Novel applications of bipolar single-valued neutrosophic competition graphs

Bipolar single-valued neutrosophic models are the generalization of bipolar fuzzy models. We first introduce the concept of bipolar single-valued neutrosophic competition graphs. We then, discuss some important propositions related to bipolar single-valued neutrosophic competition graphs. We define bipolar single-valued neutrosophic economic competition graphs and m-step bipolar single-valued neutrosophic economic competition graphs. Further, we describe applications of bipolar single-valued neutrosophic competition graphs in organizational designations and brands competition. Finally, we present our improved methods by algorithms.     

Single-Valued Neutrosophic Lie Algebras

A single-valued neutrosophic (SVN) set is a powerful general formal framework that generalizes the concept of fuzzy set and intuitionistic fuzzy set. In SVN set, indeterminacy is quantified explicitly, and truth membership, indeterminacy membership, and falsity membership are independent. In this paper, we apply the notion of SVN sets to Lie algebras. We develop the concepts of SVN Lie subalgebras and SVN Lie ideals. We describe some interesting results of SVN Lie ideals.     

Accessible single-valued neutrosophic graphs

This paper derived single-valued neutrosophic graphs from single-valued neutrosophic hypergraphs via strong equivalence relation. We show that any weak single-valued neutrosophic graph is a derived single-valued neutrosophic graph and any linear weak single-valued neutrosophic tree is an extendable linear single-valued neutrosophic tree.     

一种基于TOPSIS法的单值中智多属性决策新方法

单值中智集(SVNS)是中智集(NS)的一种特殊情况,它可以描述现实世界中大量存在的不精确、不确定和不一致信息。由于语言评价的模糊性,传统的模糊评价方法在解决多属性决策(MADM)问题上效果不佳。针对这种情况,提出了一种基于TOPSIS法的单值中智多属性决策新方法。首先介绍了中智集的一些基本概念和运算规则,给出了两个单值中智集之间的广义距离公式;然后构建了聚合专家权重的单值中智决策矩阵,把TOPSIS法推广到单值中智集的环境下;接着通过偏好排序确定了最佳的决策方案。最后通过一个仿真实例,说明了该方案的有效和实用性。     

A Survey on Single-Valued Neutrosophic $K$-Algebras

In this survey, we first present a brief overview of logical algebras. We then discuss concepts of single-valued neutrosophic $K$-subalgebras, single-valued neutrosophic soft $K$-algebras and single-valued neutrosophic topological $K$-algebras. Moreover, we discuss various fundamental concepts which include interior, closure, $C{_5}$-connectivity, super connectivity, compactness and Hausdorffness of single-valued neutrosophic topological $K$-algebras.     

Intuitionistic fuzzy soft graphs with applications

We present different types of new concepts, including intuitionistic fuzzy soft graphs, complete intuitionistic fuzzy soft graph, strong intuitionistic fuzzy soft graph and self complement of intuitionistic fuzzy soft graph. We describe various methods of their construction, and investigate some of their related properties. We also discuss applications of intuitionistic fuzzy soft graphs in communication network and decision making.     

Single valued neutrosophic cross-entropy for multicriteria decision making problems

A single valued neutrosophic set (SVNS) is an instance of a neutrosophic set, which give us an additional possibility to represent uncertainty, imprecise, incomplete, and inconsistent information which exist in real world. It would be more suitable to apply indeterminate information and inconsistent information measures. In this paper, the cross entropy of SVNSs, called single valued neutrosophic cross entropy, is proposed as an extension of the cross entropy of fuzzy sets. Then, a multicriteria decision-making method based on the proposed single valued neutrosophic cross entropy is established in which criteria values for alternatives are SVNSs. In decision making process, we utilize the single-valued neutrosophic weighted cross entropy between the ideal alternative and an alternative to rank the alternatives corresponding to the cross entropy values and to select the most desirable one(s). Finally, a practical example of the choosing problem of suppliers is provided to illustrate the application of the developed approach.     

A rough set approach to intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. Since its appearance, there has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. The intuitionistic fuzzy soft set is a combination of an intuitionistic fuzzy set and a soft set. The rough set theory is a powerful tool for dealing with uncertainty, granuality and incompleteness of knowledge in information systems. Using rough set theory, this paper proposes a novel approach to intuitionistic fuzzy soft set based decision making problems. Firstly, by employing an intuitionistic fuzzy relation and a threshold value pair, we define a new rough set model and examine some fundamental properties of this rough set model. Then the concepts of approximate precision and rough degree are given and some basic properties are discussed. Furthermore, we investigate the relationship between intuitionistic fuzzy soft sets and intuitionistic fuzzy relations and present a rough set approach to intuitionistic fuzzy soft set based decision making. Finally, an illustrative example is employed to show the validity of this rough set approach in intuitionistic fuzzy soft set based decision making problems.     

Certain types of irregular <Emphasis Type="Italic">m</Emphasis>-polar fuzzy graphs

The notion of an m-polar fuzzy set is a generalization of a bipolar fuzzy set. We apply the concept of m-polar fuzzy sets to graphs. We introduce certain types of irregular m-polar fuzzy graphs and investigate some of their properties. We describe the concepts of types of irregular m-polar fuzzy graphs with several examples. We also present applications of m-polar fuzzy graphs in decision making and social network as examples.     

