جستجوی مقالات مرتبط با کلیدواژه "in$-set" در نشریات گروه "ریاضی"

‎Let $r\geq 2$. A subset $S$ of vertices of a graph $G$ is a $r$-hop independent dominating set if every vertex outside $S$ is at distance $r$ from a vertex of $S$, and for any pair $v, w\in S$, $d(v, w)\neq r$. A $r$-hop Roman dominating function ($r$HRDF) is a function $f$ on $V(G)$ with values $0,1$ and $2$ having the property that for every vertex $v \in V$ with $f(v) = 0$ there is a vertex $u$ with $f(u)=2$ and $d(u,v)=r$. A $r$-step Roman dominating function ($r$SRDF) is a function $f$ on $V(G)$ with values $0,1$ and $2$ having the property that for every vertex $v$ with $f(v)=0$ or $2$, there is a vertex $u$ with $f(u)=2$ and $d(u,v)=r$. A $r$HRDF $f$ is a $r$-hop Roman independent dominating function if for any pair $v, w$ with non-zero labels under $f$, $d(v, w)\neq r$. We show that the decision problem associated with each of $r$-hop independent domination, $r$-hop Roman domination, $r$-hop Roman independent domination and $r$-step Roman domination is NP-complete even when restricted to planar bipartite graphs or planar chordal graphs.

In this article, we first consider the $L$-fuzzy powerset monad on a completely distributive lattice $L$. Then for $L=[n]$, we investigate the fuzzy powerset monad on $[n]$ and we introduce simple, subsimple and quasisimple $L$-fuzzy sets. Finally, we provide necessary and sufficient conditions for the existence of an equalizer of a given pair of morphisms in the Kleisli category associated to this monad. Several illustrative examples are also provided.

It is important to have an intuitionistic fuzzy set that allows each set element to have a membership value, a non-membership value, and a hesitancy value. This is because each element of the set can possess all three values. We will focus on one type of continuous intuitionistic fuzzy number, called trapezoidal intuitionistic fuzzy numbers, because they are more flexible in representing information about membership and non-membership functions and are continuous. This research aims to introduce a parametric ranking and distance measure to compare and obtain the distinction value between intuitionistic trapezoidal fuzzy numbers. Parametric measures offer more flexibility than deterministic measurement tools in modeling real-world problems by considering a suitable variety of responses based on different levels of parameters. After presenting the structure and effective indicators of the proposed tool, we have detailed its features and basic principles. Moreover, based on this measure, a hybrid process is designed for multi-criteria group decision-making (MCGDM) problems with trapezoidal intuitionistic fuzzy data. A numerical example is also examined to elucidate the implementation process of this integrated methodology. Additionally, comparative analysis with some related methods confirms the adequate performance of the new parametric measure in combined methods with similar subjects.

‎Consider a graph $G=(V(G),E(G))$‎, ‎where a perfect matching in $G$ is defined as a subset of independent edges with $\frac{|V(G)|}{2}$ elements‎. ‎A global forcing set is a subset $S$ of $E$ such that no two disjoint perfect matchings of $G$ coincide on it‎. ‎The minimum cardinality of global forcing sets of $G$ is called the global forcing number (GFN for short)‎. ‎This paper addresses the NP-hard problem of determining the global forcing number for perfect matchings‎. ‎The focus is on a Genetic Algorithm (GA) that utilizes binary encoding and standard genetic operators to solve this problem‎. ‎The proposed algorithm is implemented on some chemical graphs to illustrate the validity of the algorithm‎. ‎The solutions obtained by the GA are compared with the results from other methods that have been presented in the literature‎. ‎The presented algorithm can be applied to various bipartite graphs‎, ‎particularly hexagonal systems‎. ‎Additionally‎, ‎the results of the GA improve some results that‎ have already been presented for finding GFN‎.

In order to balance uncertainty, a reasonable approximation of a crisp set that yields lower as well as upper approximations of the set is made. Here, first, a special class of Fermatean Neutrosophic Set is devised by associating the Neutrosophic Set with the Fermatean Fuzzy Set. A relatively new concept of Fermatean Neutrosophic Approximation Space and Fermatean Neutrosophic approximation operators are introduced. In this context, a new class of Fermatean Neutrosophic Rough set is established, and a few of its characteristics are mentioned. Also, the cut sets of Fermatean Neutrosophic Rough sets, which characterize Fermatean Neutrosophic rough approximation operators, are investigated.

