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Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders

Bustince, H.; Marco-Detchart, C.; Fernandez, J.; Wagner, C.; Garibaldi, J.M.; Takáč, Z.

Authors

H. Bustince

C. Marco-Detchart

J. Fernandez

Z. Takáč



Abstract

In this work we study a new class of similarity measures between interval-valued fuzzy sets. The novelty of our approach lays, firstly, on the fact that we develop all the notions with respect to total orders of intervals; and secondly, on that we consider the width of intervals so that the uncertainty of the output is strongly related to the uncertainty of the input. For constructing the new interval-valued similarity, interval valued aggregation functions and interval-valued restricted equivalence functions which take into account the width of the intervals are needed, so we firstly study these functions, both in line with the two above stated features. Finally, we provide an illustrative example which makes use of an interval-valued similarity measure in stereo image matching and we show that the results obtained with the proposed interval-valued similarity measures improve numerically (according to the most widely used measures in the literature) the results obtained with interval valued similarity measures which do not consider the width of the intervals.

Journal Article Type Article
Publication Date Apr 6, 2019
Journal Fuzzy Sets and Systems
Print ISSN 0165-0114
Publisher Elsevier
Peer Reviewed Peer Reviewed
APA6 Citation Bustince, H., Marco-Detchart, C., Fernandez, J., Wagner, C., Garibaldi, J., & Takáč, Z. (2019). Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders. Fuzzy Sets and Systems, https://doi.org/10.1016/j.fss.2019.04.002
DOI https://doi.org/10.1016/j.fss.2019.04.002
Keywords Interval-valued fuzzy sets; Admissible order; Total order; Interval-valued similarity measure; Equivalence and restricted equivalence functions; Interval-valued aggregation function
Publisher URL https://www.sciencedirect.com/science/article/pii/S0165011418304494?via%3Dihub
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