直觉 Fuzzy集的基本定理

提出直觉 Fuzzy集的截集的概念 ,并详细讨论其基本性质 ,在此基础上建立直觉 Fuzzy集的一系列分解定理、表现定理与扩张原理 .     

Bipolar neutrosophic planar graphs

Fuzzy graph theory is used for solving real-world problems in different fields, including theoretical computer science, engineering, physics, combinatorics and medical sciences. In this paper, we present conepts of bipolar neutrosophic multigraphs, bipolar neutrosophic planar graphs, bipolar neutrosophic dual graphs, and study some of their related properties. We also describe applications of bipolar neutrosophic graphs in road network and electrical connections.     

A novel approach to interval-valued intuitionistic fuzzy soft set based decision making

The soft set theory, originally proposed by Molodtsov, can be used as a general mathematical tool for dealing with uncertainty. The interval-valued intuitionistic fuzzy soft set is a combination of an interval-valued intuitionistic fuzzy set and a soft set. The aim of this paper is to investigate the decision making based on interval-valued intuitionistic fuzzy soft sets. By means of level soft sets, we develop an adjustable approach to interval-valued intuitionistic fuzzy soft sets based decision making and some numerical examples are provided to illustrate the developed approach. Furthermore, we also define the concept of the weighted interval-valued intuitionistic fuzzy soft set and apply it to decision making.     

模糊数直觉模糊集

定义一种新的模糊数直觉模糊集,同时给出了它的一些运算,并讨论了它与直觉模糊集、区间值直觉模糊集的关系。     

基于二元关系的直觉模糊近似空间与直觉模糊拓扑

讨论在一般二元关系下直党模糊近似空间诱导的直党模糊拓扑空问的若干性质;由直觉模糊拓扑空间诱导直觉模糊近似空同所需的TC条件及其所得近似空间的近似算子若干性质.     

An approach to decision making based on intuitionistic fuzzy rough sets over two universes

Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.     

A complex multi-attribute large-group PLS decision-making method in the interval-valued intuitionistic fuzzy environment

In the complex multi-attribute large-group decision-making (CMALGDM) problems in interval-valued intuitionistic fuzzy (IVIF) environment, attributes of the alternatives are often stratified and correlated. This paper proposes a decision-making method for these problems based on partial least squares (PLS) path modelling, which not only fully exploits the decision information of decision makers (DMs), but also effectively addresses the relativity problem in the decision attributes and objectively assigned weights to the primary decision attributes (i.e., “latent variables for decision making”). The method can be outlined in three steps. First, a two-stage method is proposed to transform the interval-valued intuitionistic fuzzy number (IVIFN) samples into single-valued samples. In this step, an improved C-OWA operator is first given to transform the IVIFN samples into intuitionistic fuzzy number (IFN) samples, which makes the preference information of the DMs more objectively aggregated. Then a proposed membership-based method is applied to reduce the information loss and transform the IFN samples into single-valued samples. Second, the estimated values and weights of the “latent variables for decision-making” are obtained by means of the PLS path modelling algorithm. Finally, a multi-alternative sorting method is devised in accordance with the estimated values and weights. An example is provided to illustrate the proposed technique and evaluate its feasibility and validity.     

基于TOPSIS的区间直觉模糊多属性决策法

对基于区间直觉模糊信息的多属性决策问题进行了研究。给出了区间直觉模糊数之间的距离公式,并定义了区间直觉模糊正、负理想点,进而提出了一种基于TOPSIS的区间直觉模糊多属性决策方法。最后进行了实例分析。     

直觉模糊正规子群与直觉模糊商群

在直觉模糊子群的基础上 ,引入直觉模糊正规子群与直觉模糊商群概念 ,并讨论了它们的一些性质 ,最后研究了群同态下 ,直觉模糊正规子群的对应关系     

Multi-person multi-attribute decision making models under intuitionistic fuzzy environment

Intuitionistic fuzzy numbers, each of which is characterized by the degree of membership and the degree of non-membership of an element, are a very useful means to depict the decision information in the process of decision making. In this article, we investigate the group decision making problems in which all the information provided by the decision makers is expressed as intuitionistic fuzzy decision matrices where each of the elements is characterized by intuitionistic fuzzy number, and the information about attribute weights is partially known, which may be constructed by various forms. We first use the intuitionistic fuzzy hybrid geometric (IFHG) operator to aggregate all individual intuitionistic fuzzy decision matrices provided by the decision makers into the collective intuitionistic fuzzy decision matrix, then we utilize the score function to calculate the score of each attribute value and construct the score matrix of the collective intuitionistic fuzzy decision matrix. Based on the score matrix and the given attribute weight information, we establish some optimization models to determine the weights of attributes. Furthermore, we utilize the obtained attribute weights and the intuitionistic fuzzy weighted geometric (IFWG) operator to fuse the intuitionistic fuzzy information in the collective intuitionistic fuzzy decision matrix to get the overall intuitionistic fuzzy values of alternatives by which the ranking of all the given alternatives can be found. Finally, we give an illustrative example.     

直觉模糊关系的截集性质

定义了直觉模糊关系的截集以及并给出了它们的基本性质,同时分别讨论了自反、对称、传递直觉模糊关系与经典二元关系之间的等价刻画;其次,提出直觉模糊关系的定义域与值域的概念;最后,分析了直觉模糊关系合成的截集性质.