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This paper aims to support decision-makers improve their ability to accurately capture and represent their judgment in a wide range of situations. To do this, we propose a new type of fuzzy set called a p,q-cubic quasi-rung orthopair fuzzy set (p,q-CQOFS). The p,q-CQOFS allows for a more flexible and detailed expression of incomplete information through the use of an additional parameter. The paper describes the concept of p,q-CQOFS and its relationship to other types of fuzzy sets, introduces score and accuracy functions for p,q-CQOFS and analyzes some of its mathematical properties, defines the Hamming distance measure between two p,q-CQOFSs and examines some of its important properties, investigates the basic operations of p,q-CQOFSs and extends these laws to aggregation operators, and introduces weighted averaging and geometric aggregation operators for combining p,q-cubic quasi-rung orthopair fuzzy data.

In this paper, we define the new concepts of a triangular neutrosophic cubic fuzzy number (TNCFN), the basic operational laws of TNCFNs, and the score function of TNCFNs. Then, we develop a triangular neutrosophic cubic fuzzy weighted arithmetic averaging (TNCFWAA) operator and a triangular neutrosophic cubic fuzzy weighted geometric averaging (TNCFWGA) operator to aggregate triangular neutrosophic cubic fuzzy number (TNCFN) information and investigate their properties. Furthermore, a multiple attribute decision-making method based on the triangular neutrosophic cubic fuzzy weighted arithmetic averaging (TNCFWAA) operator and triangular neutrosophic cubic fuzzy weighted geometric averaging (TNCFWGA) operator and the score function of triangular neutrosophic cubic fuzzy number (TNCFN) is established under a triangular neutrosophic cubic fuzzy number (TNCFN) environment. Finally, an illustrative example of investment alternatives is given to demonstrate the application and effectiveness of the developed approach.

In this paper, we define linguistic hesitant fuzzy sets. We introduce cubic linguistic fuzzy sets and their operational laws. We propose a cubic linguistic hesitant fuzzy sets and their operational laws. We describe aggregation operators for cubic linguistic hesitant fuzzy sets which extended the generalized cubic linguistic hesitant fuzzy averaging (geometric) operator, generalized cubic linguistic hesitant fuzzy weighted averaging (GLCHFWA) operator, generalized cubic linguistic hesitant fuzzy weighted geometric (GCHFWG) operator, generalized cubic linguistic hesitant fuzzy ordered weighted average (GCLHFOWA) operator, generalized cubic linguistic hesitant fuzzy ordered weighted geometric (GCLHFOWG) operator, generalized cubic linguistic hesitant fuzzy hybrid averaging (GCLHFHA) operator and generalized cubic linguistic hesitant fuzzy hybrid geometric (GCLHFHG) operator. Moreover, we relate these aggregation operators to develop an approach to multiple-attribute group decision-making with cubic linguistic-hesitant fuzzy information. Finally, the overall ranking of an alternative is obtained. This example is presented to illustrate the feasibility and effectiveness of the proposed approach.

This article presents a novel concept of complex cubic picture fuzzy sets (CCPFS) and introduces one more new idea of complex interval-valued picture fuzzy sets (CIVPFS) as foundational framework of CCPFS. The proposed CCPFS combines CIVPFS and complex picture fuzzy sets (CPFS), where CPFS extends the complex intuitionistic fuzzy set by incorporating a neutral membership degree. This unique model offers an expanded range of values using degrees of membership, neutral membership, and non-membership, within the unit disk of a complex plane. Additionally, we introduce two more new ideas of internal complex cubic picture fuzzy sets (ICCPFS) and external complex cubic picture fuzzy sets (ECCPFS) to further enhance the versatility of the approach. To facilitate practical applications, complement, score, and accuracy functions are developed and defined for CCPFS. Moreover, three types of averaging aggregation operators based on complex cubic picture fuzzy sets are introduced, including complex cubic picture fuzzy weighted geometric (CCPFWG) operators, complex cubic picture fuzzy ordered weighted geometric (CCPFOWG) operator, and complex cubic picture fuzzy hybrid weighted geometric (CCPFHWG) operator. The CCPFHWG operator generalizes both CCPFWG and CCPFOWG operators, providing a comprehensive framework for aggregating complex cubic picture fuzzy data. To demonstrate the practicality of the proposed approach, a multi-criteria decision-making (MCDM) problem is presented, showcasing its effectiveness in addressing today's complex decision structures. The utilization of complex cubic picture fuzzy sets and the corresponding aggregation operators in MCDM highlights their applicability and relevance in tackling real-world complexities.

