Multi Criteria Decision Making Using Linguistic Fermatean Neutrosophic Number

E. Madhavan Pillai¹, S. Vijayan², R. Sundareswaran³, Said Broumi^4,*

¹Department of Mechanical Engineering, Loyala College of Engineering, India

²Department of Mechanical Engineering, Sri Sivasubramaniya Nadar College of Engineering, India

³Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, India

⁴Laboratory of Information Processing, Faculty of Science Ben M’Sik, University of Hassan II, Casablanca, Morocco &     STIE team, Regional Center for the Professions of Education and Training, Casablanca- Settat, Morocco

Emails: drmadhavanpillai.e@licet.ac.in;vijayans@ssn.edu.in; sundareswaranr@ssn.edu.in; s.broumi@flbenmsik.ma

Abstract

The article aims to introduce the Linguistic Fermatean Neutrosophic set (LFNS) which is an important mathematical tool that helps to solve decision-making problems. LFNS is a generalization of the Linguistic Fermatean Fuzzy set (LFFS), by adding the truth, falsity and indeterminacy membership degrees to denote the uncertain information. Score and Accuracy functions are introduced to distinguish any two or more linguistic Pythagorean Neutrosophic Numbers. Weighted averaging and geometric aggregation operators with respect to linguistic Pythagorean neutrosophic weighted average and geometric, ordered weighted average are proposed. OEE (Overall Equipment Effectiveness) is the industry standard for measuring manufacturing productivity. It defines the percentage of manufacturing time that is productive. A 100% OEE score means that you are creating only high-quality products as soon as possible, with no downtime. By measuring OEE and the underlying losses, you will gain critical insights on how to systematically optimize your manufacturing process. OEE is the single most effective measure for detecting losses, assessing progress, and improving manufacturing equipment productivity (i.e., reducing waste). To adopt OEE practices in manufacturing industries, we must first understand, measure, and enhance OEE. The purpose of this research is to better understand OEE practices and their crucial aspects. The Human Arena, Engineering, Management, and Social elements are assessed, with sub-factors aggregated by similarity and analyzed using a LFNN. This method helps to comprehend the impact of each factor and ranks the group based on their influence in implementing the OEE practices effectively in an organization. The Engineering aspects and the Management aspects contribute a major role in the success of OEE. In this study, the assessment of numerous components and sub-factors involving determining the influence factor leading to OEE is translated into a Multi-Attribute Group Decision Making (MAGDM) problem and illustrated in the last section utilizing LFNN.

Keywords: Fermatean Neutrosophic Set; Multi-Attribute Group Decision Making; Overall Equipment Effectiveness