Group Decision Making in Conditions of Uncertainty using Fermat’s Weak Fuzzy Graphs and Beal’s Weak Fuzzy Graphs

Authors

  • Nishad T. M. Bharathidasan University Tiruchirappalli Tamilnadu
  • B Mohamed Harif Bharathidasan University Tiruchirappalli Tamilnadu
  • A Prasanna Department of Mathematics, Jamal Mohamed College (Autonomous),(Affiliated to Bharathidasan University), Tiruchirappalli,-620020, Tamilnadu, India

DOI:

https://doi.org/10.23755/rm.v43i0.854

Keywords:

Fuzzy Graph, Weak Fuzzy Graph, Fermat’s Fuzzy Graph, Fermat’s Weak Fuzzy Graphs, Beal’s Fuzzy Graph, Beal’s Weak Fuzzy Graphs.

Abstract

Decision making is a process of solving problems for choosing the best alternative. The best way to illustrate the alternatives and relation between them is a graph. Developing a fuzzy graph is the convenient way of illutration if there is uncertainty in alternatives or in their relation. In group decision making problems, according to a group of experts, the relation between alternatives involves measure of preference and non preference. Intuitionistic fuzzy graph has limitations to model such problems. In n- Pythagorean fuzzy graphs the hesitancy degree and other decision tools are restricted to second degree.To overcome the flaws of intuitionistic fuzzy graphs and n- Pythagorean fuzzy graphs, we introduced Fermat’s Fuzzy Graphs in 2022. In this  paper the decision tools are generalized for Fermat’s Fuzzy Graphs. A practical example of selection of investement scheme is illustrated. Finally, Beal’s Fuzzy graphs is developed as generalization of Fermat’s Fuzzy Graphs.

Author Biographies

  • Nishad T. M., Bharathidasan University Tiruchirappalli Tamilnadu

    Research Scholar

    Department of Mathematics

    Rajah Serfoji Govt College Thanjavur

    Bharathidasan University

    Tiruchirappalli

    Tamilnady

  • B Mohamed Harif, Bharathidasan University Tiruchirappalli Tamilnadu

    Research Supervisor

    Department of Mathematics

    Rajah Serfoji Govt College Thanjavur

    Bharathidasan University

    Tiruchirappalli

    Tamilnady

References

L.A.Zadeh Fuzzy sets,Inform.and Control 8 (1965), 338-353.

A.Rosenfeld,Fuzzy graphs,in:L.A.Zadeh,K.S.Fu,K.Tanaka,M.Shimura Fuzzy sets and Their Applications to Cognitive and Decision Process, Academic Press,1975,pp.77-95.

A.Prasanna and T.M.Nishad,Some properties of weak fuzzy graphs,Math. Comput.Sci.11(3) (2021), 3594-3601.

Ju Hongmei and Wang Lianhua, Interval-valued fuzzy sub semigroups and subgroups associated by interval-valued fuzzy graphs,Global congress on Intelligent Systems (2009), 484-487.

A.A.Talebi and H. Rashmanlou, Isomorphism on interval-valued fuzzy graphs,Annals of Fuzzy Mathematics and Informatics 6(1) (2013), 47-58.

Muhammed Akram, et al., Specific types of Pythagorean Fuzzy Graphs and Applications to Decision-Making, Math. Comput. Appl. 23(3) (2018),42.

B.Mohamed Harif and T.M Nishad ,Interval valued Weak Fuzzy Graphs and Fermat’s Weak Fuzzy Graphs,Advances and Applications in Mathematical Sciences,Volume 22,Issue 2, Dec.2022.

R.Daniel Mauldin (1997). A Generalization of Fermat's Last Theorem: The Beal Conjecture and Prize Problem (PDF). Notices of the AMS. 44 (11): 1436–1439.

Downloads

Published

2022-12-30

Issue

Vol. 43 (2022)

Section

Volume 43-2022

License

This journal provides immediate open access to its content on the principle that making research freely available to the public supports a greater global exchange of knowledge. The journal is committed to real and immediate open access for academic work. All of the journal articles are free to access immediately from the date of publication. There are no charge for readers to download articles and reviews for their own scholarly use. Benefits of open access for authors, include:

  • Free access for all users worldwide
  • Increased visibility and readership
  • Rapid publication
  • No spatial constraints
  • Authors can share their research papers on their personal web-pages (i.e. ResearchGate, etc.)

Ratio Mathematica publishes open access articles under the terms of the Creative Commons Attribution (CC BY) License. The Creative Commons Attribution License (CC-BY) allows users to copy, distribute and transmit an article, adapt the article and make commercial use of the article. The CC BY license permits commercial and non-commercial re-use of an open access article, as long as the author is properly attributed. Copyright on any research article published by Ratio Mathematica is retained by the author(s). Authors grant Ratio Mathematica a license to publish the article and identify itself as the original publisher. Authors also grant any third party the right to use the article freely as long as its original authors, citation details and publisher are identified. 
For further information visit: https://creativecommons.org/licenses/by/3.0/. The following logo will appear in any paper that will be published from the volume number 31/2016 onwards.