The picture fuzzy set, briefly as; PFS and its extensions, spherical fuzzy set (SFS), and T-spherical fuzzy set (T-SFS) are all effective tools to express uncertain and incomplete cognitive information with membership, neutral membership, and non-membership degrees. The cubical fuzzy set (CFS) introduced in this paper, carries out uncertain and imprecise information smartly in exercising decision-making than PFS and SFS. Cubical fuzzy set (CFS)is an extension of the picture fuzzy set and spherical fuzzy set. In CFS, the membership grades satisfy the condition 0≤μ3(x)+η3x+ν3x≤1instead of 0≤μ2(x)+η2x+ν2x≤1, which is the condition of a spherical fuzzy set (SFS). In the course of this article, we first devise some operations on CFS, discuss the basic properties, and propose the cubical fuzzy arithmetic and geometric aggregation operators. We introduce the concept of cubical fuzzy weighted average (CFWA) operator, cubical fuzzy ordered weighted average (CFOWA) operator, and cubical fuzzy hybrid average (CFHA) operator. In the second section, we develop cubical fuzzy weighted geometric (CFWG) operator, cubical fuzzy ordered weighted geometric (CFOWG) operator, and cubical fuzzy hybrid geometric (CFHG) operator. We define the distance measure between two CFSs and study some of its properties. In the last section, the developed operators are utilized to devise approaches for solving multiple attribute decision-making problems (MADM) in a cubical fuzzy environment. A practical example of enterprise resource planning (ERP) system selection is given to verify the developed approach and to demonstrate the practicality and effectiveness of the proposed operators.

Pythagorean hesitant fuzzy set plays a significant role to deal with vagueness and hesitation which can be precisely and perfectly defined in terms of the opinions of decision-makers. In this paper, we proposed a broad new extension of classical VIKOR method for multi-attribute decision-making (MADM) problems with Pythagorean hesitant fuzzy information. Basically VIKOR method of compromise ranking determines a compromise solution, which provides a maximum “group utility” for the “majority” and a minimum of an “individual regret” for the “opponent” and is an effective tool to solve MADM problems. To do this first we give some basic definitions and analogous concepts, and the basic steps of classical VIKOR method are introduced. Different situations of attribute weight information are considered. If attribute weights are partly known a linear programming model is set up based on the idea that reasonable weights should make the relative closeness of each alternative evaluation value to the Pythagorean hesitant fuzzy positive ideal solution as large as possible. If attribute weights are unknown completely, an optimization model is set up based on the maximum deviation method. We describe a MADM problem and present the steps of VIKOR method under the Pythagorean hesitant fuzzy environment. Finally, a numerical example is presented to illustrate feasibility and practical advantages of the proposed method.

Pythagorean hesitant fuzzy set (PHFS) is a powerful tool to deal with uncertainty and vagueness. Therefore, based on Pythagorean hesitant fuzzy information in this paper we develop hybrid aggregation operators for Pythagorean hesitant fuzzy information namely, Pythagorean hesitant fuzzy hybrid weighted averaging operator, Pythagorean hesitant fuzzy hybrid weighted geometric operator. These developed operators can weigh both the argument and their ordered positions. Additionally, some numerical examples are given to illustrate the developed operators. Moreover we develop a multi-attribute group decision making approach based on the proposed operators. Finally, we give a numerical example to show the effectiveness and flexibility of the proposed method.

The cubic uncertain fuzzy linguistic variable can easily express the fuzzy information, and the power average (PA) operator is a useful tool which provides more versatility in the information aggregation procedure. In this paper, we will combine the PA operator and Einstein operations to cubic uncertain linguistic environment and propose some new PA operators. Firstly, the definition and some basic operations of cubic uncertain linguistic number, power aggregation (PA) operator and Einstein operations are introduced. Then, we propose cubic uncertain linguistic fuzzy powered Einstein averaging operator, cubic uncertain linguistic fuzzy powered Einstein weighted (CULFPEWA) operator, cubic uncertain linguistic fuzzy Einstein geometric operator and cubic uncertain linguistic fuzzy Einstein weighted geometric (CULFPEWG) operator and discuss some properties of these in detail. Furthermore, we develop the decision-making methods for multi-attribute group decision-making problems with cubic uncertain linguistic information and give the detail decision steps. At last, an illustrate example is given to show the process of decision making and the effectiveness of the proposed method.

Pythagorean fuzzy set is a useful tool to deal with the fuzziness and vagueness. Many aggregation operators have been proposed by many researchers based on Pythagorean fuzzy sets. But the current methods are under the assumption that the decision makers and the attributes are at the same priority level. However, in real group decision-making problems the attribute and decision makers may have different priority level. Therefore, in this paper, we develop multi-attribute group decision-making based on Pythagorean fuzzy sets where there exists a prioritization relationship over the attributes and decision makers. First, we develop Pythagorean fuzzy prioritized weighted average operator and Pythagorean fuzzy prioritized weighted geometric operator. Then we study some of its desirable properties such as idempotency, boundary and monotonicity in detail. Moreover, we propose a multi-attribute group decision-making approach based on the developed operators under Pythagorean fuzzy environment. Finally, a numerical example is provided to illustrate the practicality of the proposed approach.

