scholarly journals On Certain Products of Complex Intuitionistic Fuzzy Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abida Anwar ◽  
Faryal Chaudhry
Keyword(s):  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Specific Information ◽  
Intuitionistic Fuzzy ◽  
Modular Product ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Wide Range ◽  
Complex Intuitionistic Fuzzy Set ◽  
Intuitionistic Fuzzy Graphs

A complex intuitionistic fuzzy set (CIFS) can be used to model problems that have both intuitionistic uncertainty and periodicity. A diagram composed of nodes connected by lines and labeled with specific information may be used to depict a wide range of real-life and physical events. Complex intuitionistic fuzzy graphs (CIFGs) are a broader type of diagram that may be used to manipulate data. In this paper, we define the key operations direct, semistrong, strong, and modular products for complex intuitionistic fuzzy graphs and look at some interesting findings. Further, the strong complex intuitionistic fuzzy graph is defined, and several significant findings are developed. Furthermore, we study the behavior of the degree of a vertex in the modular product of two complex intuitionistic fuzzy graphs.

scholarly journals Complement of max product of intuitionistic fuzzy graphs

2021 ◽  
Author(s):  
S. Yahya Mohamed ◽  
A. Mohamed Ali
Keyword(s):  
Hamming Distance ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Degree Of A Vertex ◽  
Intuitionistic Fuzzy Graphs

AbstractIn this paper, the complement of max product of two intuitionistic fuzzy graphs is defined. The degree of a vertex in the complement of max product of intuitionistic fuzzy graph is studied. Some results on complement of max product of two regular intuitionistic fuzzy graphs are stated and proved. Finally, we provide an application of intuitionistic fuzzy graphs in school determination using normalized Hamming distance.

scholarly journals Connectivity Indices of Intuitionistic Fuzzy Graphs and Their Applications in Internet Routing and Transport Network Flow

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Tulat Naeem ◽  
Abdu Gumaei ◽  
Muhammad Kamran Jamil ◽  
Ahmed Alsanad ◽  
Kifayat Ullah
Keyword(s):  
Network Flow ◽  
Real Life ◽  
Vital Role ◽  
Transport Network ◽  
Internet Routing ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Connectivity Indices ◽  
Intuitionistic Fuzzy Graphs

Connectivity index CI has a vital role in real-world problems especially in Internet routing and transport network flow. Intuitionistic fuzzy graphs IFGs allow to describe two aspects of information using membership and nonmembership degrees under uncertainties. Keeping in view the importance of CI s in real life problems and comprehension of IFGs , we aim to develop some CI s in the environment of IFGs . We introduce two types of CI s , namely, CI and average CI , in the frame of IFGs . In spite of that, certain kinds of nodes called IF connectivity enhancing node IFCEN , IF connectivity reducing node IFCRN , and IF neutral node are introduced for IFGs . We have introduced strongest strong cycles, θ -evaluation of vertices, cycle connectivity, and CI of strong cycle. Applications of the CI s in two different types of networks are done, Internet routing and transport network flow, followed by examples to show the applicability of the proposed work.

scholarly journals New Concepts of Picture Fuzzy Graphs with Application

Mathematics ◽  
2019 ◽  
Vol 7 (5) ◽  
pp. 470 ◽  
Author(s):  
Cen Zuo ◽  
Anita Pal ◽  
Arindam Dey
Keyword(s):  
Fuzzy Set ◽  
Cartesian Product ◽  
Intuitionistic Fuzzy Set ◽  
Real Life ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Strong Product ◽  
Fuzzy Graphs ◽  
Life Problems ◽  
Picture Fuzzy Set

The picture fuzzy set is an efficient mathematical model to deal with uncertain real life problems, in which a intuitionistic fuzzy set may fail to reveal satisfactory results. Picture fuzzy set is an extension of the classical fuzzy set and intuitionistic fuzzy set. It can work very efficiently in uncertain scenarios which involve more answers to these type: yes, no, abstain and refusal. In this paper, we introduce the idea of the picture fuzzy graph based on the picture fuzzy relation. Some types of picture fuzzy graph such as a regular picture fuzzy graph, strong picture fuzzy graph, complete picture fuzzy graph, and complement picture fuzzy graph are introduced and some properties are also described. The idea of an isomorphic picture fuzzy graph is also introduced in this paper. We also define six operations such as Cartesian product, composition, join, direct product, lexicographic and strong product on picture fuzzy graph. Finally, we describe the utility of the picture fuzzy graph and its application in a social network.

scholarly journals Degree of a Vertex in Max-Product of Intuitionistic Fuzzy Graph

2019 ◽  
Vol 8 (4) ◽  
pp. 2902-2905 ◽  
Keyword(s):  
Automata Theory ◽  
Fuzzy Graph ◽  
Graph Theoretic ◽  
Fuzzy Models ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Wide Range ◽  
Theoretic Problem ◽  
Intuitionistic Fuzzy Graphs ◽  
Necessary And Sufficient

Graph theory has applications in many areas of computer science, including data mining, image segmentation, clustering and networking. Product on graphs has a wide range of application in networking system, automata theory, game theory and structural mechanics. In many cases, some aspects of a graph-theoretic problem may be uncertain. Intuitionistic fuzzy models provide more compatible to the system compared to the fuzzy models. An intuitionistic fuzzy graph can be derived from two given intuitionistic fuzzy graphs using max-product. In this paper, we studied the degree of vertex in intuitionistic fuzzy graph by the max-product of two given intuitionistic fuzzy graph. Also find the necessary and sufficient condition for max-product of two intuitionistic fuzzy graphs to be regular.

