Multicriteria Decision Making using SR-Fuzzy Sets

Year : 2024 | Volume : 01 | Issue : 02 | Page : 12 20
    By

    Anita Kumari,

  • Beulah Rana,

  • Mayank Agari,

  • Umang,

  1. Assistant Professor, Department of Mathematics, D.S.B. Campus, Kumaun University Nainital, Uttarakhand, India
  2. Research Scholar, Department of Mathematics, D.S.B. Campus, Kumaun University Nainital, Uttarakhand, India
  3. Research Scholar, Department of Mathematics, D.S.B. Campus, Kumaun University Nainital, Uttarakhand, India
  4. Assistant professor, Department of Computer Science, D.S.B Campus, Kumaun University, Nainital, Uttarakhand, India

Abstract

In this study, we introduce and explore square-root fuzzy sets (SR-Fuzzy sets), a novel extension within the realm of fuzzy set theory. We begin by establishing a comparative analysis between SR-Fuzzy sets and two well-known fuzzy set models: Intuitionistic Fuzzy Sets (IFS) and Pythagorean Fuzzy Sets (PFS). This comparison highlights the unique characteristics and mathematical structure of SR-Fuzzy sets. A particular focus is placed on the complement operator, which plays a critical role in the logical framework and functional behavior of SR-Fuzzy sets. Additionally, we define a set of fundamental mathematical operations specific to SR-Fuzzy sets, laying the groundwork for further theoretical development. To facilitate practical applications, an accuracy function is formulated, along with a scoring function that enables effective ranking of SR-Fuzzy sets. We also investigate the use of Euclidean distance as a metric for measuring dissimilarity between two SR-Fuzzy sets. Building on these foundations, we propose a novel SR-Fuzzy Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) approach, tailored for addressing multiple-criteria decision-making (MCDM) problems. The robustness and applicability of the proposed methodology are illustrated through a comprehensive, real-world numerical example, thereby demonstrating its relevance, practicality, and potential advantages over existing methods.

Keywords: SR-Fuzzy sets, Euclidean distance, Multicriteria decision making, complement operator, fuzzy decision-making

[This article belongs to Recent Trends in Mathematics ]

How to cite this article:
Anita Kumari, Beulah Rana, Mayank Agari, Umang. Multicriteria Decision Making using SR-Fuzzy Sets. Recent Trends in Mathematics. 2025; 01(02):12-20.
How to cite this URL:
Anita Kumari, Beulah Rana, Mayank Agari, Umang. Multicriteria Decision Making using SR-Fuzzy Sets. Recent Trends in Mathematics. 2025; 01(02):12-20. Available from: https://journals.stmjournals.com/rtm/article=2025/view=223220


References

  1. Yager RR (2017) Generalized orthopair fuzzy sets. IEEE Trans Fuzzy Syst 25(5):1222–1230
  2. Yager RR (2014) Pythagorean membership grades in multicriteria decision making. IEEE Trans Fuzzy Syst 22:958–965
  3. Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593–611
  4. Ren P, Xu Z, Gou X (2016) Pythagorean fuzzy TODIM approach to multi-criteria decision making. Appl Soft Comput 42:246–259
  5. Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers, and decision making. Int J Intell Syst 28:436–452
  6. Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30:1133–1160
  7. Reformat MZ, Yager RR (2014) Suggesting recommendations using Pythagorean fuzzy sets illustrated using Netflix movie data. In: Laurent A, Strauss O, Bouchon-Meunier B, Yager RR (eds) Information processing and management of uncertainty in knowledge-based systems, Springer, Berlin, pp. 546–556
  8. Gou X, Xu Z, Ren P (2016) The Properties of Continuous Pythagorean Fuzzy Information. Int J Intell Syst 31:401–42
  9. Senapati T, Yager RR (2019). Fermatean Fuzzy sets. Journal of Ambient Intell and Humanized Comp 11: 663-674
  10. Shami T, Ibrahim H, Azzam A, Maghrabi A (2022) SR-Fuzzy sets and their weighted Aggregated operators in Application to Decision making. Hindawi Journal of Function Spaces. https://doi.org110.1155/2022/3653225
  11. Yager RR (2013) Pythagorean fuzzy subsets. Joint IFSA World Congress and NAFIPS Annual Meeting pp. 57-61
  12. Garg H, Nancy J (2018) Linguistic single-valued neutrosophic prioritized aggregation operators and their applications to multiple-attribute group decision-making. J Ambient Intell Human Comput 9:1975–1997
  13. Golshannavaz S, Khezri R, Esmaeeli M, Siano P (2018) A two-stage robust-intelligent controller design for efficient LFC based on Kharitonov theorem and fuzzy logic. J Ambient Intell Human Comput 9:1445–1454
  14. Zhang X (2016) A novel approach based on similarity measure for Pythagorean fuzzy multiple criteria group decision making. Int J Intell Syst 31:593-611
  15. Zhang C, Wang C, Zhang Z, Tian D (2018) A novel technique for multiple attribute group decision making in interval-valued hesitant fuzzy environments with incomplete weight information. J Ambient Intell Human Comput. https://doi.org/10.1007/s1265 2-018-0912-2
Regular Issue Subscription Review Article
Volume 01
Issue 02
Received 24/04/2025
Accepted 21/07/2025
Published 05/08/2025
Publication Time 103 Days
193

Login


My IP

PlumX Metrics