In this paper we study topological spaces, frames, and their confrontation in the presheaf topos of $M$-sets for a monoid $M$. We introduce the internalization, of the frame of open subsets for topologies, and of topologies of points for frames, in our universe. Then we find functors between the categories of topological spaces and of frames in our universe.We show that, in contrast to the classical case, the obtained functors do not have an adjoint relation for a general monoid, but in some cases such as when $M$ is a group, they form an adjunction. Furthermore, we define and study soberity and spatialness for our topological spaces and frames, respectively. It is shown that if $M$ is a group then the restriction of the adjunction to sober spaces and spatial frames becomes into an isomorphism.

Let A, B, C, and D be posets. Assume C and D are finite with a greatest element. Also assume that AC ≅B D. Then there exist posets E, X, Y , and Z such that A ≅E X, B ≅E Y , C≅Y ×Z, and D≅X×Z. If C≅D, then A≅B. This generalizes a theorem of Jónsson and McKenzie, who proved it when A and B were meet-semilattices.

As the digital landscape continues to evolve, the selection of an appropriate online shop-ping platform has become increasingly crucial for both consumers and businesses. This paper introduces a novel approach that combines the Fermatean fuzzy set theory with the triangular divergence distance measure in Compromise Ranking of Alternatives from Distance to Ideal Solution (CRADIS) method to streamline the decision-making process in online platform selection. Through a comprehensive example, we illustrate the application of this approach in evaluating and ranking four distinct online shopping latforms based on multiple criteria. Through this integrated approach, decision-makers can gain valuable insights into the rela-tive merits of each online shopping platform, allowing them to make informed choices aligned with their preferences and requirements. Furthermore, by accommodating uncertainty and imprecision, the Fermatean fuzzy set theory enhances the robustness of the decision-making process, minimizing the risk of making suboptimal decisions. Overall, this paper demon-strates the practical applicability of Fermatean fuzzy set theory in decision support systems for online platform selection. To demonstrate the proposed method’s applicability, we have compared the results with existing Multi-attribute decision making (MADM) methods. To establish its stability, we conducted a sensitivity analysis. By leveraging the CRADIS method alongside Fermatean fuzzy set theory, decision-makers can navigate the complex landscape of online shopping platforms with greater confidence and efficiency, ultimately leading to more satisfactory outcomes for both consumers and businessesalike.

The notion of fuzzy convergence, a prominent tool in fuzzy analysis, has wide applications in fuzzy inference. The present paper examines the distinctive features of the cluster points of fuzzy sequences in various fuzzy topological spaces. A characterization of the fuzzy indiscrete space regarding the cluster points is obtained. Moreover, a detailed study of the cluster points of fuzzy sequences in fuzzy indiscrete, fuzzy discrete, fuzzy co-countable and fuzzy co-finite spaces is presented and characterizations of the cluster points in each space are established. Furthermore, the concepts of maximal cluster points, $c$-sets, $c_m$-sets and fuzzy $c$-sets of fuzzy sequences are proposed and their properties are investigated.

The Jun’s YεJ -fuzzy set is applied to the Sheffer stroke BL-algebra, and the notions of an (∈, ∈)- YεJ -fuzzy quasisubalgebra and an (∈, ∈ ∨q)-YεJ -fuzzy quasi-subalgebra in Sheffer stroke BL-algebras are introduced, and several  properties are explored. Characterizations of (∈, ∈)- YεJ - fuzzy quasi-subalgebras and (∈, ∈ ∨q)- YεJ -fuzzy  quasisubalgebras are investigated, and the relationships between the fuzzy quasi-subalgebra, the (∈, ∈)- YεJ -fuzzy quasi- subalgebra and the (∈, ∈ ∨q)- YεJ -fuzzy quasisubalgebra are considered. Conditions for a fuzzy set to be an (∈, ∈∨q)- YεJ -fuzzy quasi-subalgebra are displayed.

