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Normal Bipolar Soft Subgroups 正常双极软子组
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2021-01-02 DOI: 10.1080/16168658.2021.1915453
Faruk Karaaslan, A. Ullah, Imtiaz Ahmad
In this study, we introduce the concept of normal bipolar soft subgroup and investigate some properties of normal bipolar soft subgroups. We also define notions of bipolar soft left and right cosets of a bipolar soft group and the concept of conjugate bipolar soft subgroup, and obtain some of their properties.
本文引入了正规双极性软子群的概念,研究了正规双极性软子群的一些性质。定义了双极性软群的双极性软左、右上集和共轭双极性软子群的概念,并得到了它们的一些性质。
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引用次数: 1
On Soft Lattice Topological Spaces 关于软点阵拓扑空间
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2021-01-02 DOI: 10.1080/16168658.2021.1929744
Sandhya S. Pai, T. Baiju
In this paper, we introduce Soft Lattice topological spaces which are defined over a soft lattice L with a fixed set of parameter P and it is also a generalisation of soft topological spaces. The notion of soft L-open sets, soft L-closed sets, soft L-closure, soft L-interior point and soft L-neighbourhood are introduced. Further some basic properties of Soft L-Topology are also investigated.
本文引入了定义在具有固定参数集P的软格L上的软格拓扑空间,它也是软拓扑空间的推广。引入了软l开集、软l闭集、软l闭集、软l内点和软l邻域的概念。进一步研究了软l -拓扑的一些基本性质。
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引用次数: 2
Characterisation of p-ideals in Hemirings on the Basis of Hemiregularity, Prime and Normal Fuzzy Ideals 基于半正则、素数和正规模糊理想的半模糊中p理想的刻画
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2021-01-02 DOI: 10.1080/16168658.2021.1915569
M. Touqeer, Atiqa Maryam, Muhammad Saeed
In p-hemiregular hemirings, some properties of ‘prime fuzzy p-ideals’ are examined. In the case of fuzzy p-ideal, p-hemiregular hemiring is also characterised. It is showed that in the case of hemiring , fuzzy subset φ is a ‘prime fuzzy left p-ideal’ in if and only if φ is having two values, set having all values of i?> in so that φ(p) equals to one is a ‘prime left(right) p-ideal’ in , φ(0) = 1. In hemirings for ‘maximal fuzzy left(right) p-ideals’, some related properties are also studied.
在p-半正则半分中,研究了“素数模糊p理想”的一些性质。在模糊p-理想的情况下,也刻画了p-半正则半环。证明了在半环的情况下,模糊子集φ是一个'素数模糊左p理想'当且仅当φ有两个值,集合有i?因此φ(p) = 1是'素数左(右)p理想'在φ(0) = 1。在“极大模糊左(右)p理想”的分划中,还研究了一些相关性质。
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引用次数: 0
Total and Secure Domination for Corona Product of Two Fuzzy Soft Graphs 两个模糊软图的电晕积的完全和安全支配
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2021-01-02 DOI: 10.1080/16168658.2021.1915456
A. Karbasioun, R. Ameri
Fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. On the other domination is a rapidly developing area of research in graph theory, and its various applications to ad hoc networks, distributed computing, social networks and web graphs partly explain the increased interest. This concept was introduced by [Benecke S, Cockayne EJ, Mynhardt CM. Secure total domination in graphs. Util Math. 2007;74:247–259.] in 2007 and Go and Canoy continue the study of these notions [Canoy RS, Go CE. Domination in the corona and join of graphs. Int Math Forum. 2011;6(16):763–771.] and afterward introduce total dominating and secure total dominating sets. Also graph operations like corona product play a very important role in mathematical chemistry, since some chemically interesting graphs can be obtained from some simpler graphs by different graph operations. In this paper, we characterised the dominating, total dominating, and secure total dominating sets in the corona of two fuzzy soft connected.
