Table 3.

Definition of key mathematical notations

Symbol	Definition
Low (L), Medium (M), High (H)	Experience level using in the placement problem
Light (L), Normal (M), Heavy (H)	Experience level using in the deployment problem
μL(w)	Membership function, μL(w)={w∈L,μL(w)∈[0,1]}
μM(w)	Membership function, μL(w)={w∈M,μM(w)∈[0,1]}
μH(w)	Membership function, μL(w)={w∈H,μH(w)∈[0,1]}
a	WLAN delay
b	MAN delay
c	Local edge VM utilization
d	Candidate edge VM utilization
x	WAN bandwidth
y	Length of the incoming application task
z	VM utilization on the edge server
t	Delay sensitivity of the related application
Ri	Fuzzy rule at index ith
${\mu }_i^{R_i}$	The minimum (min) function to determine how the results of multiple rules are combined
	within Ri. ${\mu }_i^{R_i}=\mathit{\text{min}}\left\{{\mu }_a^{R_i}\right(m),{\mu }_b^{R_i}(n),{\mu }_c^{R_i}(l),{\mu }_d^{R_i}(k\left)\right\}$
{m,n,l,k}	The measured experiment value, as crisp data, is the input parameter to be fuzzified
μr	The maximum (max) function to determine how the results of multiple rules have the same decision r on the Fuzzy rules
ω	The center of gravity (COG) of the area under the curve by using the centroid defuzzifier method
T	Incoming task
O	Target of offload