A novel decision-making approach for the selection of best deep learning techniques under logarithmic fractional fuzzy set information

Naseer Ullah; Muhammad Azam; Muhammad Abbas; Wajid Hussain; Asnake Birhanu; Khaled A Gepreel

doi:10.1038/s41598-025-03389-7

A novel decision-making approach for the selection of best deep learning techniques under logarithmic fractional fuzzy set information

Sci Rep. 2025 Jul 1;15(1):20598. doi: 10.1038/s41598-025-03389-7.

Authors

Naseer Ullah¹, Muhammad Azam², Muhammad Abbas³, Wajid Hussain⁴, Asnake Birhanu⁵, Khaled A Gepreel⁶

Affiliations

¹ School of Mathematics, Statistics and Mechanics, Beijing University of Technology, Beijing, 100124, China.
² Key Laboratory of Urban Security and Disaster Engineering of the Ministry of Education, Beijing University of Technology, Beijing, 100124, China.
³ Department of Mathematics, University of Sargodha, Sargodha, 40100, Pakistan.
⁴ Faculty of Material and Manufacturing, Beijing University of Technology, Beijing, 100124, China.
⁵ Department of Mathematics, College of Science, Hawassa University, Hawassa, Ethiopia. asnakeb@hu.edu.et.
⁶ Department of Mathematics and Statistics, College of Science, Taif University, Taif, 21944, Saudi Arabia.

Abstract

Deep learning (DL), which is a branch of machine learning (ML) and artificial intelligence (AI), has become a fundamental element of contemporary technological advancements. To facilitate such processes, data representation is crucial, often transitioning from crisp sets to generalized forms like fuzzy sets (FS), introduced by Zadeh. This paper extends the concept by defining a special class of FS known as Logarithmic Fractional Fuzzy Sets (Log-FFS). Moreover, a set of aggregation operators (AoPs) is formulated using logarithmic operational principles, such as the Logarithmic Fractional Fuzzy Weighted Average (Log-FFWA) and its variations, with their core properties thoroughly detailed. The study also incorporates known methodologies such as the Complex Proportional Assessment (COPRAS) and an extended TOPSIS method under Log-FFS information. Finally, the proposed approaches are confidently applied to selecting deep learning techniques, demonstrating their capability to yield optimal results.

Keywords: COPRAS method; Deep learning; Fuzzy credibility set; Fuzzy set; Rough set.