Construction of Interval-Valued Fuzzy Relations With Application to the Generation of Fuzzy Edge Images

In this paper, we present a new construction method for interval-valued fuzzy relations (interval-valued fuzzy images) from fuzzy relations (fuzzy images) by vicinity. This construction method is based on the concepts of triangular norm (
t
-norm) and triangular conorm (
t
-conorm). We analyze the effect of using different
t
-norms and
t
-conorms. Furthermore, we examine the influence of different sizes of the submatrix around each element of a fuzzy relation on the interval-valued fuzzy relation. Finally, we apply our construction method to image processing, and we compare the results of our approach with those obtained by means of other, i.e., fuzzy and nonfuzzy, techniques.