Evaluation of steady state vector of fuzzy autocatalytic set of fuzzy graph type-3 of an incineration process

Authors:
Sumarni Abu Bakar;Tahir Ahmad;Sabariah Baharun
Affiliations:
Department of Mathematics & Theoretical & Computational Modeling for Complex Systems, Faculty of Science, UTM, Skudai, Johor, Malaysia;Department of Mathematics & Theoretical & Computational Modeling for Complex Systems, Faculty of Science, UTM, Skudai, Johor, Malaysia;Department of Mathematics & Theoretical & Computational Modeling for Complex Systems, Faculty of Science, UTM, Skudai, Johor, Malaysia
Venue:
WSEAS Transactions on Mathematics
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 theory. This paper employs Markov chain to the evaluation of steady state of an incineration process. Novel definition of transition probability matrix of FACS is presented. Steady state vector of Markov chain for incineration process is determined and graph of convergence of its norm difference is presented. This study led to some relation of Markov process and Perron-Frobenius Theorem.