121 Results Found

We propose and develop a unified framework for Weyl-type symmetry in von Neumann algebras. Motivated by recent automorphism-rigidity phenomena that identify finite Weyl groups inside automorphism groups of crossed products arising from lattice action...

As a generalization of interval-valued fuzzy sets and fuzzy sets, the concept of hyperfuzzy sets was introduced by Ghosh and Samanta in the paper [J. Ghosh and T.K. Samanta, Hyperfuzzy sets and hyperfuzzy group, Int. J. Advanced Sci Tech. 41 (2012),...

In the present paper, we examined the extendibility of evolution subalgebras generated by idempotents of evolution algebras. The extendibility of the isomorphism of such subalgebras to the entire algebra was investigated. Moreover, the existence of a...

The nonlinear phenomena in numbers are modelled in a wide range of fields such as chemical physics, ocean physics, optical fibres, plasma physics, fluid dynamics, solid-state physics, biological physics and marine engineering. This research article s...

In this paper, we discuss the notion of an m-polar fuzzy (normal) subalgebra in B-algebras and its related properties. We consider characterizations of an m-polar fuzzy (normal) subalgebra. We define the concept of an m-polar intuitionistic fuzzy (no...

In this paper, the notions of L-fuzzy subalgebra degree and L-subalgebras on an effect algebra are introduced and some characterizations are given. We use four kinds of cut sets of L-subsets to characterize the L-fuzzy subalgebra degree. We induce an...

Intuitionistic falling shadow is introduced, and applied to $BCK/BCI$ -algebras. Falling intuitionistic subalgebra and falling intuitionistic ideal of $BCK/BCI$ -algebras are introduced, and related properties are investigated....

In the given study, we intended to gain familiarity with the idea of fuzzy Hom–Lie subalgebras (ideals) of Hom–Lie algebras. It primarily seeks to study a few of their properties. This research investigates the relationship between fuzzy...

In this study, we examine bipolar fuzzy SBCK-subalgebras and their corresponding level sets of bipolar fuzzy sets in the setting of Sheffer stroke BCK-algebras. These concepts contribute significantly to the analysis of bipolar logical structures wit...

This study investigates linear Diophantine fuzzy structures within the framework of Sheffer stroke BCK-algebras (SBCK-algebras). We introduce and characterize linear Diophantine fuzzy SBCK-subalgebras and linear Diophantine fuzzy SBCK-ideals, establi...

We construct an optimal system of one-dimensional subalgebras for a class of soil water equations and then use it to obtain an optimal system of two-dimensional subalgebras. We also present a few group-invariant solutions of rank one corresponding t...

The study introduces the concept of intuitionistic fuzzy SBE-subalgebras, ideals, and filters, along with level sets of intuitionistic fuzzy sets within the framework of Sheffer stroke BE-algebras. These concepts are shown to be crucial for understan...

This study introduces the concept of an intuitionistic fuzzy SBCK-subalgebra (SBCK-ideal) and explores the level set of an intuitionistic fuzzy set within the context of Sheffer stroke BCK-algebras. These newly defined concepts are crucial for unders...

In this paper, we explore the application of fuzzy set theory in the context of triangular norms, with a focus on strong Sheffer stroke NMV-algebras. We introduce the concepts of $\mathfrak{T}$-fuzzy subalgebras and $\mathfrak{T}$-fuzzy filters, analyze their properties, and...

In this paper, we apply the concept of linear Diophantine fuzzy sets in $BCK/BCI$-algebras. In this respect, the notions of linear Diophantine fuzzy subalgebras and linear Diophantine fuzzy (commutative) ideals are introduced and some vital properties...

Neutrosophic $\mathcal{N}$ -structures with applications in $BCK/BCI$ -algebras is discussed. The notions of a neutrosophic $\mathcal{N}$ -subalgebra and a (closed) neutrosophic $\mathcal{N}$ -ideal in a $BCK/BCI$ -algebra are introduced, and severa...