The objective of the present work is divided into two folds. Firstly, interval-valued Pythagorean fuzzy Einstein hybrid weighted averaging aggregation operator has been introduced along with their several properties, namely idempotency, boundedness and monotonicity. Secondly, we apply the proposed operator to deal with multi-attribute group decision-making problem under Pythagorean fuzzy information. For this, we construct an algorithm for multi-attribute group decision making. At the last, we construct a numerical example for multi-attribute group decision making. The main advantage of using the proposed operator is that this operator provides more accurate and precise results is compared to the existing methods.

In this paper, we construct an extended version of the TOPSIS method by using cubic information, and provide a numerical application to verify and demonstrate the practicality of the method. A new extension of the gray relation analysis (GRA) method is introduced by using cubic information. We also propose the cubic fuzzy multi-attribute group decision-making model, and the relation between the cubic TOPSIS method and the cubic gray relation analysis (CGRA) method is introduced. Finally, the proposed method is used for selection in sol–gel synthesis of titanium carbide nanopowders. We analyzed the proposed method by using a numerical application to sol–gel synthesis of titanium carbide nanopowders.

Cubic Pythagorean fuzzy (CPF) set (CPFS) is a hybrid set that can hold much more information and can be used to describe both an interval-valued Pythagorean fuzzy set (IVPFS) and Pythagorean fuzzy set (PFS) at the same time to handle data uncertainties. Based on it, the present study is classified into three phases. The first phase is to modify the existing operational laws and aggregation operators (AOs) in the article presented by Abbas et al. (Journal of Intelligent & Fuzzy Systems, vol. 37, no. 1, pp. 1529–1544, (2019)). The main objective of improved operational laws is to eliminate the flows and ambiguities in existing AOs. Secondly, based on these laws, various AOs to aggregate the information are acquired along with their requisite properties and relations. Lastly, an approach for interpreting the multi-attribute decision-making (MCDM) problem based on the stated operators is given and illustrated with an example. Some of the existing models are used to perform a comprehensive comparative analysis to demonstrate their impacts.

Trapezoidal cubic fuzzy numbers (TzCFNs) are an extraordinary cubic fuzzy set on a real number set. TzCFNs are useful for dealing with well-known quantities in decision data and decision making problems themselves. This paper is about multi-attribute group decision making problems in which the attribute values are stated with TzCFNs, which are solved by developing a new decision method based on power average operators of TzCFNs. The new operation laws for TzCFNs are given. Hereby, the power average operator of real numbers is extended to four kinds of power average operators of TzCFNs, involving the power average operator of TzCFNs, the weighted power average operator of TzCFNs, the power ordered weighted average operator of TzCFNs, and the power hybrid average operator of TzCFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TzCFNs. Applying the hybrid average operator of TzCFNs, the specific general evaluation standards of alternatives are then combined into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method.

Pythagorean fuzzy set is one of the successful extensions of the intuitionistic fuzzy set for handling uncertainties in information. Under this environment, in this paper, we introduce the notion of Pythagorean fuzzy Einstein hybrid averaging (PFEHA) aggregation operator along with some of its properties, namely idempotency, boundedness, and monotonicity. PFEHA aggregation operator is the generalization of Pythagorean fuzzy Einstein weighted averaging aggregation operator and Pythagorean fuzzy Einstein ordered weighted averaging aggregation operator. The operator proposed in this paper provides more accurate and precise results as compared to the existing operators. Therefore, this method plays a vital role in real-world problems. Finally, we applied the proposed operator and method to multiple-attribute group decision making.

The aim of this paper is to define some new operation laws for the trapezoidal linguistic cubic fuzzy number and Hamming distance. Furthermore, we define and use the trapezoidal linguistic cubic fuzzy TOPSIS method to solve the multi criteria decision making (MCDM) method. The new ranking method for trapezoidal linguistic cubic fuzzy numbers (TrLCFNs) are used to rank the alternatives. Finally, an illustrative example is given to verify and prove the practicality and effectiveness of the proposed method.

In the investigations presented here, an efficient computing approach is applied to solve Human Immunodeficiency Virus (HIV) infection spread. This approach involves CD4+ T-cells by feed-forward artificial neural networks (FF-ANNs) trained with particle swarm optimization (PSO) and interior point method (IPM), i.e., FF-ANN-PSO-IPM. In the proposed solver FF-ANN-PSO-IPM, the FF-ANN models of differential equations are used to develop the fitness functions for an infection model of T-cells. The training of networks through minimization problem are proficiently conducted by integrated heuristic capability of PSO-IPM. The reliability, stability and exactness of the proposed FF-ANN-PSO-IPM are established through comparison with outcomes of standard numerical procedure with Adams method for both single and multiple autonomous trials with precision of order 4 to 8 decimal places of accuracy. The statistical measures are effectively used to validate the outcomes of the proposed FF-ANN-PSO-IPM. [ABSTRACT FROM AUTHOR]