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- W2011594829 abstract "In many domains of information processing, bipolarity is a core feature to be considered: positive information represents what is possible or preferred, while negative information represents what is forbidden or surely false. If the information is moreover endowed with vagueness and imprecision, as is the case for instance in spatial information processing, then bipolar fuzzy sets constitute an appropriate knowledge representation framework. In this paper, we focus on mathematical morphology as a tool to handle such information and reason on it. Applying mathematical morphology to bipolar fuzzy sets requires defining an appropriate lattice. We extend previous work based on specific partial orderings to any partial ordering leading to a complete lattice. We address the case of algebraic operations and of operations based on a structuring element, and show that they have good properties for any partial ordering, and that they can be useful for processing in particular spatial information, but also other types of bipolar information such as preferences and constraints. Particular cases using Pareto and lexicographic orderings are illustrated. Operations derived from fuzzy bipolar erosion and dilation are proposed as well." @default.
- W2011594829 created "2016-06-24" @default.
- W2011594829 creator A5088407901 @default.
- W2011594829 date "2012-10-01" @default.
- W2011594829 modified "2023-10-03" @default.
- W2011594829 title "Mathematical morphology on bipolar fuzzy sets: general algebraic framework" @default.
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- W2011594829 doi "https://doi.org/10.1016/j.ijar.2012.05.003" @default.
- W2011594829 hasPublicationYear "2012" @default.
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