Recent trends in modern information processing have focused on polarizing information, and and bipolar fuzzy sets can be useful. Bipolar fuzzy sets are one of the important tools that can be used to distinguish between positive information and negati...

The notions of hyperfuzzy ideals in $BCK/BCI$ -algebras are introduced, and related properties are investigated. Characterizations of hyperfuzzy ideals are established. Relations between hyperfuzzy ideals and hyperfuzzy subalgebras are dis...

The concept of complex fuzzy sets, where the unit disk of the complex plane acts as the codomain of the membership function, as an extension of fuzzy sets. The objective of this article is to use complex fuzzy sets in BCK/BCI-algebras. We present the...

As a new extension of a cubic set, the notion of a cubic interval-valued intuitionistic fuzzy set is introduced, and its application in $BCK/BCI$ -algebra is considered. The notions of $\alpha$ -internal, $\beta$ -internal, $\alpha$ -external a...

Cubic multipolar structure with finite degree (briefly, cubic k-polar ($C_{k}P$) structure) is a new hybrid extension of both k-polar fuzzy (${}_{k}PF$) structure and cubic structure in which $C_{k}P$ structure consists of two parts; the first one is an interval-valu...

The concept of strong atoms in Q-algebras is discussed herein. In this work, some properties of strong atoms are provided. We show that there is no Q-algebra X with $\left|X\right|\ge 3$ such that all elements are strong atoms. We also find that any two-element s...

In this paper, the notion of cubic intuitionistic q-ideals in $BCI$ -algebras is introduced. A relationship between a cubic intuitionistic subalgebra, a cubic intuitionistic ideal, and a cubic intuitionistic q-ideal is discussed. Conditions fo...

When events occur in everyday life, it is sometimes advantageous to approach them in two directions to find a solution for them. As a mathematical tool to handle these things, we can consider the intuitionistic fuzzy set. However, when events are com...

In this paper, we apply the notion of bipolar-valued fuzzy set to UP-algebras. We introduce the notions of bipolar fuzzy UP-subalgebras (resp., bipolar fuzzy UP-filters, bipolar fuzzy UP-ideals, and bipolar fuzzy strongly UP-ideals) of UP-algebras an...

In this paper, we utilize the Lukasiewicz t-norm to construct a novel class of fuzzy sets, termed $\zeta$-Lukasiewicz fuzzy sets, derived from a given fuzzy framework. These sets are then applied to the structure of Sheffer stroke BE-algebras (SBE-alg...

This article deals with Lie algebra $\mathfrak{G}$ of all infinitesimal affine transformations of the manifold $\mathcal{M}$ with an affine connection, its stationary subalgebra $ℌ\subset \mathfrak{G}$, the Lie group $\mathcal{G}$ corresponding to the algebra $\mathfrak{G}$, and its subgroup $\mathcal{H}\subset \mathcal{G}$ correspon...

The notions of the neutrosophic hesitant fuzzy subalgebra and neutrosophic hesitant fuzzy filter in pseudo-BCI algebras are introduced, and some properties and equivalent conditions are investigated. The relationships between neutrosophic hesitant fu...

Following the notions of $\mathrm{\Omega }$-set and $\mathrm{\Omega }$-algebra where $\mathrm{\Omega }$ is a complete lattice, we introduce P-algebras, replacing the lattice $\mathrm{\Omega }$ by a poset P. A P-algebra is a classical algebraic structure in which the usual equality is replaced...

The submodel of ideal gas motion being invariant with respect to the time translation and the space translation by one direct has 4 integrals in the case of vortex flows with the varying entropy. The system of nonlinear differential equations of the...

We study the relationship between the classification of three-dimensional nonconjugate subalgebras of the Lie algebra of the Poincaré group $P(1,4)$ and the types of symmetry reduction of the eikonal equation to ordinary differential equat...

