Modified methods to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems

Raina Ahuja; Meraj Ali Khan; Parul Tomar; Amit Kumar; S. S. Appadoo; Ibrahim Al-Dayel; Raina Ahuja; Meraj Ali Khan; Parul Tomar; Amit Kumar; S. S. Appadoo; Ibrahim Al-Dayel

doi:10.3934/math.2025421

AIMS Mathematics

2025, Volume 10, Issue 4: 9150-9170. doi: 10.3934/math.2025421

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Modified methods to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems

1.
Department of Mathematics, Thapar Institute of Engineering & Technology (Deemed to be University), Patiala, Punjab, India
2.
Department of Mathematics and Statistics, College of Science, Imam Mohammad Ibn Saud Islamic University, Riyadh, Saudi Arabia
3.
Department of Mathematics, Marwadi University, Rajkot, Gujrat, India
4.
Department of Supply Chain Management, Asper School of Business, University of Manitoba, Winnipeg, Canada

Received: 09 February 2025 Revised: 30 March 2025 Accepted: 14 April 2025 Published: 21 April 2025
MSC : 03E72, 94D05, 90B50

In a recently published paper, two methods were proposed to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems (those in which the rating value of each alternative over each criterion is represented by an interval-valued Fermatean fuzzy number). In this paper, some numerical examples are considered to show that these existing methods fail to find the correct ranking of the alternatives. Also, the reasons for the failure of these existing methods are pointed out. Furthermore, new methods are proposed to solve the interval-valued Fermatean fuzzy multi-criteria decision-making problems by modifying existing methods. Moreover, the proposed modified methods are illustrated with the help of numerical examples. Finally, the ranking of the alternatives of the two existing real-life interval-valued Fermatean fuzzy multi-criteria decision-making problems is obtained by the proposed methods.
- interval-valued Fermatean fuzzy sets,
- score function,
- distance measure,
- multi-criteria decision-making problems
Citation: Raina Ahuja, Meraj Ali Khan, Parul Tomar, Amit Kumar, S. S. Appadoo, Ibrahim Al-Dayel. Modified methods to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems[J]. AIMS Mathematics, 2025, 10(4): 9150-9170. doi: 10.3934/math.2025421

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Abstract

In a recently published paper, two methods were proposed to solve interval-valued Fermatean fuzzy multi-criteria decision-making problems (those in which the rating value of each alternative over each criterion is represented by an interval-valued Fermatean fuzzy number). In this paper, some numerical examples are considered to show that these existing methods fail to find the correct ranking of the alternatives. Also, the reasons for the failure of these existing methods are pointed out. Furthermore, new methods are proposed to solve the interval-valued Fermatean fuzzy multi-criteria decision-making problems by modifying existing methods. Moreover, the proposed modified methods are illustrated with the help of numerical examples. Finally, the ranking of the alternatives of the two existing real-life interval-valued Fermatean fuzzy multi-criteria decision-making problems is obtained by the proposed methods.

References

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