Concept Of Homomorphism Research Articles

On the Differentiation of Integrals in Measure Spaces Along Filters: II

Let X be a complete measure space of finite measure. The Lebesgue transform of an integrable function f on X encodes the collection of all the mean-values of f on all measurable subsets of X of positive measure. In the problem of the differentiation of integrals, one seeks to recapture f from its Lebesgue transform. In previous work we showed that, in all known results, f may be recaptured from its Lebesgue transform by means of a limiting process associated to an appropriate family of filters defined on the collection A\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${{\\,\\mathrm{{\\mathcal {A}}}\\,}}$$\\end{document} of all measurable subsets of X of positive measure. The first result of the present work is that the existence of such a limiting process is equivalent to the existence of a Von Neumann-Maharam lifting of X. In the second result of this work we provide an independent argument that shows that the recourse to filters is a necessary consequence of the requirement that the process of recapturing f from its mean-values is associated to a natural transformation, in the sense of category theory. This result essentially follows from the Yoneda lemma. As far as we know, this is the first instance of a significant interaction between category theory and the problem of the differentiation of integrals. In the Appendix we have proved, in a precise sense, that natural transformations fall within the general concept of homomorphism. As far as we know, this is a novel conclusion: Although it is often said that natural transformations are homomorphisms of functors, this statement appears to be presented as a mere analogy, not in a precise technical sense. In order to achieve this result, we had to bring to the foreground a notion that is implicit in the subject but has remained hidden in the background, i.e., that of partial magma.

Semimedial Near Rings

Objectives: To define the term ‘semimediality’ in the near ring and to demonstrate its presence with an example and to employ several attributes in near rings to analyse its features. Methods: Semimedial near rings are examined in terms of their characteristics using commutativity, distributivity and regular property. The distinction is observed using the concept of homomorphism. Findings: Every near ring which is weak commutative is proved to be semimedial and the converse exists with some additional axioms. The semimedial near ring’s anti-homomorphic image is also observed. Additionally, the correlation between the semimedial near ring and the reduced property is identified. Novelty: This study provides a novel method to medial near ring, which is the semimedial near ring. Keywords: Identity, Left Self Distributive, Nilpotent, Regular, Weak Commutative

Contemporary Algebraic Attributes of the q‐Rung Orthopair Complex Fuzzy Subgroups

A more advanced form of complex fuzzy sets is q‐rung orthopair complex fuzzy (q -ROCF) sets, which offer an additional and broad visualization of the uncertainty present in the unit disk. In comparison to complex intuitionistic fuzzy sets and complex bipolar fuzzy sets, the q -ROCF set is more appropriate and versatile. Their ability to describe a broader range of unclear information makes them distinguishable because the real part of a complex‐valued membership degree and the real part of a complex‐valued nonmembership degree have a sum of qth powers that is equal to or less than one (similarly for the imaginary part of a complex‐valued). In terms of the characteristics of the q -ROCF set, we propose the concept of q -ROCF subgroups and investigate some fundamental features under the q -ROCF set. Moreover, we show that every intuitionistic complex fuzzy subgroup is a q -ROCF subgroup. Also, we use this approach to define q -ROCF level subgroups, q -ROCF cosets, and q -ROCF normal subgroups of a certain group as well as to investigate some of their algebraic characteristics. Furthermore, we develop the concept of group homomorphism, images, and preimages under the influence of the q -ROCF subgroup.

New Kind of Banach Algebra Via Proximit structure

This article introduces the concept of Banach proximit algebra and examines several results in this new context. We give new definitions for the terms "proximit algebra," "commutative proximit algebra," "identity proximit algebra," and "normed proximit algebra." However, we introduce the concepts of subproximit algebra, proximit homomorphism, and proximit isomorphism of Banach proximit algebras in a natural way. Finally, we offer a few intriguing possibilities to support our arguments.

