scholarly journals Graph Dynamics of Fuzzy Autocatalytic Set of Fuzzy Graph Type-3 of a Clinical Waste Incineration Process

2014 ◽  
Vol 8 (4) ◽  
Author(s):  
Sumarni Abu Bakar ◽  
Tahir Ahmad ◽  
Sabariah Baharun
Keyword(s):  
Transition Matrix ◽  
Waste Incineration ◽  
Actual Process ◽  
Fuzzy Graph ◽  
Graph Type ◽  
Graph Dynamics ◽  
Incineration Process ◽  
Type 3 ◽  
Perron Vector

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.

scholarly journals Interactive graph dynamics for fuzzy autocatalytic set of fuzzy graph of type-3 for combustion process in a circulating fluidized bed boiler

2015 ◽  
Vol 11 (1) ◽  
Author(s):  
Hazwani Hashim ◽  
Sumarni Abu Bakar
Keyword(s):  
Fluidized Bed ◽  
Chemical Reactions ◽  
Transition Matrix ◽  
Circulating Fluidized Bed ◽  
Combustion Process ◽  
Fuzzy Graph ◽  
The Real ◽  
Real Process ◽  
Graph Dynamics ◽  
Type 3

Dynamical changes of chemical reactions which occurred during combustion process in Circulating Fluidized Bed boiler (CFB) has been modelled using adjacency matrix of Fuzzy Autocatalytic Set (FACS) of fuzzy graph type-3. Analysis of sequence of changes in the reactions at time t through Perron-Frobenious eigenvector (PFE) of the matrix in the Graph Dynamic Algorithm (GDA) shows that end-product of the combustion process in the CFB namely Water and Hydrogen is not really potrayed the real process.  Therefore, in this study, transition matrix of FACS is utilized to analyse the dynamical changes of the reactions and the GDA is modified and improvised and known as Interactive Graph Dynamics (IGD) is subsequently use to facilitate the analysis. The result shows that by using the transition matrix of FACS, the end-product of the combustion process in CFB is in accordance to the real process. Whilst the IGD is able to reduced computer running time as compared to the existing GDA. This paper describes the development of IGD and the analysis of sequence of changes of chemical reactions during combustion process in CFB by using transition matrix with the helped of MATLAB. 

scholarly journals Fuzzy autocatalytic set (FACS) as fuzzy vector space

2016 ◽  
Vol 12 (2) ◽  
Author(s):  
Rossiana Edhelyn ◽  
Tahir Ahmad
Keyword(s):  
Vector Space ◽  
Euclidean Distance ◽  
Waste Incineration ◽  
Fuzzy Graph ◽  
Mathematical Structures ◽  
Laplacian Matrices ◽  
Graph Type ◽  
Euclidean Distance Matrices ◽  
Type 3 ◽  
Fuzzy Vector

Dynamic model of clinical waste incineration process in Malacca has been successfully developed using Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type 3. FACS combines the concept of fuzzy graph and autocatalytic set and has been proven to yield more precise results than using crisp graph. Next, the graph of its process has been transformed from non-coordinated FACS to coordinated FACS in Euclidean space. Some mathematical structures related to the transformation are adjacency, transition and Laplacian matrices of FACS. Furthermore, it is found that FACS to be primitive, irreducible and aperiodic. The set of adjacency matrices of FACS of Fuzzy Graph Type 3 is predicted to be seen as fuzzy vector space, and the set of Euclidean distance matrices represent coordinated FACS is also expected to be fuzzy vector space as well. As a recently developed theory, FACS has great capabilities in generating new mathematical theories and structures that would enrich the theory itself. this study is made to attempt the formulation of new algebraic structure in FACS which is fuzzy vector space.

Coordinated Transformation for Fuzzy Autocatalytic Set of Fuzzy Graph Type-3

2015 ◽  
Vol 11 (4) ◽  
pp. 119-127
Author(s):  
Tahir Ahmad ◽  
Sumarni Abu Bakar ◽  
Sabariah Baharun ◽  
Faisal A.M. Binjadhnan
Keyword(s):  
Fuzzy Graph ◽  
Graph Type ◽  
Type 3

scholarly journals Some properties of fuzzy quasi-metric space for FACS of fuzzy graph type-3

2015 ◽  
Vol 11 (2) ◽  
Author(s):  
Umilkeram Qasim Obaid ◽  
Tahir Ahmad
Keyword(s):  
Metric Space ◽  
Fuzzy Graph ◽  
Graph Type ◽  
Type 3

In this paper, we investigate some properties and characteristics of fuzzy quasi-metric space of Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3. These properties are used to justify an aperiodicity of a graph. 

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