu: 1968, Organismic Supercategories
- 3 Baianu, I.C.: 1977, A Logical Model of Genetic Activities in Łukasiewicz Algebras: The Non-linear Theory. Bulletin of Mathematical Biology, 39: 249-258.
- 4 Baianu, I. C.: 1986–1987a, Computer Models and Automata Theory in Biology and Medicine., in M. Witten (ed.),Mathematical Models in Medicine, vol. 7., Ch.11 Pergamon Press, New York, 1513 -1577; URLs:http://doe.cern.ch//archive/electronic/other/ext/ext-2004-072.pdfCERN Preprint No. EXT-2004-072 ,and http://en.scientificcommons.org/1857371html Abstract.
- 5 Baianu, I. C.: 1987b, Molecular Models of Genetic and Organismic Structures
- 6 Baianu, I.C.: 2004. Łukasiewicz-Topos Models of Neural Networks, Cell Genome and Interactome Nonlinear Dynamic Models (2004). Eprint: w. Cogprints at Sussex Univ.
- 7 Zadeh, L.A., Fuzzy Sets, Information and Control, 8 (1965) 338ÃÆÃâÃÂ-353.
- 8 Zadeh L. A., The concept of a linguistic variable and its application to approximate reasoning I, II, III, Information Sciences, vol. 8, 9(1975), pp. 199-275, 301-357, 43-80.