Trapezoidal-valued fermatean fuzzy numbers (TpVFFNs) are essential for handling daily decision-making issues in the engineering and management fields. Accumulation processes on the set of TpVFFN are used to address decision-making problems described in this environment as necessary. The primary goal of this paper is to provide the concept of Dombi t-norm $\left(D_{tn}\right)$- and Dombi t-conorm $\left(D_{tcn}\right)$-based accumulation operators on the class of TpVFFN, emphasizing how they behave symmetrically in aggregation processes to maintain consistency and fairness. To use s to illustrate mathematical circumstances, we first create a trapezoidal-valued fermatean fuzzy Dombi’s weighted geometric operator, hexagonal hybird geometric operator, fermatean fuzzy order weighted geometric operator. Second, we use a multi-attribute group decision-making (MAGDM) approach to compute the recommended accumulation operators. Finally, we demonstrate the potential practical application of the proposed decision-making problem related to the pink cab.

In applications requiring uncertain, imprecise, and multi-dimensional data, where traditional distance measures frequently fall short of capturing the full complexity of interactions among elements, a distance measure for complex intuitionistic fuzzy sets (DMCIFSs) becomes essential. Although DMCIFSs have been developed, most of them do not account for the hesitation degree, which is crucial for capturing ambiguity and uncertainty in human reasoning. As extensions of the normalized Hamming and Euclidean distance measures, this work proposes two new measures namely the Hesitance DMCIFSs (HDMCIFSs) and the Euclidean Hesitance DMCIFSs (EHDMCIFSs). These newly proposed measures provide a more comprehensive framework for modeling uncertainty by explicitly incorporating the hesitancy component. In addition to the proposed measures, several fundamental procedures and theoretical results are also presented. Furthermore, a novel decision-making method utilizing these distance measures is developed and applied to multi-criteria decision-making (MCDM) problems. The effectiveness of the proposed methods is demonstrated through a comparative study, highlighting their potential for improved sensitivity and accuracy in practical decision-making scenarios.

Multi-attribute decision-making (MADM) problems often involve uncertain, bipolar, and complex information that cannot be adequately represented by conventional fuzzy set models. To address this limitation, this study introduces the Circular Bipolar Complex Neutrosophic Fuzzy Set (CBCNFS) framework and develops two aggregation operators: the Circular Bipolar Complex Neutrosophic Fuzzy Frank Power Averaging (CBCNFFPA) operator and the Circular Bipolar Complex Neutrosophic Fuzzy Frank Power Geometric (CBCNFFPG) operator. The proposed operators enable the aggregation of multidimensional uncertain information and satisfy fundamental properties, including idempotency, boundedness, and monotonicity. Based on these operators, a score-function-based MADM algorithm is developed to evaluate and rank alternatives. A numerical example involving hypothetical electric vehicle charging stations illustrates the application of the proposed framework to information characterised by bipolarity, complex-valued representations, neutrosophic uncertainty, and circular structures. Sensitivity analyses are conducted to examine the effects of variations in the Frank parameter, criterion weights, and CBCNF evaluations on the resulting rankings. The results illustrate the applicability of the proposed aggregation operators and their responses to changes in the considered parameters and evaluation conditions. The proposed framework provides an integrated approach to representing and aggregating multidimensional uncertain information in MADM problems.

This paper introduces trapezoidal-valued Fermatean fuzzy (TpVFF) numbers based on the Aczel-Alsina (AA) t-norm and t-conorm operations. New operational laws, including addition, multiplication, and scalar multiplication, are defined. Based on these operations, several geometric aggregation operators, including weighted, ordered weighted, and hybrid operators, are developed, and their fundamental properties are established. A TOPSIS-based multi-criteria group decision-making method is proposed within the developed framework. An illustrative disaster relief allocation problem using the TpVFF-TOPSIS framework demonstrates the applicability of the proposed approach. Sensitivity and Monte Carlo analyses are conducted to examine variations in the decision results under changes in the AA parameter and criterion weights. The results indicate that the ranking is sensitive to changes in the AA parameter and criterion weights, although it remains unchanged in a substantial proportion of the tested scenarios.