This paper deals with the use of Lie group methods to solve optimization problems in blind signal processing (BSP), including Independent Component Analysis (ICA) and Independent Subspace Analysis (ISA). The paper presents the theoretical fundamental...

The notion of hybrid ideals in $BCK/BCI$ -algebras is introduced, and related properties are investigated. Characterizations of hybrid ideals are discussed. Relations between hybrid ideals and hybrid subalgebras are considered. Characteriz...

For $i,j,k,l,m,n\in \{1,2,3,4\}$ , the notion of $\left(T\right(i,j),I(k,l),F(m,n\left)\right)$ -interval neutrosophic subalgebra in $BCK/BCI$ -algebra is introduced, and their properties and relations are investiga...

In this paper, we mainly study free $U\left(\mathfrak{h}\right)$-modules over the $N=1$ Heisenberg–Virasoro superalgebra. We construct a family of non-weight modules that are free of rank 2 when regarded as modules over the Cartan subalgebra. Moreover, we classify the f...

Yang, Roh and Jun recently introduced kernels of homomorphisms in OBCI-algebras and left an ordered generalization of those kernels as a future work. As its answer, we introduce the concept of ordered kernels of OBCI-algebras in the homomorphism envi...

In this paper, a supersymmetric extension of the minimal surface equation is formulated. Based on this formulation, a Lie superalgebra of infinitesimal symmetries of this equation is determined. A classification of the one-dimensional subalgebras is...

The Guéant and Pu model of option pricing and hedging, which takes into account transaction costs, and the impact of operations on the market is studied by group analysis methods. The infinite-dimensional continuous group of equivalence transf...

In this paper, we introduce the notion of intuitionistic fuzzy GE-algebra by combining the concepts of GE-algebras and intuitionistic fuzzy sets. We provide a necessary and sufficient condition for an intuitionistic fuzzy set to form an intuitionisti...

The study of symmetry is one of the most important and beautiful themes uniting various areas of contemporary arithmetic. Algebraic structures are useful structures in pure mathematics for learning a geometrical object’s symmetries. In order to...

Dividing the world into subsystems is an important component of the scientific method. The choice of subsystems, however, is not defined a priori. Typically, it is dictated by experimental capabilities, which may be different for different agents. He...

In this paper, we formulate a supersymmetric extension of the Euler system of equations. We compute a superalgebra of Lie symmetries of the supersymmetric system. Next, we classify the one-dimensional subalgebras of this superalgebra into 49 equivale...

A fuzzy logical algebra has diverse applications in various domains such as engineering, economics, environment, medicine, and so on. However, the existing techniques in algebra do not apply to delta-algebra. Therefore, the purpose of this paper was...

Molodtsov originated soft set theory, which followed a general mathematical framework for handling uncertainties, in which we encounter the data by affixing the parameterized factor during the information analysis. The aim of this paper is to establi...

The notion of a neutrosophic quadruple $BCK/BCI$-number is considered, and a neutrosophic quadruple $BCK/BCI$-algebra, which consists of neutrosophic quadruple $BCK/BCI$-numbers, is constructed. Several properties are investigated, and a (positive implicat...

The concept of a $(\in ,$ $\in )$ -neutrosophic ideal is introduced, and its characterizations are established. The notions of neutrosophic permeable values are introduced, and related properties are investigated. Conditions for the ne...

Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where conformal...

In this paper, we extend the notion of generalized tracial approximation to the non-unital case. An example of this approximation, which comes from dynamical systems, is also provided. We use the machinery of Cuntz subequivalence to work in this non-...

As a generalization of a neutrosophic set, the notion of MBJ-neutrosophic sets is introduced by Mohseni Takallo, Borzooei and Jun, and it is applied to BCK/BCI-algebras. In this article, MBJ-neutrosophic set is used to study commutative ideal in BCI-...

First, semigroup structure is constructed by providing binary operations for the crossing cubic set structure. The concept of commutative crossing cubic ideal is introduced by applying crossing cubic set structure to commutative ideal in BCK-algebra,...