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

Author

Barrenechea, Edurne ; Bustince, Humberto ; De Baets, Bernard ; Lopez-Molina, Carlos

Author_Institution

Dept. de Autom. y Comput., Univ. Publica de Navarra, Pamplona, Spain

Volume

19

Issue

5

fYear

2011

Firstpage

819

Lastpage

830

Abstract

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.

Keywords

edge detection; fuzzy set theory; matrix algebra; construction method; fuzzy edge image generation; image processing; interval valued fuzzy relations; submatrix; triangular conorm; triangular norm; Decision making; Detectors; Fuzzy sets; Image edge detection; Pixel; Upper bound; Fuzzy edge; fuzzy relation (FR); image processing; interval-valued fuzzy relation (IVFR); triangular norm ($t$-norm);

fLanguage

English

Journal_Title

Fuzzy Systems, IEEE Transactions on

Publisher

ieee

ISSN

1063-6706

Type

jour

DOI

10.1109/TFUZZ.2011.2146260

Filename

5754566