Related papers: Fuzzy Lie Groups
We describe simply connected compact exceptional simple Lie groups in very elementary way. We first construct all simply connected compact exceptional Lie groups G concretely. Next, we find all involutive automorphisms of G, and determine…
The present paper links the representation theory of Lie groupoids and infinite-dimensional Lie groups. We show that smooth representations of Lie groupoids give rise to smooth representations of associated Lie groups. The groups envisaged…
In this study, after given the definition of soft sets and their basic operations we define convex soft sets which is an important concept for operation research, optimization and related problems. Then, we define concave soft sets and give…
We introduced and study fuzzy gamma-hypersemigroups, according to fuzzy semihyper- groups as previously defined [33] and prove that results in this respect. In this regard first we introduce fuzzy hyperoperation and then study fuzzy…
A fuzzy mnesor space is a semimodule over the positive real numbers. It can be used as theoretical framework for fuzzy sets. Hence we can prove a great number of properties for fuzzy sets without refering to the membership functions.
Real-world phenomena often exhibit vagueness, partial truth, and incomplete information. To model such uncertainty in a mathematically rigorous way, many generalized set-theoretic frameworks have been introduced, including Fuzzy Sets [1],…
In this paper, the concept of a picture fuzzy subgroup of a group is studied, and the notion of the direct product of picture fuzzy subgroups is introduced. Several characterisations of the direct product of picture fuzzy subgroups are…
A pro-Lie group is a projective limit of a family of finite-dimensional Lie groups. In this note we show that a pro-Lie group $G$ is a Lie group in the sense that its topology is compatible with a smooth manifold structure for which the…
A family of fuzzy orbifolds are generated by looking at sub-algebras of the fuzzy sphere. One of them is actually commutative and can be mapped exactly onto a lattice. The others are fuzzy approximations of S^2/Z_N where Z_N is the cyclic…
A group, defined as set with associative multiplication and inverse, is a natural structure describing the symmetry of a space. The concept of group generalizes to group objects internal to other categories than sets. But there are yet more…
It is known that fuzzy set theory can be viewed as taking place within a topos. There are several equivalent ways to construct this topos, one is as the topos of \'{e}tal\'{e} spaces over the topological space $Y=[0,1)$ with lower topology.…
In fairly elementary terms this paper presents how the theory of preordered fuzzy sets, more precisely quantale-valued preorders on quantale-valued fuzzy sets, is established under the guidance of enriched category theory. Motivated by…
In this article, by using basic properties of fuzzy soft topology we defined fuzzy soft compactness. We also introduced some basic definitions and theorems of the concept.
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…
Right feeble groups are defined as groupoids $(X,*)$ such that (i) $x, y\in X$ implies the existence of $a, b \in X$ such that $a*x = y$ and $b*y = x$. Furthermore, (ii) if $x, y, z \in X$ then there is an element $w\in X$ such that…
Soft set theory serves as a mathematical framework for handling uncertain information, and hesitant fuzzy sets find extensive application in scenarios involving uncertainty and hesitation. Hesitant fuzzy sets exhibit diverse membership…
In this paper, the notations of $\alpha$-Q-fuzzy subset and $\alpha$-Q-fuzzy subgroup are introduced, and necessary properties related to these two concepts are proven. In the past part in this work, the effect of the $\alpha$-Q-fuzzy…
In this paper, we present the concept of relations in intuitionistic fuzzy soft set and study some of their properties and also discuss symmetric, transitive and reflexive intuitionistic fuzzy soft relations.
Given a group action, known by its infinitesimal generators, we exhibit a complete set of syzygies on a generating set of differential invariants. For that we elaborate on the reinterpretation of Cartan's moving frame by Fels and Olver…
We introduce the basic notions and present examples and results on Lie categories -- categories internal to the category of smooth manifolds. Demonstrating how the units of a Lie category $\mathcal C$ dictate the behavior of its invertible…