Convergence of Markov process for fuzzy autocatalytic set of fuzzy graph type-3 of an incineration process

  • Authors:

  • Sumarni Abu Bakar;Tahir Ahmad;Sabariah Baharun

  • Affiliations:

  • Theoretical & Computational Modeling for Complex Systems, Ibnu Sina Institute for Fundamental Science Studies & Department of Mathematics, Faculty of Science, UTM, Skudai, Johor, Malaysia;Theoretical & Computational Modeling for Complex Systems, Ibnu Sina Institute for Fundamental Science Studies & Department of Mathematics, Faculty of Science, UTM, Skudai, Johor, Malaysia;Theoretical & Computational Modeling for Complex Systems, Ibnu Sina Institute for Fundamental Science Studies & Department of Mathematics, Faculty of Science, UTM, Skudai, Johor, Malaysia

  • Venue:
  • NN'10/EC'10/FS'10 Proceedings of the 11th WSEAS international conference on nural networks and 11th WSEAS international conference on evolutionary computing and 11th WSEAS international conference on Fuzzy systems
  • Year:
  • 2010

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Abstract

Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph of Type-3 incorporates the concept of fuzzy, graph and autocatalytic set. It was initially defined and used in the modeling of a clinical waste incineration process which has produced more accurate results than using crisp graph. As it is a newly developed theory, FACS seems to have great potentials in generating new mathematical theories and structures that would enrich the theory itself. With this in mind, we have embarked the study into the Markovian approach. This paper applies the theory of classical Markov chain to the evaluation of steady state of an incineration process. New definition for transition probability matrix of FACS is presented. Two methods for obtaining steady state vector of Markov chain for incineration process are implemented. Our study on FACS with regard to the system led to some relation of a Markov process and Perron-Frobenius Theorem for stochastic matrix.