Power Aggregation Operators Based on t-Norm and t-Conorm under the Complex Intuitionistic Fuzzy Soft Settings and Their Application in Multi-Attribute Decision Making

Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative information is not always symmetric because the alternatives do not have complete information, so asymmetric information is often involved. In this analysis, we use the massive dominant and more consistent principle of power aggregation operators (PAOs) based on general t-norm and t-conorm, which manage awkward and inconsistent data in real-world dilemmas such as medical diagnosis, pattern recognition, cleaner production evaluation in gold mines, the analysis of the cancer risk factor, etc. The principle of averaging, geometric, Einstein, and Hamacher aggregation operators are specific cases of generalized PAOs. We combine the principle of complex intuitionistic fuzzy soft (CIFS) information with PAOs to initiate CIFS power averaging (CIFSPA), CIFS weighted power averaging (CIFSWPA), CIFS ordered weighted power averaging (CIFSOWPA), CIFS power geometric (CIFSPG), CIFS weighted power geometric (CIFSWPG), and CIFS ordered weighted power geometric (CIFSOWPG), and their flexible laws are elaborated. Certain specific cases (such as averaging, Einstein, and Hamacher operators) of the explored operators are also illustrated with the help of different t-norm and t-conorm operators. A MADM process is presented under the developed operators based on the CIFS environment. Finally, to investigate the supremacy of the demonstrated works, we employed a sensitivity analysis and geometrical expressions of the initiated operators with numerous prevailing works to verify the efficiency of the proposed works. This manuscript shows how to make decisions when there is asymmetric information about enterprises

Topological Data Analysis of m-Polar Spherical Fuzzy Information with LAM and SIR Models

The concept of m-polar spherical fuzzy sets (mPSFS) is a combination of m-polar fuzzy sets (mPFS) and spherical fuzzy sets (SFS). An mPSFS is an optimal strategy for addressing multipolarity and fuzziness in terms of ordered triples of positive membership grades (PMGs), negative membership grades (NMGs), and neutral grades (NGs). In this study, the innovative concept of m-polar spherical fuzzy topology (mPSF-topology) is proposed for data analysis and information aggregation. We look into the characteristics and results of mPSF-topology with the help of several examples. Topological structures on mPSFSs help with both the development of new artificial intelligence (AI) tools for different domain strategies and the study of different kinds of uncertainty in everyday life problems. These strategies make it possible to recognise and look into a situation early on, which helps professionals to reduce certain risks. In order to address various group decision-making issues in the m-polar spherical fuzzy domain, one suggestion has been to apply an extended linear assignment model (LAM) along with the SIR method known as superiority and inferiority ranking methodology in order to analyze road accident issues and dispute resolution. In addition, we examine the symmetry of optimal decision and perform a comparative study between the research carried out using the suggested methodology and several existing methods

Spherical Linear Diophantine Fuzzy Soft Rough Sets with Multi-Criteria Decision Making

Modeling uncertainties with spherical linear Diophantine fuzzy sets (SLDFSs) is a robust approach towards engineering, information management, medicine, multi-criteria decision-making (MCDM) applications. The existing concepts of neutrosophic sets (NSs), picture fuzzy sets (PFSs), and spherical fuzzy sets (SFSs) are strong models for MCDM. Nevertheless, these models have certain limitations for three indexes, satisfaction (membership), dissatisfaction (non-membership), refusal/abstain (indeterminacy) grades. A SLDFS with the use of reference parameters becomes an advanced approach to deal with uncertainties in MCDM and to remove strict limitations of above grades. In this approach the decision makers (DMs) have the freedom for the selection of above three indexes in [0,1]. The addition of reference parameters with three index/grades is a more effective approach to analyze DMs opinion. We discuss the concept of spherical linear Diophantine fuzzy numbers (SLDFNs) and certain properties of SLDFSs and SLDFNs. These concepts are illustrated by examples and graphical representation. Some score functions for comparison of LDFNs are developed. We introduce the novel concepts of spherical linear Diophantine fuzzy soft rough set (SLDFSRS) and spherical linear Diophantine fuzzy soft approximation space. The proposed model of SLDFSRS is a robust hybrid model of SLDFS, soft set, and rough set. We develop new algorithms for MCDM of suitable clean energy technology. We use the concepts of score functions, reduct, and core for the optimal decision. A brief comparative analysis of the proposed approach with some existing techniques is established to indicate the validity, flexibility, and superiority of the suggested MCDM approach