کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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394775 | 665841 | 2015 | 14 صفحه PDF | دانلود رایگان |
Mathematical morphology is based on the algebraic framework of complete lattices and adjunctions, which endows it with strong properties and allows for multiple extensions. In particular, extensions to fuzzy sets of the main morphological operators, such as dilation and erosion, can be done while preserving all properties of these operators. Another extension concerns bipolar fuzzy sets, where both positive information and negative information are handled, along with their imprecision. We detail these extensions from the point of view of the underlying lattice structure. In the case of bipolarity, its two-components nature raises the question of defining a proper partial ordering. In this paper, we consider Pareto (component-wise) and lexicographic orderings.
Journal: Information Sciences - Volume 181, Issue 10, 15 May 2011, Pages 2002–2015