In mathematics, distance and similarity are known as dual concepts. However, the concept of similarity is interpreted as fuzzy similarity or
T-equivalence relation, where
T is a triangular norm (
t-norm in brief), when we discuss a fuzzy environment. Dealing with
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In mathematics, distance and similarity are known as dual concepts. However, the concept of similarity is interpreted as fuzzy similarity or
T-equivalence relation, where
T is a triangular norm (
t-norm in brief), when we discuss a fuzzy environment. Dealing with multi-polarity in practical examples with fuzzy data leadsus to introduce a new concept called
m-polar
-equivalence relations based on a finitely multivalued
t-norm
, and to study the metric behavior of such relations. First, we study the new operators including the
m-polar triangular norm
and conorm
as well as
m-polar implication
and
m-polar negation
, acting on the Cartesian product of
m-times.Then, using the
m-polar negations
, we provide a method to construct a new type of metric spaces, called
m-polar
-pseudo-ultrametric, from the
m-polar
-equivalences, and reciprocally for constructing
m-polar
-equivalences based on the
m-polar
-pseudo-ultrametrics. Finally, the link between fuzzy graphs and
m-polar
-pseudo-ultrametrics is considered. An algorithm is designed to plot a fuzzy graph based on the
m-polar
-pseudo-ultrametric, where
is the
m-polar Lukasiewicz
t-conorm, and is illustrated by a numerical example which verifies our method.
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