Abstract
Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 (FACS) has been successfully implemented in modeling clinical waste incineration process. Six important variables identified in the process are represented as nodes and the catalytic relationships are represented by fuzzy edges in the graph. However, in this paper, graph dynamics of FACS is further investigated using left Perron vector of its transition matrix of fuzzy graph of FACS. This paper will highlight two important variables in the incineration process with regards to the actual process.
Highlights
The emergence of fuzzy graph to autocatalytic sets has instigated a new concept named Fuzzy Autocatalytic Set (FACS) [1, 2]
Dynamic model of the incineration process using PerronFrobenius eigenvector (PFE) of its adjacency matrix which resulted on the evolution of variables on a longer time scale had been discussed [1] such that the dynamic model provided information of the by- products of the incineration process which are CO2 and H2O and other pollutants
From Lemma 3.1 [9], it shows that transition matrix of FACS, P* is irreducible
Summary
The emergence of fuzzy graph to autocatalytic sets has instigated a new concept named Fuzzy Autocatalytic Set (FACS) [1, 2]. It is defined as a subgraph where each of whose nodes has at least one incoming link with membership value μ(ei )∈ A clinical waste incineration process in Malacca [1, 2] is modelled using this concept where it incorporates fuzzy graph of type-3, GF3 , where both the vertex and edge sets are crisp, but the edges have fuzzy heads and tails.
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