The aim of this work is to put forward the concept of a novel decision support model for multi-criteria group decision making problems with multi-granular fractional orthotriple fuzzy 2-tuple linguistic (FOF2TL) information. The idea of fractional orthotriple fuzzy 2-tuple linguistic (2TL) model is put forward by integrating the advantages of fractional orthotriple fuzzy set and 2-tuple linguistic method. We define a transformation function to deal the consistency of multi-granular FOF2TL information. Secondly, the Archimedean coupla as well as the co-coupla are used to define operational laws for fractional orthotriple fuzzy 2-tuple linguistic numbers (FOF2TLNs). We take the relationship between attribute and experts, and defined fractional orthotriple fuzzy 2-tuple linguistic Banzhaf Choquet-Copula aggregation (FOF2TLBCCA) operators. Third, a method explains how to determine the fuzzy measure of expert and attribute sets. Next, the suggested operators are used to develop associated decision-making approaches. Finally, a numerical case is offered to demonstrate the concept's usefulness, along with pertinent comments; the merits of the suggested methodology are also evaluated by comparing it to several existing decision approaches.

The theory investigated in this analysis is substantially more suitable for evaluating the dilemmas in real life to manage complicated, risk-illustrating, and asymmetric information. The complex Pythagorean fuzzy set is expanded upon by the complex q-rung orthopair fuzzy set (Cq-ROFS). They stand out by having a qth power of the real part of the complex-valued membership degree and a qth power of the real part and imaginary part of the complex-valued non-membership degree that is equal to or less than 1. We define the comparison method for two complex q-rung orthopair fuzzy numbers as well as the score and accuracy functions (Cq-ROFNs). Some averaging and geometric aggregation operators are examined using the Cq-ROFSs operational rules. Additionally, their main characteristics have been fully illustrated. Based on the suggested operators, we give a novel approach to solve the multi-attribute group decision-making issues that arise in environmental contexts. Making the best choice when there are asymmetric types of information offered by different specialists is the major goal of this work. Finally, we used real data to choose an ideal extinguisher from a variety of options in order to show the effectiveness of our decision-making technique. The effectiveness of the experimental outcomes compared to earlier research efforts is then shown by comparing them to other methods.

The fractional orthotriple fuzzy set (FOFS) model is a recently created extension of fuzzy sets (FS) for coping with ambiguity in DM. The purpose of this study is to define new exponential and Einstein exponential operational (EO) laws for fractional orthotriple fuzzy sets and the aggregation procedures that accompany them. We present the operational laws for exponential and Einstein exponential FOFSs which have crisp numbers as base values and fractional orthotriple fuzzy numbers as exponents (weights). The proposed operations’ qualities and characteristics are then explored. Based on the defined operation laws regulations, various new FOFS aggregation operators, named as fractional orthotriple fuzzy weighted exponential averaging (FOFWEA), fractional orthotriple fuzzy ordered weighted exponential averaging (FOFOWEA), fractional orthotriple fuzzy hybrid weighted averaging (FOFHWEA), fractional orthotriple fuzzy Einstein weighted exponential averaging (FOFEWEA), fractional orthotriple fuzzy Einstein ordered weighted exponential averaging (FOFEOWEA), and fractional orthotriple fuzzy Einstein hybrid weighted exponential averaging (FOFEHWEA) operators are presented. A decision-making algorithm based on the newly defined aggregation operators is proposed and applied to a multicriteria group decision-making (MCGDM) problem related to bank security. Finally, we compare our proposed method with other existing methods.

In this research, we provide tools to overcome the information loss limitation resulting from the requirement to estimate the results in the discrete initial expression domain. Through the use of 2-tuples, which are made up of a linguistic term and a numerical value calculated between $[0.5,0.5)$, the linguistic information will be expressed. This model supports continuous representation of the linguistic data within its scope, permitting it to express any information counting received through an aggregation procedure. This study provides a novel approach to develop a linguistic multi-attribute group decision-making (MAGDM) approach with complex fractional orthotriple fuzzy 2-tuple linguistic (CFOF2TL) assessment details. Initially, the concept of a complex fractional orthotriple fuzzy 2-tuple linguistic set (CFO2TLS) is proposed to convey uncertain and fuzzy information. In the meantime, simple aggregation operators, such as CFOF2TL weighted average and geometric operators, are defined. In addition, the CFOF2TL Maclaurin’s symmetric mean (CFOF2TLMSM) operators and their weighted shapes are presented, and their attractive characteristics are also discussed. A new MAGDM approach is built using the developed aggregation operators to address managing economic crises under COVID-19 with the CFOF2TL information. As a result, the effectiveness and robustness of the developed method are accompanied by an empirical example, and a comparative study is carried out by contrasting it with previous approaches.

It was recently proposed to extend the spherical fuzzy set to spherical fuzzy credibility sets (SFCSs). In this paper, we define the concept of SFCSs. We then define new operational laws for SFCSs using Dombi operational laws. Various spherical fuzzy credibility aggregation operators such as spherical fuzzy credibility Dombi weighted averaging (SFCDWA), spherical fuzzy credibility Dombi ordered weighted averaging (SFCDOWA), spherical fuzzy credibility Dombi weighted geometric (SFCDWG), and spherical fuzzy credibility Dombi ordered weighted geometric (SFCDOWG) are defined. We also show the boundedness, monotonicity, and idempotency aspects of the suggested operators. We proposed the spherical fuzzy credibility entropy to find the unknown weight information of the attributes. Symmetry analysis is a useful and important tool in artificial intelligence that may be used in a variety of fields. To calculate the significant factor, we determine the multi-attribute decision-making (MADM) method using the suggested operators for SFCSs to increase the value of the assessed operators. To demonstrate the effectiveness and superiority of the suggested approach, we compare our findings to those of many other approaches.