Complex intuitionistic fuzzy Maclaurin symmetric mean operators and its application to emergency program selection

2021 ◽  
pp. 1-22
Author(s):  
Riaz Ali ◽  
Saleem Abdullah ◽  
Shakoor Muhammad ◽  
Muhammad Naeem ◽  
Ronnason Chinram
Keyword(s):  
Decision Making ◽  
Fuzzy Sets ◽  
Fuzzy Set ◽  
Intuitionistic Fuzzy Set ◽  
Score Functions ◽  
Intuitionistic Fuzzy Numbers ◽  
Intuitionistic Fuzzy ◽  
Program Selection ◽  
Maclaurin Symmetric Mean ◽  
Complex Intuitionistic Fuzzy Set

Due to the indeterminacy and uncertainty of the decision-makers (DM) in the complex decision making problems of daily life, evaluation and aggregation of the information usually becomes a complicated task. In literature many theories and fuzzy sets (FS) are presented for the evaluation of these decision tasks, but most of these theories and fuzzy sets have failed to explain the uncertainty and vagueness in the decision making issues. Therefore, we use complex intuitionistic fuzzy set (CIFS) instead of fuzzy set and intuitionistic fuzzy set (IFS). A new type of aggregation operation is also developed by the use of complex intuitionistic fuzzy numbers (CIFNs), their accuracy and the score functions are also discussed in detail. Moreover, we utilized the Maclaurin symmetric mean (MSM) operator, which have the ability to capture the relationship among multi-input arguments, as a result, CIF Maclarurin symmetric mean (CIFMSM) operator and CIF dual Maclaurin symmetric mean (CIFDMSM) operator are presented and their characteristics are discussed in detail. On the basis of these operators, a MAGDM method is presented for the solution of group decision making problems. Finally, the validation of the propounded approach is proved by evaluating a numerical example, and by the comparison with the previously researched results.

scholarly journals An Intuitionistic Fuzzy Graph’s Signless Laplacian Energy

2018 ◽  
Vol 7 (4.10) ◽  
pp. 892
Author(s):  
Obbu Ramesh ◽  
S. Sharief Basha
Keyword(s):  
Adjacency Matrix ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Laplacian Energy ◽  
Signless Laplacian ◽  
Intuitionistic Fuzzy Graphs

We are extending concept into the Intuitionistic fuzzy graph’ Signless Laplacian energy  instead of the Signless Laplacian energy of fuzzy graph. Now we demarcated an Intuitionistic fuzzy graph’s Signless adjacency matrix and also  an Intuitionistic fuzzy graph’s Signless Laplacian energy. Here we find the Signless Laplacian energy ‘s Intuitionistic fuzzy graphs above and below   boundaries of   an with suitable examples.   

scholarly journals Perfectly Regular and Perfectly Edge-Regular Intuitionistic Fuzzy Graphs

2019 ◽  
Vol 9 (1) ◽  
pp. 6348-6352
Keyword(s):  
Spectral Properties ◽  
Constant Function ◽  
Fuzzy Graph ◽  
Intuitionistic Fuzzy ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

A Perfectly regular intuitionistic fuzzy graph is an intuitionistic fuzzy graph that is both regular and totally regular. In this paper we introduce and classify these types of intuitionistic fuzzy graphs and study several of their properties, including how two classes of intuitionistic fuzzy graphs structurally relate to one another and several of their spectral properties such as isospectral intuitionistic fuzzy graphs and when the energy of intuitionistic fuzzy graph is proportional to the energy of their underlying crisp graphs. These properties are studied in particular due to having at least one constant function and .

scholarly journals Specific Types of Pythagorean Fuzzy Graphs and Application to Decision-Making

2018 ◽  
Vol 23 (3) ◽  
pp. 42 ◽  
Author(s):  
Muhammad Akram ◽  
Amna Habib ◽  
Farwa Ilyas ◽  
Jawaria Dar
Keyword(s):  
Decision Making ◽  
Research Study ◽  
Symmetric Difference ◽  
Intuitionistic Fuzzy ◽  
Research Article ◽  
Fuzzy Graphs ◽  
Intuitionistic Fuzzy Graphs

The purpose of this research study is to present some new operations, including rejection, symmetric difference, residue product, and maximal product of Pythagorean fuzzy graphs (PFGs), and to explore some of their properties. This research article introduces certain notions, including intuitionistic fuzzy graphs of 3-type (IFGs3T), intuitionistic fuzzy graphs of 4-type (IFGs4T), and intuitionistic fuzzy graphs of n-type (IFGsnT), and proves that every IFG(n−1)T is an IFGnT (for n ≥ 2). Moreover, this study discusses the application of Pythagorean fuzzy graphs in decision making.

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