46,116 research outputs found
Basic generated universal fuzzy measures
AbstractThe concept of basic generated universal fuzzy measures is introduced. Special classes and properties of basic generated universal fuzzy measures are discussed, especially the additive, the symmetric and the maxitive case. Additive (symmetric) basic universal fuzzy measures are shown to correspond to the Yager quantifier-based approach to additive (symmetric) fuzzy measures. The corresponding fuzzy integral-based aggregation operators are introduced, including the generated OWA operators
Cultural dialects of real and synthetic emotional facial expressions
In this article we discuss the aspects of designing facial expressions for virtual humans (VHs) with a specific culture. First we explore the notion of cultures and its relevance for applications with a VH. Then we give a general scheme of designing emotional facial expressions, and identify the stages where a human is involved, either as a real person with some specific role, or as a VH displaying facial expressions. We discuss how the display and the emotional meaning of facial expressions may be measured in objective ways, and how the culture of displayers and the judges may influence the process of analyzing human facial expressions and evaluating synthesized ones. We review psychological experiments on cross-cultural perception of emotional facial expressions. By identifying the culturally critical issues of data collection and interpretation with both real and VHs, we aim at providing a methodological reference and inspiration for further research
A kernel-based framework for learning graded relations from data
Driven by a large number of potential applications in areas like
bioinformatics, information retrieval and social network analysis, the problem
setting of inferring relations between pairs of data objects has recently been
investigated quite intensively in the machine learning community. To this end,
current approaches typically consider datasets containing crisp relations, so
that standard classification methods can be adopted. However, relations between
objects like similarities and preferences are often expressed in a graded
manner in real-world applications. A general kernel-based framework for
learning relations from data is introduced here. It extends existing approaches
because both crisp and graded relations are considered, and it unifies existing
approaches because different types of graded relations can be modeled,
including symmetric and reciprocal relations. This framework establishes
important links between recent developments in fuzzy set theory and machine
learning. Its usefulness is demonstrated through various experiments on
synthetic and real-world data.Comment: This work has been submitted to the IEEE for possible publication.
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Toward a probability theory for product logic: states, integral representation and reasoning
The aim of this paper is to extend probability theory from the classical to
the product t-norm fuzzy logic setting. More precisely, we axiomatize a
generalized notion of finitely additive probability for product logic formulas,
called state, and show that every state is the Lebesgue integral with respect
to a unique regular Borel probability measure. Furthermore, the relation
between states and measures is shown to be one-one. In addition, we study
geometrical properties of the convex set of states and show that extremal
states, i.e., the extremal points of the state space, are the same as the
truth-value assignments of the logic. Finally, we axiomatize a two-tiered modal
logic for probabilistic reasoning on product logic events and prove soundness
and completeness with respect to probabilistic spaces, where the algebra is a
free product algebra and the measure is a state in the above sense.Comment: 27 pages, 1 figur
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