Related papers: Fuzzy vectors via convex bodies
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…
We study the motion of smooth, strictly convex bodies in $\mathbb{R}^n$ expanding in the direction of their normal vector field with speed depending on Gauss curvature and support function.
Tensor models can be regarded as theories of dynamical fuzzy spaces, and provide background independent theories of space. Their classical solutions correspond to classical background spaces, and the small fluctuations around them can be…
In this paper, we derive uniqueness and stability results for surface tensors. Further, we develop two algorithms that reconstruct shape of $n$-dimensional convex bodies. One algorithm requires knowledge of a finite number of surface…
Motivated by the relative differential geometry, where the Euclidean normal vector of hypersurfaces is generalized by a relative normalization, we introduce anisotropic area measures of convex bodies, constructed with respect to a gauge…
Here, we propose an unsupervised fuzzy rule-based dimensionality reduction method primarily for data visualization. It considers the following important issues relevant to dimensionality reduction-based data visualization: (i) preservation…
We derive an explicit expression for an associative *-product on fuzzy complex projective spaces. This generalises previous results for the fuzzy 2-sphere and gives a discrete non-commutative algebra of functions on fuzzy complex projective…
We study $SO(m)$ covariant Matrix realizations of $ \sum_{i=1}^{m} X_i^2 = 1 $ for even $m$ as candidate fuzzy odd spheres following hep-th/0101001. As for the fuzzy four sphere, these Matrix algebras contain more degrees of freedom than…
After a concise introduction to the square of opposition, in particular, and, Aristotelian Diagrams, in general, I describe how one can create a mathematical universe to host these objects. Since these objects assume that the underlying…
We construct spherical harmonics for fuzzy spheres of even and odd dimensions, generalizing the correspondence between finite matrix algebras and fuzzy two-spheres. The finite matrix algebras associated with the various fuzzy spheres have a…
Regarding the rapid growth of the size and complexity of simulation applications, designing applicable and affordable verification and validation (V&V) structures is an important problem. On the other hand, nowadays human behavior models…
In this paper, three topics in bipolar fuzzy soft hypervector spaces are investigated. At first, four equivalent conditions to definition of a bipolar fuzzy soft hypervector space are presented, from different point of views. Then some new…
Theories defined in higher than four dimensions have been used in various frameworks and have a long and interesting history. Here we review certain attempts, developed over the last years, towards the construction of unified particle…
Use of curvilinear coordinates is sometimes indicated by the inherent geometry of a fluid dynamics problem, but this introduces fictitious forces into the momentum equations that spoil strict conservative form. If one is willing to work in…
This article is the first part of series of articles that aim to present the foundations for fuzzy variational calculus for functions taking values in the space of linearly correlated fuzzy numbers $\mathbb{R}_{\mathcal{F}(A)}$. Recall that…
Strong-uniform fuzzy partition is necessary for the accuracy of fuzzy partition-based histograms. Most previous research focused on constructing one-dimensional strong-uniform fuzzy partitions. While to the best of our knowledge, few have…
This paper initiates the study of picture fuzzy topological spaces. In order to develop a mechanism to construct picture fuzzy topological spaces, we prove some basic results related to picture fuzzy sets together with the introduction of…
We construct a fuzzy $S^4$, utilizing the fact that ${\bf CP}^3$ is an $S^2$ bundle over $S^4$. We find that a fuzzy $S^4$ can be described by a block-diagonal form whose embedding square matrix represents a fuzzy ${\bf CP}^3$. We discuss…
In this article, we have introdued D-fuzzy sets. We have discussed the notions of inclusion, union, intersection, complementation and convexity of such D-fuzzy sets. Also we have proved separation theorem of convex D-fuzzy sets.
It is well-known that the theories of semi-vector spaces and semi-algebras -- which were not much studied over time -- are utilized/applied in Fuzzy Set Theory in order to obtain extensions of the concept of fuzzy numbers as well as to…