Exploring the Foundations of Fuzzy Systems in Logic, Sets and Graphs

Authors

  • Badri Vishal Padamwar Department of Mathematics, ISBM University, Raipur, India

Keywords:

Fuzzy Logic, Fuzzy Set Theory, Fuzzy Graph Theory, Decision Making Systems, Intelligence Cycle, Applications, Fuzzy Systems, Trends, Overview

Abstract

This review article offers a comprehensive exploration of the intricate foundations of fuzzy systems, encompassing their integration into logic, sets, and graphs. Drawing insights from seminal works by Animesh Kumar Sharma, Lotfi A. Zadeh, and other notable researchers, the study aims to provide a nuanced understanding of the multifaceted landscape of fuzzy systems. The focal point is on trends in fuzzy graphs, applications of fuzzy logic and fuzzy set theory, and the conceptual framework of fuzzy graph theory. The review seeks to weave together diverse perspectives to shed light on the evolution and applications of these fundamental theories. The analysis begins with a critical examination of Sharma et al.'s work on trends in fuzzy graphs (2013), elucidating evolving patterns within fuzzy graph theory. Complementing this, Zadeh's foundational contributions to fuzzy logic (Zadeh, 2023) provide a historical context, offering a panoramic view of the development of fuzzy systems. The study seamlessly integrates recent advancements, such as the application of complex Dombi fuzzy graphs in decision-making problems (Butt et al., 2022) and the computation of domination sets in intuitionistic fuzzy graphs (Bozhenyuk et al., 2021). By incorporating a diverse array of references, ranging from foundational works to contemporary studies, this review aspires to encompass the breadth and depth of the fuzzy systems domain, offering a comprehensive synthesis of the foundational elements and modern developments in fuzzy logic, fuzzy set theory, and fuzzy graph theory.

References

Animesh Kumar Sharma, B.V.Padamwar, & C L Dewangan. (2013). Trends in Fuzzy Graphs. International Journal of Innovative Research in Science, Engineering and Technology, 2(9), 4636–4640.

Sharma, A. K. (2012). Application of Fuzzy Logic in Decision Making Systems. Abhinav Journal of Research in Science & Technology, 1(12), 1–6.

Sharma, A. K. (2013). Fuzzy Logic for Utilization in Intelligence Cycle and in Generation of Alternatives. Abhinav Journal of Reasearch in Science & Technology, 2(1), 1–4.

Sharma, A. K. (2019). Overview of Some Applications of Fuzzy Generated Systems. International Journal of Innovative Research in Technology, 6(6), 12–15. https://ijirt.org/master/publishedpaper/IJIRT148746_PAPER.pdf

Sharma, A. K. (2020a). A Brief Overview of Fuzzy Logic Theory. International Journal of Multidisciplinary Educational Research, 9(2(2)), 74–84.

http://s3-ap-southeast-1.amazonaws.com/ijmer/pdf/volume9/volume9-issue2(2)-2020.pdf

Sharma, A. K. (2020b). The Applicability of Concepts of Fuzzy Set Theory. International Journal of Research in Engineering, Science and Management, 3(1), 201–206.

https://www.ijresm.com/Vol.3_2020/Vol3_Iss1_January20/IJRESM_V3_I1_46.pdf

Zadeh, L. A. (2023). Fuzzy logic. In Granular, Fuzzy, and Soft Computing (pp. 19-49). New York, NY: Springer US.

Butt, E. M. A., Mahmood, W., Tawfiq, F. M., Xin, Q., &Shoaib, M. (2022). A Study of Complex Dombi Fuzzy Graph with Application in Decision Making Problems. IEEE Access, 10, 102064-102075.

Bozhenyuk, A., Belyakov, S., Knyazeva, M., &Rozenberg, I. (2021). On computing domination set in intuitionistic fuzzy graph. International Journal of Computational Intelligence Systems, 14(1), 617-624.

Abdul, M., Rao T, N., Rao, J. V., Emani, R. K. S., & Kumar D, S. (2021, October). Analytical study of various dominations on bipolar fuzzy graphs. In AIP Conference Proceedings (Vol. 2375, No. 1). AIP Publishing.

Xiao, W., Dey, A., & Son, L. H. (2020). A study on regular picture fuzzy graph with applications in communication networks. Journal of Intelligent & Fuzzy Systems, 39(3), 3633-3645.

Mordeson, J. N., Mathew, S., &Gayathri, G. (2023). Fuzzy Graph Theory: Applications to Global Problems (Vol. 424). Springer Nature.

Talebi, A. A., Kacprzyk, J., Rashmanlou, H., &Sadati, S. H. (2020). A New Concept of An Intuitionistic Fuzzy Graph with Applications. Journal of Multiple-Valued Logic & Soft Computing, 35.

Shahbazova, S. N., Sugeno, M., Kacprzyk, J., &Zadeh, L. (2020). Recent developments in fuzzy logic and fuzzy sets. Recent Developments in Fuzzy Logic and Fuzzy Sets, Berlin, Germany: Springer, 391.

Voskoglou, M. (2020). Fuzzy sets, fuzzy logic and their applications. Basel, Switzerland: MDPI-Multidisciplinary Digital Publishing Institute.

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Published

2023-12-28

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Section

Articles

How to Cite

Exploring the Foundations of Fuzzy Systems in Logic, Sets and Graphs. (2023). International Journal of Futuristic Innovation in Engineering, Science and Technology (IJFIEST), 2(3), 16-22. https://journal.inence.org/index.php/ijfiest/article/view/224

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