New concepts in neutrosophic graphs with application

A neutrosophic set is a generalization of an intuitionistic fuzzy set. Neutrosophic models give more flexibility, precisions and compatibility to the system as compared to intuitionistic fuzzy models. In this research study, we apply the concept of neutrosophic sets to graphs and discuss certain concepts of single-valued neutrosophic graphs. We illustrate the concepts by several examples. We investigate some interesting properties. We describe an application of single-valued neutrosophic graph in decision making process. We also present the procedure of our proposed method as an algorithm.     

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.     

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.     

半环的直觉模糊软h-左理想

将直觉模糊软集的概念与半环理论相结合,给出了半环的一种有边界值的直觉模糊软h-左理想的概念,对其部分性质进行了探讨,并利用有边界值的直觉模糊软h-左理想,对h-左正则半环的刻画问题进行了讨论.     

An adjustable approach to intuitionistic fuzzy soft sets based decision making

Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. In this paper we generalize the adjustable approach to fuzzy soft sets based decision making. Concretely, we present an adjustable approach to intuitionistic fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzy soft sets and give some illustrative examples. The properties of level soft sets are presented and discussed. Moreover, we also introduce the weighted intuitionistic fuzzy soft sets and investigate its application to decision making.     

Completely Continuous Functions in Intuitionistic Fuzzy Topological Spaces

In this paper, after giving the basic results related to the product of functions and the graph of functions in intuitionistic fuzzy topological spaces, we introduce and study the concept of fuzzy completely continuous functions between intuitionistic fuzzy topological spaces.     

Fuzzy k-competition graphs and p-competition fuzzy graphs

Fuzzy competition graph as a generalization of competition graph is introduced here. Two generalizations of fuzzy competition graph as fuzzy k-competition graphs and p-competition fuzzy graphs are also defined. These graphs are related to fuzzy digraphs. Fuzzy neighbourhood graphs, related to fuzzy graphs, are also defined here. Besides, some relations between fuzzy competition graphs and fuzzy neighbourhood graphs have been established. And finally, several results to find strong edges of the above mentioned graphs have also been established.     

Intuitionistic Fuzzy Soft K-Algebras

Intuitionistic fuzzy sets and soft sets are two different soft computing models for representing vagueness and uncertainty. We apply these soft computing models in combination to study vagueness and uncertainty in K-algebras. We first introduce the notion of ${(\in, \in\vee q)}$ -intuitionistic fuzzy K-algebras and discuss some of their properties. Then we introduce intuitionistic fuzzy soft K-algebras and investigate some of their properties. Finally, we introduce ${(\in, \in \vee q)}$ -intuitionistic fuzzy soft K-algebras and present some of their related properties.     

Coloring Fuzzy Circular Interval Graphs

Computing the weighted coloring number of graphs is a classical topic in combinatorics and graph theory. Recently these problems have again attracted a lot of attention for the class of quasi-line graphs and more specifically fuzzy circular interval graphs.The problem is NP-complete for quasi-line graphs. For the subclass of fuzzy circular interval graphs however, one can compute the weighted coloring number in polynomial time using recent results of Chudnovsky and Ovetsky and of King and Reed. Whether one could actually compute an optimal weighted coloring of a fuzzy circular interval graph in polynomial time however was still open.We provide a combinatorial algorithm that computes weighted colorings and the weighted coloring number for fuzzy circular interval graphs efficiently. The algorithm reduces the problem to the case of circular interval graphs, then making use of an algorithm by Gijswijt to compute integer decompositions.     

毕达哥拉斯模糊软集的相似性测度及其应用

直觉模糊软集不能处理隶属度与非隶属度之和大于1的情况,且现有的直觉模糊软集的相似性测度只考虑了隶属度与非隶属度,忽视了犹豫度。针对以上问题,本文提出了一种基于隶属度、非隶属度以及犹豫度三个参数的毕达哥拉斯模糊软集的相似性测度和加权相似性测度。在为加权相似性测度的权重取值时,本文基于现有文献中直觉模糊熵存在的缺陷建立一种改进的直觉模糊熵,利用熵权法计算权重。分别讨论两相似性测度公式的性质,最后将两相似性侧度公式应用在建筑材料的模式识别问题中。     

Intuitionistic supra fuzzy topological spaces

In this paper, We introduce an intuitionistic supra fuzzy closure space and investigate the relationship between intuitionistic supra fuzzy topological spaces and intuitionistic supra fuzzy closure spaces. Moreover, we can obtain intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space. We study the relationship between intuitionistic supra fuzzy closure space and the intuitionistic supra fuzzy topological space induced by an intuitionistic fuzzy bitopological space.     

Complement and Isomorphism on Bipolar Fuzzy Graphs

In this paper, we discuss some properties of the self complement and self weak complement bipolar fuzzy graphs, and get a sufficient condition for a bipolar fuzzy graph to be the self weak complement bipolar fuzzy graph. Also we investigate relations between operations union, join, and complement on bipolar fuzzy graphs.     

