The power Bonferroni mean (PBM) operator can relieve the influence of unreasonable aggregation values and also capture the interrelationship among the input arguments, which is an important generalization of power average operator and Bonferroni mean operator, and Pythagorean fuzzy set is an effective mathematical method to handle imprecise and uncertain information. In this paper, we extend PBM operator to integrate Pythagorean fuzzy numbers (PFNs) based on the interaction operational laws of PFNs, and propose Pythagorean fuzzy interaction PBM operator and weighted Pythagorean fuzzy interaction PBM operator. These new Pythagorean fuzzy interaction PBM operators can capture the interactions between the membership and nonmembership function of PFNs and retain the main merits of the PBM operator. Then, we analyze some desirable properties and particular cases of the presented operators. Further, a new multiple attribute decision making method based on the proposed method has been presented. Finally, a numerical example concerning the evaluation of online payment service providers is provided to illustrate the validity and merits of the new method by comparing it with the existing methods.

https://onlinelibrary.wiley.com/doi/epdf/10.1002/int.22204

Pythagorean fuzzy interaction power Bonferroni mean aggregation operators in multiple attribute decision making

Multiattribute group decision making based on neutrality aggregation operators of q-rung orthopair fuzzy sets

Reasonable and effective assessment of express service quality can help express company discover its own shortcomings and overcome them, which is crucial significant to enhance its service quality. When considering the decision assessment of express company, the key issue that emerge powerful ambiguity. Pythagorean fuzzy set as an efficient math tool can capture the indeterminacy successfully. The major focus of this manuscript is to explore various interactive Hamacher power aggregation operators for Pythagorean fuzzy numbers. Firstly, we defined novel interactive Hamacher operation, on this basis we presented some Pythagorean fuzzy interactive Hamacher power aggregation operators such as Pythagorean fuzzy interactive Hamacher power average, weighted average (PFIHPWA), ordered weighted average, Pythagorean fuzzy interactive Hamacher power geometric, weighted geometric (PFIHPWG) and ordered geometric operators,respectively. Meanwhile, we verified their general properties and specific cases as well. The salient feature of proposed operators is that they can not only reduce the impact of negative data and consider the interactions between membership and nonmembership degrees, but also provide more general results through a parameter. Secondly, we defined a Pythagorean fuzzy entropy measure, and then establish a method to determine the attribute weights. Further, based on the conceived PFIHPWA and PFIHPWG operators we explored a novel approach to manage multiple attribute decision making problems. At last, the proposed techniques are carried out in a real application concerning on the assessment of express service quality to display the applicability and effectiveness, as well as the influence of changed parameters on the results. In addition, its advantages are displayed by a systematic comparison with relevant approaches.

https://link.springer.com/content/pdf/10.1007/s00500-020-05193-z.pdf

Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight

Multi-attribute decision-making approach is a widely used algorithm that needs some aggregation tools and several such aggregation operators have been developed in past decades to serve the purpose. Hamacher aggregation operator is one such operator which is based on Hamacher t-norm and t-conorm. It is observed that the Hamacher aggregation operators of intuitionistic fuzzy set, Pythagorean fuzzy set and that of picture fuzzy set has some limitations in their applicability. To serve the purpose, in this paper, some Hamacher aggregation operators based on T-spherical fuzzy numbers are introduced. The concepts of T-spherical fuzzy Hamacher-weighted averaging and T-spherical fuzzy Hamacher-weighted geometric aggregation operators are proposed which described four aspects of human opinion including yes, no, abstinence and refusal with no limitations. Such type of aggregation operators efficiently describes the cases that left unsolved by the existing aggregation operators. The validity of the proposed aggregation operators is examined, and some basic properties are discussed. The proposed new Hamacher aggregation operators are used to analyze the performance of search and rescue robots using a multi-attribute decision-making approach as their performance in an emergency is eminent. The proposed Hamacher aggregation operators have two variable parameters, namely q and $$\gamma $$
 which affects the decision-making process and their sensitivity towards decision-making results is analyzed. A comparative analysis of the results obtained using proposed Hamacher aggregation operators in view of the variable parameters q and $$\gamma $$
 is established to discuss any advantages or disadvantages.

