Abstract
Novel Structures of Normed Spaces with Fuzzy Autocatalytic Set (FACS) of Fuzzy Graph Type-3
Highlights
Fuzzy set theory was proposed by Zadeh (1965) and it has been employed in mathematical modelling of some systems
An integration of fuzzy graph into ACS was inspired to produce a new concept known as Fuzzy Autocatalytic Set (FACS) and shown to be a better in explaining the incineration process (Tahir et al, 2010)
We focus on the study of FACS of fuzzy graph Type-3 from a viewpoint of normed space and cycles in FACS
Summary
Fuzzy set theory was proposed by Zadeh (1965) and it has been employed in mathematical modelling of some systems. An integration of fuzzy graph into ACS was inspired to produce a new concept known as Fuzzy Autocatalytic Set (FACS) and shown to be a better in explaining the incineration process (Tahir et al, 2010). A new concept namely normed space of FACS of fuzzy graph Type-3 is defined and implemented in the modelling of the incineration process. The edge has fuzzy head and tail (Fig. 2) These notions namely fuzzy, graph and Autocatalytic Set (ACS) are integrated to formulate the mathematical model of the clinical incineration process. Pertaining to the construction of FACS of fuzzy graph of Type-3 for the incineration process, the graph is Umilkeram and Tahir (2014) introduced the concept of fuzzy detour FT3-distance between vertices in FACS by establishing the FT3-length of any fuzzy detour path between two distinct vertices in FACS. This notion produces a new type of normed space for FACS
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