Date of Submission


Date of Award


Institute Name (Publisher)

Indian Statistical Institute

Document Type

Doctoral Thesis

Degree Name

Doctor of Philosophy

Subject Name

Computer Science


Electronics and Communication Sciences Unit (ECSU-Kolkata)


Majumdar, Dwijesh Dutta (ECSU-Kolkata; ISI)

Abstract (Summary of the Work)

Unceriain information processing by fuzzy if-then rules has received a lot of attention. Here we have taken a different path to model a system. about which we do not have precise information namely. modelling the system by fuzy valued functions without resorting to fuzzy if-then rules. As a result. the phase (state) space of the system becomes a full set and the underlying fuzzy mapping becomes a fuzzy attainability vet mappine. A fuzzy phase space is a collection of special class of furry subsets (fuzsy points) of R&for some positive integral n. Let the collection of all fuzr, real numbers be R. A relationship of fuzzy phase spaces has been established with . A field like structure for (it has important similarities and differences with the classical ficids) has been developed and a vector space like structure (it has important similarities and differences with the classical vector spacel has been developed for 8. A metric has been defined on R&. Ii has been proved that any arbitrar fuzzy subset of R"can he penerated by a suitable collection of members of"by max-min operations. Some possible role of in pattern recognition has been explored. Incertain or fuzzy dissipative dynamical systems have been defined in systems of fuzzy atainability set mappings. A criterion for determining dissipativeness of a dynanmical system has been formulated. Attractor. stability, robustness, predictability, homoclinicity etc. for fuzzy dynamical systems have been defined. Devaney's definition of chaos has been extended to fuzzy dynamical systems. Fuzzy differentiable dynamical systems have been discussed with a particular emphasis on fuzzy differential inclusion (FDI) relations. An evolutionary algorithm for solving one dimensional FDIS has been developed. Uising this algorithm a second order FDI retation has been solved. Fuzzy fractals have been defined as attractors of contractive iterated fuzzy sets systems. which is a class of discrete fuzzy dissipative dynamical systems. Fuzzy fractals are so defined that. crisp fractals obtained as attractors of Bamsley's chaos games become special cases of fuzzy fractals. Fuzzy fractal based gery level image generation has been discussed. using this method some fuzzy fractal images have been generated. Model of a simple two dimensional turbulence, as a chaotic occurrence of vortices in a two dimensional dynamic fluid, has been proposed and simulated. Each coordinate of the position of the centre of a vorex in the dynamic fluid plain is given by a chantic value obtained by an iterated logistic function system for an appropriate parameter value. Fach vortex is modelled hy a fuzzy valued function, where uncertain parameter and variable values are fuzzy nambers. This is obtained by solving an FDI with the algorithım developed. The simulated turbulence thus obtained has been presented.The starting stage of an intense tropical storm is a system about which so tar very little precise information is available. It is recognized that a sufficiently strong initial disturbance must he present to give rise to a tropical storm of hurricane intensity under favourable climatic and geographical conditions. A mode! of this initial disturbance in the form of a vortex, created by winds coming from different directions and colliding under certain conditions.


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Creative Commons Attribution 4.0 International License
This work is licensed under a Creative Commons Attribution 4.0 International License.


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