The aims of this study is to define a cubic fuzzy set based logarithmic decision-making strategy for dealing with uncertainty. Firstly, we illustrate some logarithmic operations for cubic numbers (CNs). The cubic set implements a more pragmatic technique to communicate the uncertainties in the data to cope with decision-making difficulties as the observation of the set. In fuzzy decision making situations, cubic aggregation operators are extremely important. Many aggregation operations based on the algebraic t-norm and t-conorm have been developed to cope with aggregate uncertainty expressed in the form of cubic sets. Logarithmic operational guidelines are factors that help to aggregate unclear and inaccurate data. We define a series of logarithmic averaging and geometric aggregation operators. Finally, applying cubic fuzzy information, a creative algorithm technique for analyzing multi-attribute group decision making (MAGDM) problems was proposed. We compare the suggested aggregation operators to existing methods to prove their superiority and validity, and we find that our proposed method is more effective and reliable as a result of the comparison and sensitivity analysis.

The fractional orthotriple fuzzy sets (FOFSs) are a generalized fuzzy set model that is more accurate, practical, and realistic. It is a more advanced version of the present fuzzy set models that can be used to identify false data in real-world scenarios. Compared to the picture fuzzy set and Spherical fuzzy set, the fractional orthotriple fuzzy set (FOFS) is a powerful tool. Additionally, aggregation operators are effective mathematical tools for condensing a set of finite values into one value that assist us in decision making (DM) challenges. Due to the generality of FOFS and the benefits of aggregation operators, we established two new aggregation operators in this article using the Frank t-norm and conorm operation, which we have renamed the fractional orthotriple fuzzy Choquet-Frank averaging (FOFCFA) and fractional orthotriple fuzzy Choquet-Frank geometric (FOFCFG) operators. A few of these aggregation operators' characteristics are also discussed. To demonstrate the efficacy of the introduced work, the multi-attribute decision making (MADM) algorithm is discussed along with applications. To demonstrate the validity and value of the suggested work, a comparison of the proposed work has also been provided.

The main influence of this analysis is to derive two different types of aggregation operators under the consideration of algebraic t-norm and t-conorm and Einstein t-norm and t-conorm for CIF set theory. Because these operators are very effective for evaluating the collection of information into a singleton preference. For this, first, we discover the Algebraic and Einstein operational laws for CIF sets. Then, we aim to discover the theory of CCIFWA, CCIFOWA, CCIFWG, CCIFOWG operators and their valuable properties "idempotency, monotonicity and boundedness" and results. Furthermore, we also derive the theory of CCIFEWA, CCIFEOWA, CCIFEWG, CCIFEOWG operators and their valuable properties "idempotency, monotonicity, and boundedness" and results. Some special cases of the derived work are also described in detail. Finally, we illustrate a MADM procedure under the consideration of derived operators to enhance the worth of the presented information. Finally, we compare the presented operators with various existing operators with the help of various suitable examples for showing the reliability and stability of the derived approaches.

The degree of credibility of the fuzzy assessment value demonstrates its significance and necessity in the fuzzy decision making problem. The fuzzy assessment values should be closely related to their credibility measures in order to increase the credibility levels and degrees of fuzzy assessment values. This will increase the abundance and the credibility of the assessment information. As a new extension of the intuitionistic fuzzy concept, this study suggests the idea of an intuitionistic fuzzy credibility number (IFCN). So, based on Dombi norms, we proposed some new operational laws for intuitionistic fuzzy credibility numbers. Different intuitionistic fuzzy credibility aggregation operators are defined using Dombi t-norm and t-conorm operations. i.e., intuitionistic fuzzy credibility Dombi weighted averaging (IFCDWA), intuitionistic fuzzy credibility Dombi ordered weighted averaging (IFCDOWA), intuitionistic fuzzy credibility Dombi hybrid weighted averaging (IFCDHWA) operators. Next, we defined multiple criteria group decisions (MCGDM) approach. To ensure that their results are reliable and applicable, we also gave an example of railway train selection and discussed comparative result analysis.

The main objective of this article is to introduce the idea of a q-rung orthopair hesitant fuzzy rough set (q-ROHFRS) as a robust fusion of the q-rung orthopair fuzzy set, hesitant fuzzy set, and rough set. A q-ROHFRS is a novel approach to uncertainty modelling in multi-criteria decision making (MCDM). Various key properties of q-ROHFRS and some elementary operations on q-ROHFRSs are proposed. Based on the q-ROHFRS operational laws, novel q-rung orthopair hesitant fuzzy rough weighted averaging operators have been developed. Some interesting properties of the proposed operators are also demonstrated. Furthermore, by using the proposed aggregation operator, we develop a modified VIKOR method in the context of q-ROHFRS. The outcome of this research is to rank and select the best alternative with the help of the modified VIKOR method based on aggregation operators for q-ROHFRS. A decision-making algorithm based on aggregation operators and extended VIKOR methodology has been developed to deal with the uncertainty and incompleteness of real-world decision-making. Finally, a numerical illustration of agriculture farming is considered to demonstrate the applicability of the proposed methodology. Also, a comparative study is presented to demonstrate the validity and effectiveness of the proposed approach. The results show that the proposed decision-making methodology is feasible, applicable, and effective to address uncertainty in decision making problems.

The goal of this research is to develop many aggregation operators for aggregating various complex T-Spherical fuzzy sets (CT-SFSs). Existing fuzzy set theory and its extensions, which are a subset of real numbers, handle the uncertainties in the data, but they may lose some useful information and so affect the decision results. Complex Spherical fuzzy sets handle two-dimensional information in a single set by covering uncertainty with degrees whose ranges are extended from the real subset to the complex subset with unit disk. Thus, motivated by this concept, we developed certain CT-SFS operation laws and then proposed a series of novel averaging and geometric power aggregation operators. The properties of some of these operators are investigated. A multi-criteria group decision-making approach is also developed using these operators. The method's utility is demonstrated with an example of how to choose the best choices, which is then tested by comparing the results to those of other approaches.