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Complexity analysis, uncertainty management and fuzzy dynamical systems: A cybernetic approach

D. Dutta Majumder (Electronics and Communication Sciences Unit, Indian Statistical Institute, Calcutta, India)
Kausik Kumar Majumdar (Electronics and Communication Sciences Unit, Indian Statistical Institute, Calcutta, India)

Kybernetes

ISSN: 0368-492X

Article publication date: 1 August 2004

Abstract

In this paper, we present a brief study on various paradigms to tackle complexity or in other words manage uncertainty in the context of understanding science, society and nature. Fuzzy real numbers, fuzzy logic, possibility theory, probability theory, Dempster‐Shafer theory, artificial neural nets, neuro‐fuzzy, fractals and multifractals, etc. are some of the paradigms to help us to understand complex systems. We present a very detailed discussion on the mathematical theory of fuzzy dynamical system (FDS), which is the most fundamental theory from the point of view of evolution of any fuzzy system. We have made considerable extension of FDS in this paper, which has great practical value in studying some of the very complex systems in society and nature. The theories of fuzzy controllers, fuzzy pattern recognition and fuzzy computer vision are but some of the most prominent subclasses of FDS. We enunciate the concept of fuzzy differential inclusion (not equation) and fuzzy attractor. We attempt to present this theoretical framework to give an interpretation of cyclogenesis in atmospheric cybernetics as a case study. We also have presented a Dempster‐Shafer's evidence theoretic analysis and a classical probability theoretic analysis (from general system theoretic outlook) of carcinogenesis as other interesting case studies of bio‐cybernetics.

Keywords

Citation

Dutta Majumder, D. and Majumdar, K.K. (2004), "Complexity analysis, uncertainty management and fuzzy dynamical systems: A cybernetic approach", Kybernetes, Vol. 33 No. 7, pp. 1143-1184. https://doi.org/10.1108/03684920410534489

Publisher

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Emerald Group Publishing Limited

Copyright © 2004, Emerald Group Publishing Limited