New applications of various distance techniques to multi-criteria decision-making challenges for ranking vague sets

Murugan Palanikumar; Nasreen Kausar; Shams Forruque Ahmed; Seyyed Ahmad Edalatpanah; Ebru Ozbilge; Alper Bulut; Murugan Palanikumar; Nasreen Kausar; Shams Forruque Ahmed; Seyyed Ahmad Edalatpanah; Ebru Ozbilge; Alper Bulut

doi:10.3934/math.2023577

AIMS Mathematics

2023, Volume 8, Issue 5: 11397-11424. doi: 10.3934/math.2023577

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New applications of various distance techniques to multi-criteria decision-making challenges for ranking vague sets

1.
Department of Mathematics, Saveetha School of Engineering, Saveetha Institute of Medical and Technical Sciences, Chennai 602105, India
2.
Department of Mathematics, Faculty of Arts and Science, Yildiz Technical University, Esenler 34220, Istanbul, Turkey
3.
Science and Math Program, Asian University for Women, Chattogram, Bangladesh
4.
Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran
5.
American University of the Middle East, Department of Mathematics & Statistics, Egaila 54200, Kuwait

Received: 04 January 2023 Revised: 20 February 2023 Accepted: 23 February 2023 Published: 13 March 2023
MSC : 03B52, 06D72, 90B50

Using the Fermatean vague normal set (FVNS), problems requiring multiple attribute decision making (MADM) have been resolved in this article. This article focuses on the log Fermatean vague normal weighted averaging (log FVNWA), logarithmic Fermatean vague normal weighted geometric (log FVNWG), log generalized Fermatean vague normal weighted averaging (log GFVNWA) and log generalized Fermatean vague normal weighted geometric (log GFVNWG) operators. Described the scoring function, accuracy function and operational laws of the log FVNS. The Euclidean and Humming distance are extended with numerical examples. The features of the log FVNS based on the algebraic operations, including idempotency, boundedness, commutativity and monotonicity are also examined. A field of applied engineering called agricultural robotics has been compared to computer science and machine tool technology. Five distinct agricultural robotics including autonomous mobile robots, articulated robots, humanoid robots, cobot robots, and hybrid robots are randomly chosen. Findings can be compared to established criteria to determine which robotics are the most successful. The results of the models are expressed as a natural number $ \alpha $. We contrast several existing with those that have been developed in order to show the effectiveness and accuracy of the models.
- vague set,
- Fermatean vague set,
- aggregating operators,
- Hamming distance
Citation: Murugan Palanikumar, Nasreen Kausar, Shams Forruque Ahmed, Seyyed Ahmad Edalatpanah, Ebru Ozbilge, Alper Bulut. New applications of various distance techniques to multi-criteria decision-making challenges for ranking vague sets[J]. AIMS Mathematics, 2023, 8(5): 11397-11424. doi: 10.3934/math.2023577

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Abstract

Using the Fermatean vague normal set (FVNS), problems requiring multiple attribute decision making (MADM) have been resolved in this article. This article focuses on the log Fermatean vague normal weighted averaging (log FVNWA), logarithmic Fermatean vague normal weighted geometric (log FVNWG), log generalized Fermatean vague normal weighted averaging (log GFVNWA) and log generalized Fermatean vague normal weighted geometric (log GFVNWG) operators. Described the scoring function, accuracy function and operational laws of the log FVNS. The Euclidean and Humming distance are extended with numerical examples. The features of the log FVNS based on the algebraic operations, including idempotency, boundedness, commutativity and monotonicity are also examined. A field of applied engineering called agricultural robotics has been compared to computer science and machine tool technology. Five distinct agricultural robotics including autonomous mobile robots, articulated robots, humanoid robots, cobot robots, and hybrid robots are randomly chosen. Findings can be compared to established criteria to determine which robotics are the most successful. The results of the models are expressed as a natural number $ \alpha $. We contrast several existing with those that have been developed in order to show the effectiveness and accuracy of the models.

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