Prioritized weighted aggregation operators under complex pythagorean fuzzy information

Complex Diophantine interval-valued Pythagorean normal set for decision-making processes

A novel method for solving the multiple-attribute decision-making problem is proposed using the complex Diophantine interval-valued Pythagorean normal set (CDIVPNS). This study aims to discuss aggregating operations and how they are interpreted. We discuss the concept of CDIVPN weighted averaging (CDIVPNWA), CDIVPN weighted geometric (CDIVPNWG), generalized CDIVPN weighted averaging (CGDIVPNWA) and generalized CGDIVPN weighted geometric (CGDIVPNWG). This study aimed to examine several aggregation operators using complex Diophantine interval-valued Pythagorean normal sets. We calculated the weighted average and geometric distance based on an aggregating model. We demonstrate that complex Diophantine interval-valued Pythagorean normal sets satisfy algebraic structures such as associative, distributive, idempotent, bounded, commutative and monotonic properties. In this study, we discuss the mathematical properties of the score and accuracy values. We provide an example of how enhanced score and accuracy values are used in the real world. Machine tool technology and computer science play essential roles in robots. To evaluate robotic systems, four factors must be considered such as tasks, precision, speed and completion of the work. Consequently, it is evident that the models are significantly influenced by the natural number ∇. To further demonstrate the effectiveness of the suggested approach, flowchart based multi-criteria decision-making is provided and applied to a numerical example. Additionally, a comparative study has been carried out to demonstrate the better results that the proposed approach provides when compared to current approaches.

Archimedean Aggregation Operators Based on Complex Pythagorean Fuzzy Sets Using Confidence Levels and Their Application in Decision Making

The diagnosed complex Pythagorean fuzzy (CPF) set is a more valuable and dominant tool than the Pythagorean and intuitionistic fuzzy sets to describe awkward and unreliable information more effectively. Further, Archimedean t-norm and t-conorm have a significant influence to depict the relation among aggregated values. To take advantage of the CPF set and Archimedean t-norm and t-conorm, and assume the relation among Archimedean norms and algebraic, Einstein, Hamacher, and frank norms at the same time, in this analysis, first, we proposed the fundamental Archimedean operational laws. Second, based on these laws, we developed confidence CPF Archimedean-weighted averaging (CCPFSAWA), confidence CPF Archimedean-ordered weighted averaging (CCPFSAOWA), confidence CPF Archimedean-weighted geometric (CCPFSAWG), confidence CPF Archimedean-ordered weighted geometric (CCPFSAOWG) operators and implemented their valuable results and properties. We know that Archimedean t-norm and t-conorm are the general form of the all-aggregation operators, so by using different values of t-norm and t-conorm, we explored the confidence CPF-weighted averaging (CCPFWA), confidence CPF-ordered weighted averaging (CCPFOWA), confidence CPF Einstein-weighted averaging (CCPFEWA), confidence CPF Einstein-ordered weighted averaging (CCPFEOWA), confidence CPF Hamacher-weighted averaging (CCPFHWA), confidence CPF Hamacher-ordered weighted averaging (CCPFHOWA), confidence CPF frank-weighted averaging (CCPFFWA), confidence CPF frank-ordered weighted averaging (CCPFFOWA), confidence CPF-weighted geometric (CCPFWG), confidence CPF-ordered weighted geometric (CCPFOWG), confidence CPF Einstein-weighted geometric (CCPFEWG), confidence CPF Einstein-ordered weighted geometric (CCPFEOWG), confidence CPF Hamacher-weighted geometric (CCPFHWG), confidence CPF Hamacher-ordered weighted geometric (CCPFHOWG), confidence CPF frank-weighted geometric (CCPFFWG), and confidence CPF frank-ordered weighted geometric (CCPFFOWG) operators. Then, we developed a multi-attribute decision-making (MADM) method based on the proposed operators. Finally, many examples are used to do comparative analysis among proposed and existing methods to show the validation of the new approaches.

Analysis of Hamming and Hausdorff 3D distance measures for complex pythagorean fuzzy sets and their applications in pattern recognition and medical diagnosis

Similarity measures are very effective and meaningful tool used for evaluating the closeness between any two attributes which are very important and valuable to manage awkward and complex information in real-life problems. Therefore, for better handing of fuzzy information in real life, Ullah et al. (Complex Intell Syst 6(1): 15–27, 2020) recently introduced the concept of complex Pythagorean fuzzy set (CPyFS) and also described valuable and dominant measures, called various types of distance measures (DisMs) based on CPyFSs. The theory of CPyFS is the essential modification of Pythagorean fuzzy set to handle awkward and complicated in real-life problems. Keeping the advantages of the CPyFS, in this paper, we first construct an example to illustrate that a DisM proposed by Ullah et al. does not satisfy the axiomatic definition of complex Pythagorean fuzzy DisM. Then, combining the 3D Hamming distance with the Hausdorff distance, we propose a new DisM for CPyFSs, which is proved to satisfy the axiomatic definition of complex Pythagorean fuzzy DisM. Moreover, similarly to some DisMs for intuitionistic fuzzy sets, we present some other new complex Pythagorean fuzzy DisMs. Finally, we apply our proposed DisMs to a building material recognition problem and a medical diagnosis problem to illustrate the effectiveness of our DisMs. Finally, we aim to compare the proposed work with some existing measures is to enhance the worth of the derived measures.