(α, γ)-Anti-Multi-Fuzzy Subgroups and Some of Its Properties

Recently, fuzzy multi-sets have come to the forefront of scientists’ interest and have been used in algebraic structures such as multi-groups, multi-rings, anti-fuzzy multigroup and (α, γ)-anti-fuzzy subgroups. In this paper, we first summarize the knowledge about the algebraic structure of fuzzy multi-sets such as (α, γ)-anti-multi-fuzzy subgroups. In a way, the notion of anti-fuzzy multigroup is an application of anti-fuzzy multi sets to the theory of group. The concept of anti-fuzzy multigroup is a complement of an algebraic structure of a fuzzy multi set that generalizes both the theories of classical group and fuzzy group. The aim of this paper is to highlight the connection between fuzzy multi-sets and algebraic structures from an anti-fuzzification point of view. Therefore, in this paper, we define (α, γ)-anti-multi-fuzzy subgroups, (α, γ)-anti-multi-fuzzy normal subgroups, (α, γ)-anti-multi-fuzzy homomorphism on (α, γ)-anti-multi-fuzzy subgroups and these been explicated some algebraic structures. Then, we introduce the concept (α, γ)-anti-multi-fuzzy subgroups and (α, γ)-anti-multi-fuzzy normal subgroups and of their properties. This new concept of homomorphism as a bridge among set theory, fuzzy set theory, anti-fuzzy multi sets theory and group theory and also shows the effect of anti-fuzzy multi sets on a group structure. Certain results that discuss the (α, γ) cuts of anti-fuzzy multigroup are explored.

Valued-inverse Dombi neutrosophic graph and application

<abstract><p>Utilizing two ideas of neutrosophic subsets (NS) and triangular norms, we introduce a new type of graph as valued-inverse Dombi neutrosophic graphs. The valued-inverse Dombi neutrosophic graphs are a generalization of inverse neutrosophic graphs and are dual to Dombi neutrosophic graphs. We present the concepts of (complete) strong valued-inverse Dombi neutrosophic graphs and analyze the complement of (complete) strong valued-inverse Dombi neutrosophic graphs and self-valued complemented valued-inverse Dombi neutrosophic graphs. Since the valued-inverse Dombi neutrosophic graphs depend on real values, solving the non-equation and the concept of homomorphism play a prominent role in determining the complete, strong, complementarity and self-complementarity of valued-inverse Dombi neutrosophic graphs. We introduce the truth membership order, indeterminacy membership order, falsity membership order, truth membership size, indeterminacy membership size and indeterminacy membership size of any given valued-inverse Dombi neutrosophic graph, which play a major role in the application of valued inverse Dombi neutrosophic graphs in complex networks. An application of a valued-inverse Dombi neutrosophic graph is also described in this study.</p></abstract>

Properties of Homomorphism and Quotient Implication Algebra on Implication Algebras

The concept of homomorphisms on implication algebra is introduced. The notion of sub algebras, normal subalgebras in an implication algebra are investigated. Quotient implication algebras and kernels in an implication algebra ,and Homomorphisms and isomorphism theorems are elaborated.

Annihilator Hyperideals in Strong Bounded Dual Distributive Meet-hyperlattice

In this paper, we study the properties of annihilator hyperideals in the class of strong bounded dual distributive meet-hyperlattice. We show that the set of all closed hyperideals forms a Boolean algebra. We introduce the concept of homomorphism, which preserves the annihilator hyperideal. Suitable conditions for preserving annihilator hyperideals are obtained. Representationand characterization theorems of annihilator hyperideals in sub-meet-hyperlattice and product meet-hyperlattice are proved.

New types of rough Pythagorean fuzzy UP-filters of UP-algebras

The aim of this paper is to introduce nine types of rough Pythagorean fuzzy sets in UP-algebras and nine types of rough sets in UP-algebras. Then we study relation of these rough Pythagorean fuzzy sets and new types of Pythagorean fuzzy UP-filter under equivalence (congruence) relation. Moreover, we will also discuss \(t\)-level subsets of rough Pythagorean fuzzy sets in UP-algebras to study the relationships between rough Pythagorean fuzzy sets and rough sets in UP-algebras which we defined them above. Finally, we discuss the concept of homomorphisms between IUP-algebras and also study the direct and inverse images of four special subsets.

On r-Ideals and m-k-Ideals in BN-Algebras

A BN-algebra is a non-empty set X with a binary operation “∗” and a constant 0 that satisfies the following axioms: (B1) x∗x=0, (B2) x∗0=x, and (BN) (x∗y)∗z=(0∗z)∗(y∗x) for all x, y, z ∈X. A non-empty subset I of X is called an ideal in BN-algebra X if it satisfies 0∈X and if y∈I and x∗y∈I, then x∈I for all x,y∈X. In this paper, we define several new ideal types in BN-algebras, namely, r-ideal, k-ideal, and m-k-ideal. Furthermore, some of their properties are constructed. Then, the relationships between ideals in BN-algebra with r-ideal, k-ideal, and m-k-ideal properties are investigated. Finally, the concept of r-ideal homomorphisms is discussed in BN-algebra.

