3,138 research outputs found
Measuring Relations Between Concepts In Conceptual Spaces
The highly influential framework of conceptual spaces provides a geometric
way of representing knowledge. Instances are represented by points in a
high-dimensional space and concepts are represented by regions in this space.
Our recent mathematical formalization of this framework is capable of
representing correlations between different domains in a geometric way. In this
paper, we extend our formalization by providing quantitative mathematical
definitions for the notions of concept size, subsethood, implication,
similarity, and betweenness. This considerably increases the representational
power of our formalization by introducing measurable ways of describing
relations between concepts.Comment: Accepted at SGAI 2017 (http://www.bcs-sgai.org/ai2017/). The final
publication is available at Springer via
https://doi.org/10.1007/978-3-319-71078-5_7. arXiv admin note: substantial
text overlap with arXiv:1707.05165, arXiv:1706.0636
On Cores and Stable Sets for Fuzzy Games
AMS classifications: 90D12; 03E72;cooperative games;decision making;fuzzy games
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Super- and sub-additive envelopes of aggregation functions: interplay between local and global properties, and approximation
Super- and sub-additive transformations of aggregation functions have been recently introduced by Greco, Mesiar, Rindone and Sipeky [The superadditive and the subadditive transformations of integrals and aggregation functions, Fuzzy Sets and Systems 291 (2016), 40{53]. In this article we give a survey of the recent development regarding the existence of aggregation functions with a preassigned super- and sub-additive transformation, and address approximation of these transformations. The underpinning feature of the presented results is dependence of global properties of super- and sub-additive transformations on local properties of aggregation functions
Representation of maxitive measures: an overview
Idempotent integration is an analogue of Lebesgue integration where
-maxitive measures replace -additive measures. In addition to
reviewing and unifying several Radon--Nikodym like theorems proven in the
literature for the idempotent integral, we also prove new results of the same
kind.Comment: 40 page
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