Similarity between interval-valued fuzzy sets taking into account the width of the intervals and admissible orders
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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 int ... [++]
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. [--]
Interval-valued fuzzy sets, Admissible order, Total order, Interval-valued similarity measure, Equivalence and restricted equivalence functions, Interval-valued aggregation function
Fuzzy Sets and Systems, 2020, 390, 23-47
Universidad Pública de Navarra. Departamento de Estadística, Informática y Matemáticas / Universidad Pública de Navarra / Nafarroako Unibertsitate Publikoa. ISC - Institute of Smart Cities / Nafarroako Unibertsitate Publikoa. Estatistika, Informatika eta Matematika Saila
H. Bustince, C. Marco-Detchart and J. Fernandez were partially supported by Spanish research project TIN201677356-P (AEI/FEDER, UE). Z. Takac has been supported by Project VEGA 1/0614/18. This contribution is also the partial result of the Research & Development Operational Programme for the project University Scientific Park STU in Bratislava, ITMS 26240220084. C. Wagner and J. M. Garibaldi were partially supported by the UK EPSRC grant EP/P011918/1.
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