Mathematics and Computational Sciences

Parametric distance measure for trapezoidal intuitionistic fuzzy numbers and application in Multi-criteria group decision-making

Document Type : Original Article

Authors

Roohollah Abbasi Shureshjani 1
Gholam Hassan Shirdel 2
Madineh Farnam 3
Majid Darehmiraki 4

1 Department of Management, Humanities College, Hazrat-e Masoumeh University, Qom, Iran

2 Department of Mathematic, Faculty of Basic Sciences, University of Qom, Qom, Iran. g.h.shirdel@qom.ac.ir

3 Department of Electrical Engineering, Shohadaye Hoveizeh Campus of Technology, Shahid Chamran University of Ahvaz, Dasht-e Azadegan, Khuzestan, Iran. m.farnam@scu.ac.ir

4 Department of Mathematics, Behbahan Khatam Alanbia University of Technology, Behbahan, Khouzestan, Iran. darehmiraki@bkatu.ac.ir

https://doi.org/10.30511/mcs.2024.2044055.1247
Abstract
It is important to have an intuitionistic fuzzy set that allows each set element to have a membership value, a non-membership value, and a hesitancy value. This is because each element of the set can possess all three values. We will focus on one type of continuous intuitionistic fuzzy number, called trapezoidal intuitionistic fuzzy numbers, because they are more flexible in representing information about membership and non-membership functions and are continuous. This research aims to introduce a parametric ranking and distance measure to compare and obtain the distinction value between intuitionistic trapezoidal fuzzy numbers. Parametric measures offer more flexibility than deterministic measurement tools in modeling real-world problems by considering a suitable variety of responses based on different levels of parameters. After presenting the structure and effective indicators of the proposed tool, we have detailed its features and basic principles. Moreover, based on this measure, a hybrid process is designed for multi-criteria group decision-making (MCGDM) problems with trapezoidal intuitionistic fuzzy data. A numerical example is also examined to elucidate the implementation process of this integrated methodology. Additionally, comparative analysis with some related methods confirms the adequate performance of the new parametric measure in combined methods with similar subjects.

Keywords

Intuitionistic fuzzy set
Trapezoidal intuitionistic fuzzy number
Distance measure
Ranking
Multi-criteria group decision-making

Subjects

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Mathematics and Computational Sciences
Volume 5, Issue 4
Autumn 2024
Pages 61-84

  • Receive Date 22 October 2024
  • Revise Date 05 December 2024
  • Accept Date 07 December 2024

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