Evaluation of the Performance of Search and Rescue Robots Using T-spherical Fuzzy Hamacher Aggregation Operators

The aim of this paper is to present the novel concept of Complex q-rung orthopair fuzzy set (Cq-ROFS) which is a useful tool to cope with unresolved and complicated information. It is characterized by a complex-valued membership grade and a complex-valued non-membership grade, the distinction of which is that the sum of q-powers of the real parts (imaginary parts) of the membership and non-membership grades is less than or equal to one. To explore the study, we present some basic operational laws, score and accuracy functions and investigate their properties. Further, to aggregate the given information of Cq-ROFS, we present several weighted averaging and geometric power aggregation operators named as complex q-rung orthopair fuzzy (Cq-ROF) power averaging operator, Cq-ROF power geometric operator, Cq-ROF power weighted averaging operator, Cq-ROF power weighted geometric operator, Cq-ROF hybrid averaging operator and Cq-ROF power hybrid geometric operator. Properties and special cases of the proposed approaches are discussed in detail. Moreover, the VIKOR (“VIseKriterijumska Optimizacija I Kompromisno Resenje”) method for Cq-ROFSs is introduced and its aspects discussed. Furthermore, the above mentioned approaches apply to multi-attribute decision-making problems and VIKOR methods, in which experts state their preferences in the Cq-ROF environment to demonstrate the feasibility, reliability and effectiveness of the proposed approaches. Finally, the proposed approach is compared with existing methods through numerical examples.

https://www.mdpi.com/2227-7390/8/4/538/pdf

Power Aggregation Operators and VIKOR Methods for Complex q-Rung Orthopair Fuzzy Sets and Their Applications

The objective of this manuscript is to present the concept of interval-valued $q$ -rung orthopair 2-tuple linguistic set (IVq-RO2TLSs) and their basic operations. As a generalization of the sets, interval-valued q-rung orthopair fuzzy set is a more profitable way to express the uncertainties in the data while 2-tuple linguistic set deals with the qualitative aspects of the information. By utilizing both these features, we propose a concept of IVq-RO2TLSs and studies their properties. For it, firstly, we define the basic operational laws between the pairs of the sets and define the score, accuracy and basic operations. Secondly, based on the operational laws, we develop some weighted averaging and geometric aggregation operators for IVq-RO2TLSs and characterize their desirable properties. Thirdly, a novel approach is developed to solve multi-attribute decision making (MADM) problem with interval-valued q-rung orthopair 2-tuple linguistic information. Finally, several numerical examples are provided with some comparative study to validate the approach.

/pdf/interval-valued-q-rung-orthopair-2-tuple-linguistic-2jzzh78wqe.pdf

Interval-Valued $q$ -Rung Orthopair 2-Tuple Linguistic Aggregation Operators and Their Applications to Decision Making Process

A Pythagorean fuzzy set (PFS) is one of the extensions of the intuitionistic fuzzy set which accommodate more uncertainties to depict the fuzzy information and hence its applications are more extensive. In the modern decision-making process, aggregation operators are regarded as a useful tool for assessing the given alternatives and whose target is to integrate all the given individual evaluation values into a collective one. Motivated by these primary characteristics, the aim of the present work is to explore a group of interactive hybrid weighted aggregation operators for assembling Pythagorean fuzzy sets to deal with the decision information. The proposed aggregation operators include interactive the hybrid weighted average, interactive hybrid weighted geometric and its generalized versions. The major advantages of the proposed operators to address the decision-making problems are (i) to consider the interaction among membership and non-membership grades of the Pythagorean fuzzy numbers, (ii) it has the property of idempotency and simple computation process, and (iii) it possess an adjust parameter value and can reflect the preference of decision-makers during the decision process. Furthermore, we introduce an innovative multiple attribute decision making (MADM) process under the PFS environment based on suggested operators and illustrate with numerous numerical cases to verify it. The comparative analysis as well as advantages of the proposed framework confirms the supremacies of the method.

Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

The outbreak of the coronavirus disease (COVID-19) had put vaccine research and development (R&D) on the urgent agenda. China had taken a diversified route in vaccine research and development. It had taken an approach of first producing inactivated vaccines and then tackling mRNA vaccines, and had achieved varying degrees of progress. At present, the scale of production and the number of vaccines in China is very large, which helped to form an immune barrier. However, China's participation in international vaccine cooperation and exporting vaccines still faced some challenges, and efforts were needed to improve the effectiveness of vaccines and ensure the improvement of vaccine upgrade. 

Na Li

Papers

Pythagorean fuzzy interactive Hamacher power aggregation operators for assessment of express service quality with entropy weight

Interval-Valued $q$ -Rung Orthopair 2-Tuple Linguistic Aggregation Operators and Their Applications to Decision Making Process

Some Novel Interactive Hybrid Weighted Aggregation Operators with Pythagorean Fuzzy Numbers and Their Applications to Decision Making

Observation on the R&D Effectiveness and Application of China's Novel Coronavirus Vaccine