Rough intuitionistic fuzzy information systems

In this paper, we consider the notion of rough intuitionistic fuzzy sets and study their properties. We present an extension of rough set theory with the concept of intuitionistic fuzzy sets with several properties given. Moreover, we discuss the knowledge reduction of the classical Pawlak information systems and the intuitionistic fuzzy information systems, respectively.     

A theoretical investigation of regular equivalences for fuzzy graphs

The notion of regular equivalence or bisimulation arises in different applications, such as positional analysis of social networks and behavior analysis of state transition systems. The common characteristic of these applications is that the system under modeling can be represented as a graph. Thus, regular equivalence is a notion used to capture the similarity between nodes based on their linking patterns with other nodes. According to Borgatti and Everett, two nodes are regularly equivalent if they are equally related to equivalent others. In recent years, fuzzy graphs have also received considerable attention because they can represent both the qualitative relationships and the degrees of connection between nodes. In this paper, we generalize the notion of regular equivalence to fuzzy graphs based on two alternative definitions of regular equivalence. While the two definitions are equivalent for crisp graphs, they induce different generalizations for fuzzy graphs. The first generalization, called regular similarity, is based on the characterization of regular equivalence as an equivalence relation that commutes with the underlying graph edges. The regular similarity is then a fuzzy binary relation that specifies the degree of similarity between nodes in the graph. The second generalization, called generalized regular equivalence, is based on the definition of coloring. A coloring is a mapping from the set of nodes to a set of colors. A coloring is regular if nodes that are mapped to the same color, have the same colors in their neighborhoods. Hence, generalized regular equivalence is an equivalence relation that can determine a crisp partition of the nodes in a fuzzy graph.     

$$\varvec{}$$-Polar Fuzzy Labeling Graphs with Application

In this article, we apply the concept of m-polar fuzzy sets in labeling graphs and introduce the concept of m-polar fuzzy labeling graphs. We present properties of m-polar fuzzy labeling cycle and m-polar fuzzy labeling with bridge and cut nodes. We introduce several different types of distances, including w-distance, strongest strong distance, strong geodesic distance, \(\delta \)-distance in m-polar fuzzy labeling graph and investigate some of their properties. We also present an application of m-polar fuzzy labeling graphs in image processing.     

On intutionistic fuzzy gpr-closed sets

In this paper, a new class of intuitionistic fuzzy closed sets called intuitionistic fuzzy generalized preregular closed sets (briefly intuitionistic fuzzy gpr-closed sets) and intuitionistic fuzzy generalized preregular open sets (briefly intuitionistic fuzzy gpr-open sets) are introduced and their properties are studied. Further the notion of intuitionistic fuzzy preregular T _1/2-spaces and intuitionistic fuzzy generalized preregular continuity (briefly intuitionistic fuzzy gpr-continuity) are introduced and studied.     

基于模糊二元运算的直觉模糊群

为了使直觉模糊群也具有经典的结构,首先给出经典集合G的一种直觉模糊二元运算,利用这种直觉模糊二元运算定义了直觉模糊群,讨论这种直觉模糊群的一些性质,并给出直觉模糊群的两种等价定义。由于直觉模糊群具有和群一样经典的结构,因此,使直觉模糊代数的深入研究有了充分的理论基础。     

Intuitionistic fuzzy sublattices and ideals

We study the concept of intuitionistic fuzzy sublattices and intuitionistic fuzzy ideals of a lattice. Some characterization and properties of these intuitionistic fuzzy sublattices and ideals are established. Also we introduce the sum and product of two intuitionistic fuzzy ideals and prove that the sum and product of two Intuitionistic fuzzy ideals of a distributive lattice is again an intuitionistic fuzzy ideal. Moreover, we study the properties of intuitionistic fuzzy ideals under lattice homomorphism.     

Intuitionistic fuzzy quasi-ideals of ordered semigroups

In this paper we define intuitionistic fuzzy quasi-ideals of ordered semigroups. The main result of the paper is a characterization of quasi-ideals in terms of intuitionistic fuzzy quasi-ideals. We also characterize left simple, right simple, and completely regular ordered semigroups in terms of intuitionistic fuzzy quasi-ideals. We study the decomposition of left and right simple ordered semigroups using intuitionistic fuzzy quasi-ideals.     

The Rough Intuitionistic Fuzzy Ideals of Intuitionistic Fuzzy Subrings in a Commutative Ring

The aim of this paper is to give some definitions of rough intuitionistic fuzzy ideal, rough intuitionistic fuzzy radical, rough prime (primary) intuitionistic fuzzy ideal and rough semiprime intuitionistic fuzzy ideal of an intuitionistic fuzzy subring, and also to give some properties of such ideals. Moreover, we give their nature under homomorphism.