Received: 14 March 2023 | Revised: 25 May 2023 | Accepted: 14 June 2023 | Published online: 2 July 2023 RESEARCH ARTICLE Refined Fuzzy Soft Sets: Properties, Set-Theoretic Operations and Axiomatic Results Muhammad Saeed 1, * , Irfan Saif Ud Din 1 , Imtiaz Tariq 1 and Harish Garg 2 1 Department of Mathematics, University of Management and Technology, Pakistan 2 School of Mathematics, Thapar Institute of Engineering & Technology (Deemed University), India Abstract: This article discusses the results of an investigation into refined fuzzy soft sets, a novel variant of traditional fuzzy sets. Refined fuzzy soft sets provide a versatile method of data analysis, inspired by the need to deal with uncertainty and ambiguity in real-world data. This research expands on prior work in fuzzy set theory by investigating the nature and characteristics of refined fuzzy soft sets. They are useful in decision-making, pattern recognition, image processing, and control theory because of their capacity to deal with uncertainty, ambiguity, and the inclusion of expert information. This study analyzes these fuzzy set models and compares them to others in the field to reveal their advantages and disadvantages. The practical uses of enhanced fuzzy soft sets are also examined, along with possible future research strategies on this exciting new topic. Keywords: fuzzy set, soft set, fuzzy soft set, refined fuzzy soft set 1. Introduction Fuzzy set theory is a mathematical paradigm for dealing with uncertainty and ambiguity in data and knowledge representation. Zadeh (1965) initially proposed the idea of a fuzzy set as a method of generalizing the standard definition of a set, which presupposes that a member either belongs to or does not belong to a set. A membership function that assigns a degree of membership between [0,1] represents a fuzzy set, on the other hand, which permits partial membership of an element in a set. Since its inception, fuzzy set theory has been used in a variety of domains, including control systems, decision-making, pattern recognition, image processing, and many more. Intuitionistic fuzzy sets, type-2 fuzzy sets, and fuzzy rough sets are all examples of more complicated models based on fuzzy set theory. Fuzzy set theory's adaptability and utility have led to its broad usage in a variety of real-world applications investigated by some authors (De et al., 2000; Feng et al., 2010; Garg & Rani, 2021; Karnik & Mendel, 2001). Molodtsov (1999) was the first person to propose the idea of soft sets as a wholly novel mathematical instrument for resolving issues involving apprehensions about the future. According to Molodtsov’s description from 1999, a soft set is a parametric family of subsets of the universal set, in which each member is regarded as a collection of approximation elements of the soft set. Voskoglou (2023) suggested a parametric decision-making approach employing soft sets and gray numerals, which extends the soft set method. Kharal (2010) noted the distance and similarity measures for soft sets. Xiao (2018) proposes a hybrid approach to using FSSs in decision-making that combines fuzzy preference relations analysis based on belief entropy with the Dempster-Shafer (D-S) evidential concept. Yang et al. (2013) presented the idea of multi-FSSs as well as the ways in which they can be used in decision-making. Chen et al. (2005) presented the parameterization reduction of soft sets as well as the applications. Utilizing Sanchez's technique, Jafar et al. (2020) investigated the use of soft set interactions and soft matrices in medical treatment. Numerous researchers are drawn to soft set theory due to its various implications for disciplines such as function smoothness, decision-making, statistical inference, data processing, measurement concept, predicting, and operations investigations (Dalkilic, 2021; Molodtsov, 2001; Peng, 2019; Xiao et al., 2009; Zou & Xiao, 2008). The real world is fraught with inaccuracy, ambiguity, and uncertainty. In our everyday lives, we primarily interact with ambiguous notions rather than precise ones. Interacting with ambiguities is a major issue in many disciplines, including economics, medicine, social science, atmospheric science, and engineering. Numerous scholars are now engaged in feature vagueness in latest decades. Several classical speculations are well renowned and efficaciously model uncertainty, including fuzzy set concept (Zadeh, 1965), probability theory, vague set model (Gau & Buehrer, 1993), rough set theory (Pawlak et al., 1995), intuitionistic fuzzy set (Alaca et al., 2006), and interval-valued fuzzy set (Gorzalczany, 1987). The concept of fuzzy soft set (FSS) theory was initiated by Maji et al. (2001). Peng and Garg (2018) presented three methods to address the interval-valued fuzzy soft decision-making issue using weighted distance-based estimation, *Corresponding author: Muhammad Saeed, Department of Mathematics, University of Management and Technology, Pakistan. Email: muhammad. saeed@umt.edu.pk Journal of Computational and Cognitive Engineering 2024, Vol. 3(1) 24–33 DOI: 10.47852/bonviewJCCE3202847 © The Author(s) 2023. Published by BON VIEW PUBLISHING PTE. LTD. This is an open access article under the CC BY License (https://creativecommons.org/ licenses/by/4.0/). 24