Quotients of L-domains

It is well known that the image of a bounded complete domain, respectively a continuous lattice T under a surjective map preserving infs of nonempty subsets and directed sups is a bounded complete domain, respectively a continuous lattice and a congruence relation on T is an equivalence relation on T and a subalgebra of T × T . In this paper, we propose some counterexamples to explain that these results do not persist in L -domains. The concepts of strong homomorphisms among L -domains and congruence relation on L -domains are introduced. We prove that the image of an L -domain under a surjective map which preserves infs of nonempty subsets bounded above and directed sups and satisfies an equation is an L -domain. Meanwhile, we obtain the quotients of L -domains. Moreover, we give the Isomorphism Theorem for L -domains.

A Study of Complex Dombi Fuzzy Graph With Application in Decision Making Problems

A complex fuzzy set (CFS) is a generalization of a fuzzy set (FS) in which a limit of degrees occurs on the complex plane with unit disc. The averaging operators are a key part of turning all the data into one value. Dombi operators have exceptional flexibility with operating factors, and they are particularly efficient in decision-making problems. In this paper, we establish complex dombi fuzzy graph (CDFG). We implement dombi operators on CFSs to extend graph nomenclature. We define the complement of CDFG with an example. The idea of self-complementary in CDFG is discussed. The concepts of homomorphism, isomorphism, weak isomorphism, and co-weak isomorphism of two CDFGs are discussed. We define regular and entirely regular graphs with sufficient elaboration and examine their key properties. Furthermore, significant characteristics are used to explain the edge regularity of CDFG. Lastly, we establish an application of CDFG in decision making problem.

Hybrid ideals in near-subtraction semigroups

<abstract><p>The fuzzy set is highly beneficial for expressing people's hesitations in their everyday lives, and it is a great tool for dealing with uncertainty, which can be described precisely and perfectly from the decision-maker's point of view. Soft set theory has been developed in recent years to address real-world issues. Jun et al. merged fuzzy and soft sets to produce hybrid structures. Hybrid structures are soft set and fuzzy set speculations. The concept of hybrid ideals in near-subtraction semigroups is introduced in this paper, and their equivalent results are obtained. Additionally, we demonstrate the concept of hybrid intersection. Moreover, we define the concept of homomorphism of a hybrid structure in a near-subtraction semigroup.</p></abstract>

On partitioning ideals of (m,n)-semirings

In this paper, we prove that if [Formula: see text] is a partitioning ideal of an [Formula: see text]-semiring [Formula: see text] with respect to two subsets [Formula: see text] and [Formula: see text] of [Formula: see text], then the quotient [Formula: see text]-semirings [Formula: see text] and [Formula: see text] are isomorphic. Also, the concepts of maximal homomorphism, steady homomorphism, one-one homomorphism and [Formula: see text]-homomorphism are generalized for [Formula: see text]-semirings and obtained relation between them. Finally, the fundamental theorem of semiring homomorphism is generalized for [Formula: see text]-semirings.

Toward a diagnostic method of organizational health based on traditional Chinese medicine

PurposeThe paper aims to propose a model and a comprehensive diagnostic method of organizational health status based on traditional Chinese medicine (TCM).Design/methodology/approachThe methodology is qualitative/interpretive and uses of the concept of functional homomorphism of WR Ashby is used, establishing similarities between the way in which this ancient medicine considers the human being and their condition as healthy to transfer it to an organization that produces goods and/or services.FindingsA healthy organization is conceived as one constituted by an association of people regulated by a set of norms based on certain purposes in a state of harmonious balance of their physical and energetic dimensions. In that the physical refers to storage functions, regulation and allocation of resources; transformation of raw materials and inputs into goods and services; waste disposal, distribution and coordination and with information systems for management control, while energy is associated with the ability to act with its management and policies.Research limitations/implicationsThe current paper is a first theoretical proposal, which should be enriched with practical applications that feedback its conceptual formulation, thus contributing to its validation.Practical implicationsA comprehensive organizational diagnostic method is made available.Social implicationsThe proposed method allows a comprehensive organizational diagnosis, considering the participation of all the actors that make up this type of social systems.Originality/valueAlthough the methodological resource is old, the way it is used here is considered original, and it is also part of an original investigative process by the authors, oriented toward the search for comprehensive organizational diagnostic methods.

