Neutrosophic Incidence Graphs With Application

Akram, Muhammad; Sayed, Sidra; Smarandache, Florentín

doi:10.3390/axioms7030047

Cited by 9 publications

(4 citation statements)

References 10 publications

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“…Yager [99] introduced the concept of ordered weighted averaging aggregation operators for MCDM. Akram et al [100][101][102][103] proved the usefulness of m-polar fuzzy soft rough sets, neutrosophic incidence graphs, and m-polar fuzzy ELECTRE-Iin decision making problems. Ali et al [104] presented new abilities of soft sets and rough sets with fuzzy soft sets.…”

Section: Mcdm Based Uncertain Data Modelingmentioning

confidence: 99%

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

et al. 2020

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A q-rung orthopair fuzzy set (q-ROFS), an extension of the Pythagorean fuzzy set (PFS) and intuitionistic fuzzy set (IFS), is very helpful in representing vague information that occurs in real-world circumstances. The intention of this article is to introduce several aggregation operators in the framework of q-rung orthopair fuzzy numbers (q-ROFNs). The key feature of q-ROFNs is to deal with the situation when the sum of the qth powers of membership and non-membership grades of each alternative in the universe is less than one. The Einstein operators with their operational laws have excellent flexibility. Due to the flexible nature of these Einstein operational laws, we introduce the q-rung orthopair fuzzy Einstein weighted averaging (q-ROFEWA) operator, q-rung orthopair fuzzy Einstein ordered weighted averaging (q-ROFEOWA) operator, q-rung orthopair fuzzy Einstein weighted geometric (q-ROFEWG) operator, and q-rung orthopair fuzzy Einstein ordered weighted geometric (q-ROFEOWG) operator. We discuss certain properties of these operators, inclusive of their ability that the aggregated value of a set of q-ROFNs is a unique q-ROFN. By utilizing the proposed Einstein operators, this article describes a robust multi-criteria decision making (MCDM) technique for solving real-world problems. Finally, a numerical example related to integrated energy modeling and sustainable energy planning is presented to justify the validity and feasibility of the proposed technique.

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Section: Mcdm Based Uncertain Data Modelingmentioning

confidence: 99%

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

et al. 2020

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“…Nazeer, Rashid, Hussain, et al (2021) and Nazeer, Rashid and Keikha (2021b) also gave the applications of FIGs in human trafficking, etc. Akram et al (2018) gave the detailed study regarding the neutrosophic incidence graphs with application.…”

Section: Introductionmentioning

confidence: 99%

Optimization in Business Trade by Using Fuzzy Incidence Graphs

Rehman

Rashid

Hussain

2022

JCCE

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In classical graph theory, set of vertices in which every edge is incident to at least one of the vertex is called a vertex covering set and the problems of vertex covering (VC) are known as VC problems. The classical graphs do not reflect the impact of vertex on the edge and such impact is reflected in fuzzy incidence graphs (FIGs). We used optimization technique in a trade using clique covering (CC) in FIGs. This article includes some basic definitions such as strength of clique, strength of path, strength of minimum clique (SMC), acceptable strength of path and acceptable strength of clique, robust number, minimum covering number of the clique, close measure, some examples and theorems in FIGs, and new strategy of optimization to characterize and solve facility point problems by adopting the CC application of FIGs for a business alliance to get maximum total achievement by reducing the transportation cost. This procedure will be helpful to develop sustainable economic developmental goal of the world. Some already existing theorems in fuzzy graphs are also checked in FIGs.A mathematical model is defined and a real-life problem from a trade is solved keeping the fuzziness of the objects related to FIG.

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“…Akram and Habib [3] introduced q-rung PFGs. For a comprehensive study on PFSs and PFGs we may refer to the reader [6,15,16,22,41,42,43,45,46]. As discussed earlier, there was a lack in FGs, these were not helpful to provide detail about the impact of a vertex on an edge therefore, Dinesh [23] introduced the new notion in graph theory named fuzzy incidence graphs (FIGs).…”

Section: Introductionmentioning

confidence: 99%

Picture Fuzzy Incidence Graphs with Application

Nazeer

Rashid

2021

Punjab Univ. j. math.

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In this research article, we initiate the novel idea of picture fuzzy incidence graphs (PFIGs). We explain some innovative notions comprising of picture fuzzy cut-vertices, picture fuzzy bridges, picture fuzzy incidence cutpairs, and picture fuzzy incidence cut-vertices. Some rudimentary theorems and essential results are also examined in the PFIGs. Further, we determine the different concepts together with the order, size, and certain kinds of degrees in PFIG. A new type of PFIGs namely, complete picture fuzzy incidence graphs (CPFIGs) and complement of (PFIGs) are also furnished. A comparative analysis of PFIGs with fuzzy incidence graphs is also presented. Finally, an application of PFIGs in the control of illegal transportation of people from India to America is provided

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Neutrosophic Incidence Graphs With Application

Cited by 9 publications

References 10 publications

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

A Robust q-Rung Orthopair Fuzzy Information Aggregation Using Einstein Operations with Application to Sustainable Energy Planning Decision Management

Optimization in Business Trade by Using Fuzzy Incidence Graphs

Picture Fuzzy Incidence Graphs with Application

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