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

In this paper, we apply a rough soft set to a spe-cial algebraic hyperstructure, and give the concept of a rough soft semihypergroup. We propose the notion of lower and upper approximations concerning a special semihypergroup and obtain some properties. Moreover, we consider a connection between the lower(upper) approximation of a special semihypergroup and the lower(upper) approximation of the associated -hypergroupoid. In the last section of this research, we discuss the decision-making algorithm of rough soft semihypergroups. Afterward, we obtain a relation between the decision-making algorithm of rough soft semi-hypergroups and their associated rough soft -hypergroupoids for a special semihypergroup.

To effectively evaluate relationships in uncertain environments, such as in decision-making, the idea of Intuitionistic Fuzzy Correlation Coefficient (IFCC) is employed. Several authors have provided many methods of IFCC, but their methods have some setbacks in correctness and accuracy. In this article, some novel methods of IFCC are developed that possess better exactness and reliability compared to the existing IFCC techniques. The new IFCC techniques possess high reliability and precision based on their mathematical formulations and the inclusion of all intuitionistic fuzzy parameters. The setbacks of the existing IFCC techniques are enumerated and verified with some numerical examples. Several of their properties are discussed in order to authenticate the novel IFCC techniques. More so, utilizing the new IFCC schemes in the issue of course allocations in higher institutions is discussed. Finally, the preeminence of the novel IFCC techniques is discussed in terms of precision and consistency with correlation principles by juxtaposing their effectiveness with other IFCC methods.

This work presents a modified Pythagorean fuzzy similarity operator and utilizes its potential in the analysis of questionnaire. Similarity operator is a formidable methodology for decision-making under uncertain domains. Pythagorean fuzzy set is an extended form of intuitionistic fuzzy set with a better accuracy in complex real-world applications. Lots of discussions bordering on the uses of Pythagorean fuzzy sets have been explored based on Pythagorean fuzzy similarity operators. Among the extant Pythagorean fuzzy similarity operators, the work of Zhang et al. is significant but it contains some flaws which need to be corrected/modified to enhance reliable interpretation. To this end, this work explicates the Zhang et al.’s techniques of Pythagorean fuzzy similarity operator by pinpointing their drawbacks to develop an enhanced Pythagorean fuzzy similarity operator, which appropriately satisfies the similarity conditions and yields consistent results in comparison to the Zhang et al.’s techniques. Succinctly speaking, the aim of the work is to correct the flaws in Zhang et al.’s techniques via modifications. To theoretically validate the enhanced Pythagorean fuzzy similarity operator, we discuss it properties and find out that the similarity conditions are well satisfied. In addition, the enhanced PFSO and the Zhang et al.’s PFSOs are compared in the context of precision, and it is verified that the enhanced Pythagorean fuzzy similarity operator can successfully measure the similarity between vastly related but inconsistent PFSs and as well yields a very reasonable results. Furthermore, the enhanced Pythagorean fuzzy similarity operator is applied to the analysis of questionnaire on virtual library to ascertain the extent of awareness and effects of virtual library on students’ academic performance via real data collected from fieldwork. Finally, it is certified that the enhanced Pythagorean fuzzy similarity operator can handle diverse everyday problems more precisely than the Zhang et al.’s Pythagorean fuzzy similarity operators.

‎‎Using the concept of fuzzy points‎, ‎the notion of fuzzy filters in pre-ordered residuated systems is introduced‎, ‎and their relevant properties are investigated and analyzed‎. ‎Characterization of fuzzy filters are displayed‎. ‎Fuzzy filters are formed using filters‎. ‎The concepts of positive set‎, ‎$\in_{t}$-set‎, ‎(extended) $q_{t}$-set are defined and the conditions under which they become filters are explored‎. ‎The concept of fuzzy filter with thresholds is introduced and related properties are investigated‎.
 

The zero forcing number of a graph is the minimum cardinality among all the zero forcing sets of a graph $G$.  The aim of this article is to compute the zero forcing number of complementary prism graphs.  Some bounds on the zero forcing number of complementary prism graphs are presented. The remainder of this article discusses the following result.  Let $G$ and $\overline{G }$ be connected graphs. Then $Z(G\overline{G})\leq n-1$ if and only if  there exists two vertices $v_i,v_j \in V(G)$ and $i\neq j$ such that, either $N(v_i) \subseteq N(v_j)$ or $N[v_i] \subseteq N[v_j]$ in $G$.

‎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.

‎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.

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.

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 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.

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.

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.