模糊集和软集是表示模糊性和不确定性的两种不同的软计算模型。另一方面,图论是一个快速发展的研究领域,它在特设网络、分布式计算、社交网络和网络图中的各种应用部分地解释了人们日益增长的兴趣。这个概念是由Benecke S, Cockayne EJ, Mynhardt CM提出的。确保在图中的完全支配。数学学报。2007;74:247-259。], Go和canoe继续研究这些概念[canoe RS, Go CE]。在图的日冕和连接中的支配。国际数学论坛。2011;6(16):763-771。],然后介绍全控制集和安全全控制集。此外,像电晕积这样的图运算在数学化学中也起着非常重要的作用,因为一些化学上有趣的图可以通过不同的图运算从一些更简单的图中得到。本文对两个模糊软连通的晕上的控制集、总控制集和安全控制集进行了刻画。
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引用次数: 1
A Profit Maximisation Solid Transportation Problem Using Genetic Algorithm in Fuzzy Environment 模糊环境下基于遗传算法的利润最大化固体运输问题
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2021-01-02 DOI: 10.1080/16168658.2021.1915454
S. Samanta, A. Ojha, B. Das, S. Mondal
In this paper, a solid transportation problem has been considered in which the transportation is accomplished in two stages – firstly, from the origin(s) to the near by station(s) of the destination(s) and secondly, from the near by station(s) to the exact destination(s). Here, a fuzzy AUD (all unit discount) policy has been introduced based upon the amount of transportation along with a fuzzy fixed charge. In addition, a budget constraint has been incorporated taking fuzzy unit transportation cost. Then the proposed model has been converted into a single objective optimisation problem using interval arithmetic method. To solve the model, Genetic Algorithm (GA) has been used depending on roulette wheel selection, crossover and mutation. Finally, a numerical example has been illustrated to study the feasibility of the model.
本文研究了一个固体运输问题,在该问题中,固体运输分为两个阶段完成:第一阶段是从起点到目的地的最近站点,第二阶段是从最近站点到确切目的地。在这里,引入了基于运输量的模糊AUD(所有单位折扣)政策以及模糊固定费用。此外,还引入了模糊单位运输成本的预算约束。然后利用区间算法将模型转化为单目标优化问题。为了求解该模型,采用了基于轮盘选择、交叉和变异的遗传算法。最后通过数值算例验证了该模型的可行性。
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引用次数: 2
A New Order Function for Interval-Valued Intuitionistic Fuzzy Numbers and Its Application in Group Decision Making 区间值直觉模糊数的一种新阶函数及其在群体决策中的应用
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2021-01-02 DOI: 10.1080/16168658.2021.1936961
Sandeep Kumar, Shalu Rani, Mohit Kumar
Purpose: We introduce a multiple attribute group decision making (MAGDM) method under interval-valued intuitionistic fuzzy (IVIF) domain. In these MAGDM problems, attribute values and attribute weights are represented in terms of IVIF sets (IVIFSs). Methodology: The present methodology is divided into two parts. Firstly, an appropriate order function has been developed for IVIFSs. Secondly, an algorithm has been proposed for solving the MAGDM problems with IVIF decision information. Findings: To show the effectiveness of the proposed method, a theoretical comparative study with respect to some existing literature is provided. A real-life based numerical example is given to demonstrate the proposed solution procedure. The advantage of this method is also described. Values: Using proposed order function, interval-valued intuitionistic fuzzy hybrid geometric and ordered weighted averaging operators, the present method provides a most preferred alternative in six steps. On the basis of a comparative study, it can be observed that the present method simple and easy to implement for solving the IVIF MAGDM model occurrence in real-life decision making problems.
目的:介绍区间值直觉模糊(IVIF)域下的多属性群决策方法。在这些MAGDM问题中,属性值和属性权重用IVIF集(ivifs)表示。方法论:本研究的方法论分为两部分。首先,建立了适合ivifs的阶函数。其次,提出了一种利用体外受精决策信息求解MAGDM问题的算法。研究结果:为了证明所提出的方法的有效性,对一些现有文献进行了理论比较研究。最后给出了一个实际的数值算例来说明所提出的求解过程。并介绍了该方法的优点。利用所提出的阶函数、区间值直觉模糊混合几何算子和有序加权平均算子,本方法提供了一个最理想的选择,分为六个步骤。通过对比研究可以看出,本方法简单易行,适用于解决IVIF MAGDM模型在现实生活中出现的决策问题。
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引用次数: 1
Weak Forms of Soft Separation Axioms and Fixed Soft Points 软分离公理的弱形式和不动软点
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2020-10-01 DOI: 10.1080/16168658.2021.1924528
T. Al-shami, E. A. Abo-Tabl, Baravan A. Asaad
Realizing the importance of separation axioms in classifications of topological spaces and studying certain properties of fixed points, we formulate new soft separation axioms, namely tt-soft and tt-soft b-regular spaces. Their definitions depend on three factors: soft b-open sets, total belong and total non-belong relations. In fact, they are genuine generalizations of p-soft -spaces in the cases of i = 0, 1, 2. With the help of examples, we study the relationships between them as well as with soft and soft b-regular spaces. Some interesting properties of them are obtained under the conditions of soft hyperconnected and extended soft topological spaces. Also, we show that they are preserved under finite product soft spaces and soft -homeomorphism mappings. Finally, we introduce a concept of b-fixed soft points and investigate its main properties.