In this note, we show that automata theory is a suitable tool for analyzing monopoly-forcing processes. Also, we present the notion of mono-forcing automata by using the monopoly-forcing set for graphs. Moreover, we prove that mono-forcing automata accept more languages than zero-forcing finite automata also, we show that all results in zero-forcing finite automata for complete graphs are established for mono-forcing automata. We examine and deliberate on the language associated with mono-forcing automata for certain specified graphs. Also, we present the style of words that can be recognized with mono-forcing automata. Additionally, we delineate the types of words identifiable by mono-forcing automata. We also describe the configuration of graphs from which mono-forcing automata emerge, generating  specific languages. Several examples are provided to elucidate these concepts.

Recently, $R$-metric spaces have been introduced to generalized metric spaces. This extension is based on the construction of a new universe with interesting properties. In this paper, some topological properties of $R$-metric spaces are studied and compared to the classical metric spaces via several examples. Also, some properties of a metric space with different relations are considered. Then, the elementary tools needed for the study of two important theorems of functional analysis are presented. For example, $R$-sequentially bounded sets, $R$-bounded sets, $R$-sequentially bounded functions and $R$-bounded functions are introduced in $R$-metric spaces. Moreover, a condition is given under which an $R$-continuous function is $R$-sequentially bounded. Finally, variants of the Heine--Borel theorem and the Hahn--Banach theorem are proved for $R$-metric spaces and $R$-vector spaces, respectively.

A complete subgraph of any simple graph G on k vertices is called a k-clique of G. In this paper, we first introduce the concept of the value of a k-clique (k>1) as an extension of the idea of the degree of a given vertex. Then, we obtain the generalized version of handshaking lemma which we call it clique handshaking lemma. The well-known classical result of Mantel states that the maximum number of edges in the class of triangle-free graphs with n vertices is equal to n2/4. Our main goal here is to find an extension of the above result for the class of Kω+1-free graphs, using the ideas of the value of cliques and the clique handshaking lemma.

Let $G=(V, E)$ be a simple graph with vertex set $V$ and edge set $E$. A {\em total Roman dominating function} on a graph $G$ is a function $f:V\rightarrow \{0,1,2\}$ satisfying the following conditions: (i) every vertex $u$ {\color{blue}such that} $f(u)=0$ is adjacent to at least one vertex $v$ {\color{blue}such that} $f(v)=2$ and (ii) the subgraph of $G$ induced by the set of all vertices of positive weight has no isolated vertex. The weight of a total Roman dominating function $f$ is the value, $f(V)=\Sigma_{u\in V(G)}f(u)$. The {\em total Roman domination number} $\gamma_{tR}(G)$ of $G$ is the minimum weight of a total Roman dominating function of $G$. A subset $S$ of $V$ is a $2$-independent set of $G$ if every vertex of $S$ has at most one neighbor in $S$. The maximum cardinality of a $2$-independent set of $G$ is the $2$-independence number $\beta_2(G)$. These two parameters are incomparable in general, however, we show that if $T$ is a tree, then $\gamma_{tR}(T)\le \frac{3}{2}\beta_2(T)$ and we characterize all trees attaining the equality.

Let $G=(V,E)$ be a connected graph. A subset $S$ of $V$ is called a $\gamma$-free set if there exists a $\gamma$-set $D$ of $G$ such that $S \cap D= \emptyset$. If further the induced subgraph $H=G[V-S]$ is connected, then $S$ is called a  $cc$-$\gamma$-free set of $G$. We use this concept to identify connected induced subgraphs $H$ of a given graph $G$ such that $\gamma(H) \leq \gamma(G)$. We also introduce the concept of $\gamma$-totally-free and $\gamma$-fixed sets and present several basic results on the corresponding parameters.

This research delves into the exploration of Pythagorean fuzzy sublattices and Pythagorean fuzzy ideals within the context of lattice theory. Through a rigorous analysis of structural theorems concerning these concepts derived from Pythagorean fuzzy sets, we uncover significant parallels with classical theory. Additionally, we investigate the behavior of Pythagorean fuzzy ideals under lattice homomorphisms. Our findings shed light on the applicability and utility of Pythagorean fuzzy theory in lattice-based structures, offering insights into their properties and relationships.