Generalized Cubic Pythagorean Fuzzy Aggregation Operators and their Application to Multi-attribute Decision-Making Problems

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.

Complex Pythagorean uncertain linguistic group decision-making model based on Heronian mean aggregation operator considering uncertainty, interaction and interrelationship

To effectively solve the mixed problem of considering the uncertainty of individuals and groups, the interaction between membership degree (MD) and non-membership (ND), and the interrelationship between attribute variables in complicated multiple attribute group decision-making (MAGDM) problems, in this paper, a concept of complex Pythagorean uncertain linguistic (CPUL) set (CPULS) is introduced, the interaction operational laws (IOLs) of CPUL variables (CPULVs) are defined. The CPUL interaction weighted averaging and geometric operators are presented. A new concept of CPUL rough number (CPULRN) is further constructed. The CPUL rough interaction weighted averaging and geometric aggregation operators (AOs) are extended. The ordering rules of any two CPULRNs are defined. The CPUL rough interaction Heronian mean (HM) (CPULRIHM) operator and its weighted form are advanced, related properties and special cases are explored. An MAGDM model based on CPUL rough interaction weighted HM (CPULRIWHM) operator is built. Lastly, we conduct a case study of location selection problem for logistics town project to show the applicability of the proposed methodology. The sensitivity and methods comparison are analyzed to verify the effectively and superiority.

An approach to decision making with interval-valued complex Pythagorean fuzzy model for evaluating personal risk of mental patients

It is prominent important for managers to assess the personal risk of mental patients. The evaluation process refers to numerous indexes, and the evaluation values are general portrayed by uncertainty information. In order to conveniently model the complicated uncertainty information in realistic decision making, interval-valued complex Pythagorean fuzzy set is proposed. Firstly, with the aid of Einstein t-norm and t-conorm, four fundamental operations for interval-valued complex Pythagorean fuzzy number (IVCPFN) are constructed along with some operational properties. Subsequently, according to these proposed operations, the weighted average and weighted geometric forms of aggregation operators are initiated for fusing IVCPFNs, and their anticipated properties are also examined. In addition, a multiple attribute decision making issue is examined under the framework of IVCPFNs when employing the novel suggested operators. Ultimately, an example regarding the assessment on personal risk of mental patients is provided to reveal the practicability of the designed approach, and the attractiveness of our results is further found through comparing with other extant approaches.The main novelty of the coined approach is that it not only can preserve the original assessment information adequately by utilizing the IVCPFNs, but also can aggregate IVCPFNs effectively.

Approach-oriented and avoidance-oriented measures under complex Pythagorean fuzzy information and an area-based model to multiple criteria decision-aiding systems

The purpose of this paper is to evolve a novel area-based Pythagorean fuzzy decision model via an approach-oriented measure and an avoidance-oriented measure in support of multiple criteria decision analysis involving intricate uncertainty of Pythagorean fuzziness. Pythagorean membership grades embedded in a Pythagorean fuzzy set is featured by tensible functions of membership, non-membership, indeterminacy, strength, and direction, which delivers flexibility and adaptability in manipulating higher-order uncertainties. However, a well-defined ordered structure is never popular in real-life issues, seldom seen in Pythagorean fuzzy circumstances. Consider that point operators can make a systematic allocation of the indeterminacy composition contained in Pythagorean fuzzy information. This paper exploits the codomains of the point operations (i.e., the quantities that express the extents of point operators) to launch new measurements of approach orientation and avoidance orientation for performance ratings. This paper employs such measurements to develop an area-based performance index and an area-based comprehensive index for conducting a decision analysis. The applications and comparative analyses of the advanced area-based approach to some decision-making problems concerning sustainable recycling partner selection, company investment decisions, stock investment decisions, and working capital financing decisions give support to methodological advantages and practical effectiveness.

Decision support model with Pythagorean fuzzy preference relations and its application in financial early warnings

Pythagorean fuzzy sets (PFSs) retain the advantages of intuitionistic fuzzy sets (IFSs), while PFSs portray 1.57 times more information than IFSs. In addition, Pythagorean fuzzy preference relations (PFPRs), as a generalization of intuitionistic fuzzy preference relations (IFPRs), are more flexible and applicable. The objective of this paper is to propose a novel decision support model for solving group decision-making problems in a Pythagorean fuzzy environment. First, we define the concepts of ordered consistency and multiplicative consistency for PFPRs. Then, aiming at the group decision-making problem of multiple PFPRs, a consistency improving model is constructed to improve the consistency of group preference relations. Later, a consensus reaching model is developed to reach the degree of group consensus. Furthermore, a decision support model with PFPRs is established to derive the normalized weights and output the final result. Holding these features, this paper builds a decision support model with PFPRs based on multiplicative consistency and consensus. Finally, the described method is validated by an example of financial risk management, and it is concluded that the solvency of a company is an important indicator that affects the financial early warning system.