A fixed point theorem in strictly convex b-fuzzy metric spaces

The main motivation for this paper is to investigate the fixed point property for non-expansive mappings defined on $b$-fuzzy metric spaces. First, following the idea of S. Ješić's result from 2009, we introduce convex, strictly convex and normal structures for sets in $b$-fuzzy metric spaces. By using topological methods and these notions, we prove the existence of fixed points for self-mappings defined on $b$-fuzzy metric spaces satisfying a nonlinear type condition. This result generalizes and improves many previously known results, such as W. Takahashi's result on metric spaces from 1970. A representative example illustrating the main result is provided

A decomposition theorem for fuzzy set-valued random variables and a characterization of fuzzy random translation

Let $X$ be a fuzzy set--valued random variable (\frv{}), and \huku{X} the family of all fuzzy sets $B$ for which the Hukuhara difference X\HukuDiff B exists $\mathbb{P}$--almost surely. In this paper, we prove that $X$ can be decomposed as X(\omega)=C\Mink Y(\omega) for $\mathbb{P}$--almost every $\omega\in\Omega$, $C$ is the unique deterministic fuzzy set that minimizes $\mathbb{E}[d_2(X,B)^2]$ as $B$ is varying in \huku{X}, and $Y$ is a centered \frv{} (i.e. its generalized Steiner point is the origin). This decomposition allows us to characterize all \frv{} translation (i.e. X(\omega) = M \Mink \indicator{\xi(\omega)} for some deterministic fuzzy convex set $M$ and some random element in \Banach). In particular, $X$ is an \frv{} translation if and only if the Aumann expectation $\mathbb{E}X$ is equal to $C$ up to a translation. Examples, such as the Gaussian case, are provided.Comment: 12 pages, 1 figure. v2: minor revision. v3: minor revision; references, affiliation and acknowledgments added. Submitted versio

Some Fixed Point Theorems in Fuzzy n-Normed Spaces

The main purpose of this paper is to study the existence of a fixed points in fuzzy n-normed spaces. we proved our main results, a fixed point theorem for a self mapping and a common fixed point theorem for a pair of weakly compatible mappings on fuzzy n-normed spaces. Also we gave some remarks on fuzzy n-normed spaces

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

The compositional rule of inference with several relations

The compositional rule of inference with several relations, which is the mainly used inference rule in approximate reasoning, is considered in this paper. Stability results are given and exact computational formulae are provided