Similarity, Distance Measures and Entropy - Medical Image Processing: Advanced Fuzzy Set Theoretic Techniques - page 70

The median values of two subintervals are written as

μ () () xmx +

mx mx

()( + 1

2

− ν ( x ))

Ai Ai Ai Ai

mx () = and () =

Ai 1 Ai 2

2

In a similar way, the median value of the interval of set B , [μ B ( x i ), 1 − ν B ( x i )] i is

μ ()( x +− 1

2

ν ( x ))

Bi Bi

mx () =

Bi

and the two subintervals are [μ B ( x i ), m B ( x i )] and [ m B ( x i ), 1 − ν B ( x i )].
Likewise, the median values of the two subintervals are

μ () () xmx +

mx mx

()( + 1

2

− ν ( x ))

Bi Bi Bi Bi

mx () = and () =

Bi 1 Bi 2

2

Then the similarity measure is defined as

n

1

∑

L p

SAB (,) =− 1 ( () ( ) ϕ x + ϕ x (4.13)

p

IFS Ai Bi

p

n

i = 1

where

x mxmx

() () −

Ai Bi 1 1

()

ϕ =

Ai

2

x mxmx

() () −

Ai Bi 2 2

ϕ () =

Bi

2

4.4 Intuitionistic Fuzzy Measure
A distance measure called intuitionistic fuzzy divergence ( IFD ) is described
in [3], where three parameters, namely, the membership degree, the non-
membership degree, and the hesitation degree (or intuitionistic fuzzy index),
are considered.
Let A = {( x , μ A ( x ), ν A ( x ))| x ∈ X } and B = {( x , μ B ( x ), ν B ( x ))| x ∈ X } be two IFS s.
Considering the hesitation degree, the interval or range of the member-
ship degree of the two IFS s A and B may be represented as {μ A ( x ), (μ A ( x ) +
π A ( x ))} and {μ B ( x ), (μ B ( x ) + π B ( x ))} where μ A ( x ) and μ B ( x ) are the membership