In this work, we introduce some useful concepts  in soft set theory, such as $\overline{\alpha}$-inverse intersection and  $\overline{\alpha}$-inverse union of inverse soft sets, together with  the type soft $\overline{\alpha}$-upper, $\overline{\alpha}$-lower, $\overline{\alpha}$-intersection and $\overline{\alpha}$-union of inverse soft matrices.  Our main contribution is of proposing a new decision-making method associated with  inverse soft sets and inverse soft matrices.

Let $G=(V,E)$ be a simple graph. A set $D\subseteq V$ is a strong dominating set of $G$, if for every vertex $x\in V\setminus D$ there is a vertex $y\in D$ with $xy\in E(G)$ and $\deg(x)\leq \deg(y)$. The strong domination number $\gamma_{\rm st}(G)$ is defined as the minimum cardinality of a strong dominating set. In this paper, we study the effects on $\gamma_{\rm st}(G)$ when $G$ is modified by operations on vertices and edges of $G$.

In today's data-driven landscape‎, ‎to ensure continuous survival and betterment‎, ‎the implementation of a robust Big Data Governance Framework (BDGF) is imperative for organizations to effectively manage and harness the potential of their vast data resources‎. ‎The BDGF serves no purpose when implemented in a random manner‎. ‎This article delves into the complex decision-making challenges that emerge in the context of implementation of the BDGF under uncertain conditions‎. ‎Specifically‎, ‎we aim to analyze and evaluate the BDGF performance using the Multi-Attribute Decision-Making (MADM) techniques aiming to address the intricacies of big data governance uncertainties‎. ‎To achieve our objectives‎, ‎we explore the application of Frank operators within the framework of complex picture fuzzy (CPF) sets (CPFs)‎. ‎We introduce complex picture fuzzy Frank weighted averaging (CPFFWA) and complex picture fuzzy Frank ordered weighted averaging (CPFFOWA) operators to enable more accurate implementation of the BDGF‎. ‎Additionally‎, ‎we rigorously examine the reliability of these newly proposed fuzzy Frank (FF) operators (FFAOs)‎, ‎taking into consideration essential properties such as idempotency‎, ‎monotonicity‎, ‎and boundedness‎. ‎To illustrate the practical applicability of our approach‎, ‎we present a case study that highlights the decision-making challenges encountered in the implementation of the BDGF‎. ‎Subsequently‎, ‎we conduct a comprehensive numerical example to assess various BDGF implementation options using the MADM technique based on complex picture fuzzy Frank aggregation (CPFFA) operators‎. ‎Furthermore‎, ‎we perform a comprehensive comparative assessment of our proposed methodology‎, ‎emphasizing the significance of the novel insights and results derived‎. ‎In conclusion‎, ‎this research article offers a unique and innovative perspective on decision-making within the realm of the BDGF‎. ‎By employing the CPFFWA and the CPFFOWA operators‎, ‎organizations can make well-informed decisions to optimize their BDGF implementations‎, ‎mitigate uncertainties‎, ‎and harness the full potential of their data assets in an ever-evolving data landscape‎. ‎This work contributes to the advancement of decision support systems for big data governance (BDG)‎, ‎providing valuable insights for practitioners and scholars alike‎.

This paper introduces the concept of a bipolar fuzzy GE-algebra within the framework of GE-algebras and explores its key properties. It offers a characterization of a bipolar fuzzy GE-algebra utilizing the negative ∈λ-set and the positive ∈α-set. Additionally, a criterion is provided for identifying a bipolar fuzzy set as a bipolar fuzzy GE-algebra. The paper defines negative qλ-sets and positive qα-sets of a bipolar fuzzy set, presenting necessary conditions for these sets to be GE-subalgebras of a GE-algebra. Furthermore, it introduces the notion of a bipolar (∈, ∈∨q )-fuzzy GE-algebra and investigates its properties, including necessary and sufficient conditions for a bipolar fuzzy set to qualify as such. Finally, the characterization of a bipolar (∈, ∈∨q )-fuzzy GE-algebra using the negative ∈λ-set and the positive ∈α-set is discussed