A New Method for Ranking Interval-valued Intuitionistic Trapezoidal Fuzzy Sets(IVITrFS)

S.N. Murty  Kodukulla; V.  Sireesha

doi:10.6180/jase.202506_28(6).0019

A New Method for Ranking Interval-valued Intuitionistic Trapezoidal Fuzzy Sets(IVITrFS)

S.N. Murty KodukullaThis email address is being protected from spambots. You need JavaScript enabled to view it. and V. Sireesha

Department of Mathematics, GITAM (Deemed to be University), Visakhapatnam, India

Received: June 30, 2024
Accepted: August 10, 2024
Publication Date: September 25, 2024

Copyright The Author(s). This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY 4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are cited.

Download Citation: ||https://doi.org/10.6180/jase.202506_28(6).0019

An Interval-valued intuitionistic trapezoidal fuzzy set (IVITrFS) is a powerful tool for modelling uncertainty. The ranking of IVITrFS plays a vital role in fuzzy set theory to compare and analyze the given information. An IVITrFS is a special type of Intuitionistic Fuzzy Set (IFS) and interval-valued intuitionistic fuzzy set (IVIFS) with a consecutive domain of real numbers. The existing ranking methods are good at ranking, but there are some cases in which the existing methods fails to rank effectively, and hence there is a need for a new ranking method. With this objective, the proposed ranking method is derived in this study. In this paper, we proposed a new method for ranking IVITrFS from a geometric point of view by defining the improved score function using the concept of centroids. The comparative results shows that the proposed method is innate and effective, very useful to computational Intelligence, decision-making, predictive system analysis, and performance analysis.

Keywords: Rankin of fuzzy sets; interval-valued intuitionistic trapezoidal fuzzy sets(IVITrFS); improved score function

[1] L. A. Zadeh, (1965) “Information and control" Fuzzy sets 8(3): 338–353.
[2] K. T. Atanassov and K. T. Atanassov. Intuitionistic fuzzy sets. Springer, 1999. DOI: 10.1007/978-3-7908-1870-3_1.
[3] L. A. Zadeh, (1965) “Fuzzy sets" Information and control 8(3): 338–353. DOI: 10.1016/S0019-9958(65) 90241-X.
[4] H. Bustince and P. Burillo, (1996) “Vague sets are intuitionistic fuzzy sets" Fuzzy sets and systems 79(3): 403–405. DOI: 10.1016/0165-0114(95)00154-9.
[5] W.-L. Gau and D. J. Buehrer, (1993) “Vague sets" IEEE transactions on systems, man, and cybernetics 23(2): 610–614. DOI: 10.1109/21.229476.
[6] K. T. Atanassov and K. T. Atanassov. Interval valued intuitionistic fuzzy sets. Springer, 1999.
[7] D. J. Dubois. Fuzzy sets and systems: theory and applications. 144. Academic press, 1980.
[8] M.-H. Shu, C.-H. Cheng, and J.-R. Chang, (2006) “Using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly" Microelectronics Reliability 46(12): 2139–2148. DOI: 10.1016/j.microrel.2006.01.007.
[9] D.-F. Li, (2008) “A note on “using intuitionistic fuzzy sets for fault-tree analysis on printed circuit board assembly”" Microelectronics Reliability 48(10): 1741. DOI: 10.1016/j.microrel.2008.07.059.
[10] J. Wang, (2008) “Overview on fuzzy multi-criteria decision-making approach" Control and decision 23(6): 601–606.
[11] S.-P. Wan, (2011) “Multi-attribute decision making method based on interval-valued intuitionistic trapezoidal fuzzy number" Control and Decision 26(6):
[12] J. Wu and Y. Liu, (2013) “An approach for multiple attribute group decision making problems with intervalvalued intuitionistic trapezoidal fuzzy numbers" Computers & Industrial Engineering 66(2): 311–324. DOI: 10.1016/j.cie.2013.07.001.
[13] N. Konwar, A. Esi, and P. Debnath, (2019) “New fixed point theorems via contraction mappings in complete intuitionistic fuzzy normed linear space" New Mathematics and Natural Computation 15(01): 65–83. DOI: 10.1142/S1793005719500042.
[14] S. MurtyKodukulla, V. Sireesha, and V. Anusha, (2022) “Distance Measure Approaches to Rank IntervalValued Trapezoidal Intuitionistic Fuzzy Sets" Mathematical Statistician and Engineering Applications 71(4): 4335–4353. DOI: 10.17762/msea.v71i4.1020.
[15] N. Konwar and P. Debnath, (2017) “Continuity and Banach contraction principle in intuitionistic fuzzy nnormed linear spaces" Journal of Intelligent & Fuzzy Systems 33(4): 2363–2373. DOI: 10.3233/JIFS-17500.
[16] P. Debnath, (2012) “Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces" Computers & Mathematics with Applications 63(3): 708–715. DOI: 10.1016/j.camwa.2011.11.034.
[17] C. Mallika and V. Sireesha, (2023) “An interval-valued trapezoidal intuitionistic fuzzy TOPSIS approach for decision-making problems" SN Computer Science 4(4): 327. DOI: 10.1007/s42979-023-02488-4.
[18] S. Veeramachaneni and H. Kandikonda, (2016) “An ELECTRE Approach for Multicriteria Interval-Valued Intuitionistic Trapezoidal Fuzzy Group Decision Making Problems" Advances in Fuzzy systems 2016(1): 1956303. DOI: 10.1155/2016/1956303.
[19] W. Jianqiang and Z. Zhong, (2009) “Aggregation operators on intuitionistic trapezoidal fuzzy number and its application to multi-criteria decision making problems" Journal of Systems Engineering and Electronics 20(2): 321–326.