4.7.2 Mathematical Definition of RSS

4.7.2 Mathematical Definition of RSS

Let

RiR_iRi​

denote the relational vector associated with spatial unit iii.

The relative spatial similarity between two spatial units is defined as

RSS(i,j)=Ψ(Ri,Rj),RSS(i,j) = \Psi(R_i,R_j),RSS(i,j)=Ψ(Ri​,Rj​),

where

Ψ(⋅)\Psi(\cdot)Ψ(⋅)

represents the similarity operator adopted within the ULVF framework.

The resulting similarity coefficient satisfies

0≤RSS(i,j)≤1,0 \le RSS(i,j) \le 1,0≤RSS(i,j)≤1,

where

• 0 indicates complete spatial dissimilarity,

• 1 indicates identical relational structures.

Unlike conventional similarity measures based solely on attribute comparison, RSS evaluates the similarity of value interaction structures within the Urban Land Value Field.