998 research outputs found
New results on systems of generalized vector quasi-equilibrium problems
In this paper, we firstly prove the existence of the equilibrium for the
generalized abstract economy. We apply these results to show the existence of
solutions for systems of vector quasi-equilibrium problems with multivalued
trifunctions. Secondly, we consider the generalized strong vector
quasi-equilibrium problems and study the existence of their solutions in the
case when the correspondences are weakly naturally quasi-concave or weakly
biconvex and also in the case of weak-continuity assumptions. In all
situations, fixed-point theorems are used.Comment: 24 page
A Categorical Semantics of Fuzzy Concepts in Conceptual Spaces
We define a symmetric monoidal category modelling fuzzy concepts and fuzzy
conceptual reasoning within G\"ardenfors' framework of conceptual (convex)
spaces. We propose log-concave functions as models of fuzzy concepts, showing
that these are the most general choice satisfying a criterion due to
G\"ardenfors and which are well-behaved compositionally. We then generalise
these to define the category of log-concave probabilistic channels between
convex spaces, which allows one to model fuzzy reasoning with noisy inputs, and
provides a novel example of a Markov category.Comment: In Proceedings ACT 2021, arXiv:2211.0110
Some Fubini theorems on product sigma-algebras for non-additive measures
We give some Fubini's theorems (interversion of the order of integration and product capacities) in the framework of the Choquet integral for product sigma-algebras. Following Ghirardato this is performed by considering slice-comonotonic functions. Our results can be easily interpreted for belief functions, in the Dempster and Shafer setting.Choquet integral, product capacity.
FUZZY SOFT NUMBERS
In this paper we introduce the notion of fuzzy soft numbers. Here defined fuzzy soft number and four arithmetic operations and related properties. Also introduce Hausdorff distance, fuzzy soft metric space, convergence sequence, Cauchy sequence, Continuity, and uniform continuity of fuzzy soft numbers. At starting of this paper, we study convex and concave fuzzy soft sets andsome of their properties
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