> >Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type-3 was established in the effort to describe the underlying phenomena of a clinical waste incineration process. Further research could be explored to scrutinize this concept especially in looking at its mathematical structure. In this paper, we highlighted the mathematical structures of FACS particularly on the algebraic structures of its matrix and graph. New definitions and theorems were generated through this investigation which leads to the visualization of the concept in Euclidean space. This visualization was accomplished through the transformation of non coordinated FACS to coordinated FACS in space. Eventually, the performance of coordinated FACS is then compared to the non-coordinated FACS in respect to the clinical waste incineration process.
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