1 research outputs found
Spatial Metric Space for Pattern Recognition Problems
The definition of weighted distance measure involves weights. The paper
proposes a weighted distance measure without the help of weights. Here, weights
are intrinsically added to the measure, and for this, the concept of metric
space is generalized based on a novel divided difference operator. The proposed
operator is used over a two-dimensional sequence of bounded variation, and it
generalizes metric space with the introduction of a multivalued metric space
called spatial metric space. The environment considered for the study is a
two-dimensional Atanassov intuitionistic fuzzy set (AIFS) under the assumption
that membership and non-membership components are its independent variables.
The weighted distance measure is proposed as a spatial distance measure in the
spatial metric space. The spatial distance measure consists of three branches.
In the first branch, there is a domination of membership values, non-membership
values dominate the second branch, and the third branch is equidominant. The
domination of membership and non-membership values are not in the form of
weights in the proposed spatial distance measure, and hence it is a measure
independent of weights. The proposed spatial metric space is mathematically
studied, and as an implication, the spatial similarity measure is multivalued
in nature. The spatial similarity measure can recognize a maximum of three
patterns simultaneously. The spatial similarity measure is tested for the
pattern recognition problems and the obtained classification results are
compared with some other existing similarity measures to show its potency. This
study connects the double sequence to the application domain via a divided
difference operator for the first time while proposing a novel divided
difference operator-based spatial metric space.Comment: 2