认识到分离公理在拓扑空间分类中的重要性,并研究了不动点的某些性质,提出了新的软分离公理,即tt-soft和tt-soft b-正则空间。它们的定义取决于三个因素:软b开集、全隶属关系和全不隶属关系。事实上,在i = 0,1,2的情况下,它们是p-软空间的真正推广。通过实例研究了它们之间的关系以及它们与软b正则空间和软b正则空间之间的关系。在软超连通和扩展软拓扑空间条件下,得到了它们的一些有趣性质。此外,我们还证明了它们在有限积软空间和软同胚映射下是保持的。最后,我们引入了b固定软点的概念,并研究了它的主要性质。
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引用次数: 10
Reliability Range Through Upgraded Operation with Trapezoidal Fuzzy Number 梯形模糊数升级后的可靠性范围
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2020-10-01 DOI: 10.1080/16168658.2021.1918039
Amit Kumar, P. Dhiman
This work presents an application of upgraded arithmetic operations on trapezoidal fuzzy number to extend the reliability from point estimation to interval estimation. A realistic example of an accidental case has been taken to show the desired results. As we know that uncertainty is a disregardable phenomenon and in this situation crisp reliability may not be exact. To get a better hold on this situation, we introduce a method of trapezoidal fuzzy number and upgraded arithmetic operations. In this paper, the reliability of each factor is represented by the trapezoidal fuzzy number and the final reliability is obtained in the form of trapezoidal fuzzy number. Hence, the dejection of fuzzy number is preserved and the crisp region is increased to illustrate the highest membership grade as an interval. So it can help the decision maker to analyse the behaviour of the system and take effective decision accordingly to reduce the chance of mishappening.
提出了一种梯形模糊数的改进算法,将可靠性从点估计扩展到区间估计。以一个实际的偶然案例为例,说明了所期望的结果。正如我们所知,不确定性是一种不容忽视的现象,在这种情况下,清晰的可靠性可能不准确。为了更好地把握这种情况,我们引入了一种梯形模糊数的方法和改进的算术运算。本文将各因素的可靠度用梯形模糊数表示,并以梯形模糊数的形式得到最终的可靠度。因此,保留了模糊数的归属,并增加了清晰区域,将最高隶属度表示为一个区间。因此,它可以帮助决策者分析系统的行为,并采取有效的决策,以减少错误发生的机会。
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引用次数: 2
Solving Two Coupled Fuzzy Sylvester Matrix Equations Using Iterative Least-squares Solutions 用迭代最小二乘法求解两个耦合模糊Sylvester矩阵方程
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2020-10-01 DOI: 10.1080/16168658.2021.1923442
A. Bayoumi, M. Ramadan
ABSTRACT In this paper, five iterative methods for solving two coupled fuzzy Sylvester matrix equations are considered. The two coupled fuzzy Sylvester matrix equations are expressed by using the generalized inverse of the coefficient matrix, then iterative solutions are constructed by applying the hierarchical identification principle and by using the block-matrix inner product (the star product for short). A proposed modification to this algorithm to solve the first coupled fuzzy Sylvester matrix equations is suggested. This proposed modification is compared with the first algorithm where our modification exhibits fast convergence behavior. Also, we suggested two least-squares iterative algorithm by applying a hierarchical identification principle to solve the two coupled fuzzy Sylvester matrix equations. The proposed methods are illustrated by numerical examples.
本文研究了求解两个耦合模糊Sylvester矩阵方程的五种迭代方法。首先利用系数矩阵的广义逆表示两个耦合模糊Sylvester矩阵方程,然后应用层次辨识原理,利用分块矩阵内积(简称星形积)构造迭代解。提出了一种改进算法,用于求解第一耦合模糊Sylvester矩阵方程。并与第一种算法进行了比较,结果表明该算法具有较快的收敛性。同时,我们提出了两种最小二乘迭代算法,应用层次辨识原理求解两个耦合的模糊Sylvester矩阵方程。通过数值算例说明了所提出的方法。
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引用次数: 0
Characterization of Non-Associative Ordered Semigroups by the Properties of F-Ideals 用f理想的性质刻画非结合有序半群
IF 1.2 Q2 MATHEMATICS, APPLIED Pub Date : 2020-10-01 DOI: 10.1080/16168658.2021.1924513
N. Kausar, M. Munir, S. Kousar, M. Gulistan, K. Anitha
In this article, we present brief description on R-OAG-gpd regular ordered AG-groupoid and IR-OAG-gpd intra-regular ordered AG-groupoid by using FL-ideal, FR-ideal, FQ-ideal, FB-ideal, FB-ideal, FGB-ideal.
本文用fl -理想、fr -理想、fq -理想、fb -理想、fb -理想、fgb -理想对R-OAG-gpd正则有序AG-groupoid和IR-OAG-gpd内正则有序AG-groupoid进行了简要描述。
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引用次数: 0
期刊
Fuzzy Information and Engineering
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