EMBEDDING ORTHOMORPHISMS d-ALGEBRA IN BIORTHOMORPHISMS AS ORDERED IDEAL

In the historical development of Riesz spaces, we can trace the history of ordered vector spaces to the International Mathematical Congress in Bologna in 1928. Studies related with f-Algebras for the Dedekind complete ordered vector space defined in Riesz spaces were initiated by Nakano and their current definition was made by Amemiya, Birkhoff and Pierce.The revival of f-algebras, which had a tendency to slow down for a period of time, emerged as a result of Pagter's doctoral thesis [9] and the examination of Alkansas lecture notes by Luxemburg. 
 The concepts of homomorphism, isomorphism, orthomorphism and biorthomorphism in Riesz spaces are defined by Zaanen, Huijsmans, Boulabiar, Buskes and Triki. Algebraic structure of biorthomorphisms defined on Riesz space examined by [8]. f-Algebra on Orth(X,X) were studied by [8] and [6]. [6] demonstrated that biorthomorphisms space have an f-algebraic structure with the help of the product defined as (T_1 *_e T_2)(x,y)=T_1 (x,T_2 (e,y)) for e∈X^+, ∀x,y∈X ve T_1,T_2∈Orth(X,X).
 [8] showed that if orthomorphisms are semiprime Dedekind complete f-algebras, it is an ordered ideal in biorthomorphisms. [6] developed an alternative proof for this situation. If X Archimedean Riesz space, Orth(X) is an f-algebra according to compound operation with unit element.
 [10] showed that if the orthomorphism X is a semi-prime f-algebra, it is a d-algebra. In this study, we investigated embedding orthomorphism in biorthomorphisms when X is uniformly complete d-algebra.

Irregular vague graphs

A vague graph is a generalized structure of a fuzzy graph that gives more precision, flexibility and compatibility to a system when compared with systems that are designed using fuzzy graphs. In this paper, the new concepts of (totally) irregular, strongly (totally) irregular, highly totally irregular, neighborly totally irregular, edge-irregular of vague graphs are introduced and generalized, and some properties and related results are investigated. Then, we present the concepts of homomorphism, weak isomorphism, co-weak isomorphism and isomorphism of irregular vague graphs and some results on (total) domination number, (total) 2-domination number, (total) cobondage number and (total) 2-cobondage number. Finally, one of their applications related to location map of Fire Stations and Emergency Medical centers in urban regions of ​​a metropolis is presented.

Cartesian product and Topology On Fuzzy BI-Algebras

In this paper,the concepts of homomorphism in fuzzy BI-algebra is intro- duced, and also basic properties of homo- morphisms are investigated. The cartesian product in fuzzy ideals of BI-algebra is investigated with related prop- erties; The concepts of fuzzy topology on BI- algebra elaborated.

Hyper Brk-Algebras

In this article, BRK-Algebras presents the idea of hyper structure and some related properties are discussed. In addition, we present the concept of the hyper BRK-ideal of a hyper BRK-algebra. A few characteristics are obtained. Furthermore the concept of homomorphism is generalised to hyper BRK-Algebras

Ternary Menger Algebras: A Generalization of Ternary Semigroups

Let n be a fixed natural number. Menger algebras of rank n, which was introduced by Menger, K., can be regarded as the suitable generalization of arbitrary semigroups. Based on this knowledge, an interesting question arises: what a generalization of ternary semigroups is. In this article, we first introduce the notion of ternary Menger algebras of rank n, which is a canonical generalization of arbitrary ternary semigroups, and discuss their related properties. In the second part, we establish the so-called a diagonal ternary semigroup which its operation is induced by the operation on ternary Menger algebras of rank n and then investigate their interesting properties. Moreover, we introduce the concept of homomorphism and congruences on ternary Menger algebras of rank n. These lead us to study the quotient ternary Menger algebras of rank n and to investigate the homomorphism theorem for ternary Menger algebra of rank n with respect to congruences. Furthermore, the characterization of reduction of ternary Menger algebra into Menger algebra is presented.