Abstract
Fermatean fuzzy linguistic (FFL) set theory provides an efficient tool for modeling a higher level of uncertain and imprecise information, which cannot be represented using intuitionistic fuzzy linguistic (IFL)/Pythagorean fuzzy linguistic (PFL) sets. On the other hand, the linguistic scale function (LSF) is the better way to consider the semantics of the linguistic terms during the evaluation process. It is worth noting that the existing operational laws and aggregation operators (AOs) for Fermatean fuzzy linguistic numbers (FFLNs) are not valid in many situations, which can generate errors in real-life applications. The present study aims to define new robust operational laws and AOs under Fermatean fuzzy linguistic environment. To do so, first, we define some new modified operational laws for FFLNs based on LSF and prove some important mathematical properties of them. Next, the work defines several new AOs, namely, the FFL-weighted averaging (FFLWA) operator, the FFL-weighted geometric (FFLWG) operator, the FFL-ordered weighted averaging (FFLOWA) operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator under Fermatean fuzzy linguistic environment. Several properties of these AOs are investigated in detail. Further, based on the proposed AOs, a new decision-making approach with Fermatean fuzzy linguistic information is developed to solve group decision-making problems with multiple attributes. Finally, to illustrate the effectiveness of the present approach, a real-life supplier selection problem is presented where the evaluation information of the alternatives is given in terms of FFLNs. Compared to the existing methods, the salient features of the developed approach are (1) it can solve decision-making problems with qualitative information data using FFLNs; (2) It can consider the attitudinal character of the decision-makers during the solution process; (3) It has a solid ability to distinguish the optimal alternative.
Highlights
The intuitionistic fuzzy set (IFS) theory was introduced by Atanassov [1] in 1983 to accommodate uncertain and vague concepts more precisely in complex real-life situations
To fulfill the aim of the proposed study, firstly, the work defines some new modified operational laws for Fermatean fuzzy linguistic numbers (FFLNs) based on linguistic scale function (LSF), which overcome the drawbacks of the existing operational laws
Operator, the FFL-ordered weighted geometric (FFLOWG) operator, the FFL-hybrid averaging (FFLHA) operator and the FFL-hybrid geometric (FFLHG) operator are defined for aggregating Fermatean fuzzy linguistic information
Summary
The intuitionistic fuzzy set (IFS) theory was introduced by Atanassov [1] in 1983 to accommodate uncertain and vague concepts more precisely in complex real-life situations. An IFS assigns each element a degree of membership (DM) and a degree of non-membership (DNM), whose sum is always less than or equal to one It has become an important and widely studied generalization of fuzzy sets [2]. Several information measures have been proposed under an intuitionistic fuzzy environment, including distance measure [15,16,17,18], similarity measure [19,20,21,22], entropy measure [23,24,25,26], divergence measure [27,28,29], and inaccuracy measure [30] and applied them in different application areas including pattern recognition, medical diagnosis, and decision making
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
