Qasim, Umilkeram (2016) Fuzzy autocatalytic set of fuzzy graph type3 based on functional analysis theory. PhD thesis, Universiti Teknologi Malaysia.

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Abstract
Fuzzy Autocatalytic Set (FACS) of fuzzy graph Type3 is one of the newly capable graphs for a breakthrough of the relationship between fuzzy graph and autocatalytic set. It was successfully used to model an incineration process of a regional clinical waste in 2005. In this research, the mathematical structures of FACS and its properties were explored based on the suitable concept of fuzzy and nonfuzzy metric structure and fuzzy and nonfuzzy normed structure with the structure of its graph. In other words, the possible new structures of FACS have been explored via two new insights of its metric fuzziness and its normed fuzziness. Firstly, a fuzzy detour FT3distance between vertices in FACS was investigated whereby a quasipseudoFT3metric fuzziness on FACS which depends on this distance was established, followed by an introduction to the concept FT3cycle space of FACS as a vector space which is then proven as a normed space. These concepts have led to the visualization of the structure of FACS in a fuzzy norm, hence some propositions and theorems were established. In addition, the study on these structures of FACS was exploited, in particular the connection with functional analysis features and the application of these structures to the clinical incineration process.
Item Type:  Thesis (PhD) 

Uncontrolled Keywords:  nonfuzzy metric structure, Fuzzy Autocatalytic Set (FACS) 
Subjects:  Q Science > QA Mathematics 
Divisions:  Science 
ID Code:  81642 
Deposited By:  Narimah Nawil 
Deposited On:  10 Sep 2019 01:53 
Last Modified:  10 Sep 2019 01:53 
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