Omega algebra model of clinical waste incineration process

Abstract

This research shows how the Fuzzy Autocatalytic Set (FACS) is transformed into a semigroup. Omega algebra is used as the main aspect to relate the FACS to the transformation semigroup of omega algebra of the FACS. Clinical waste incineration process is used as an example in supporting the developed theorems and lemmas. C++ programming is used to develop a customized program that computes the necessary data in supporting new theorems and lemmas. First, the FACS is defined in terms of omega algebra, giving the omega algebra of FACS. Next, the semigroup of omega algebra of FACS is constructed using the omega algebra of FACS. The membership value of fuzzy edge connectivity is also determined to complete the definition of the omega algebra of FACS. New definitions and terminologies are used to model the clinical waste incineration process in terms of omega algebra. As a result, the new model is shown to be able to comprehensively explain the catalytic relation amongst the chemical elements in the clinical waste incineration process. The established semigroup of omega algebra of FACS is then defined to be a transformation semigroup of omega algebra of FACS. The results show that FACS of the clinical waste incineration process and the structure of transformation semigroup of omega algebra of the clinical waste incineration process are “compatible”. In addition, the manifold representation of the transformation semigroup of omega algebra of FACS is proposed for further studies.