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.

The interval-valued Pythagorean fuzzy set (IVPFS), as a new generalization of Pythagorean fuzzy set, which can be used to model complex uncertainty in the real multiple attribute group decision making (MAGDM) problems. This paper aims to develop some new operators for dealing with MAGDM issue with interval-valued Pythagorean fuzzy information, such as continuous interval-valued Pythagorean fuzzy ordered weighted quadratic averaging (C-IVPFOWQA) operator, weighted C-IVPFOWQA operator, ordered weighted C-IVPFOWQA operator and hybrid C-IVPFOWQA operator. The proposed operators not only improve the accuracy of decision making but also can reflect the decision makers’ risk preferences. Additionally, some desirable properties and special cases of these operators are investigated in detail. Later, we present a MAGDM method based on the hybrid C-IVPFOWQA operator. Finally, a numerical example is presented to illustrate the proposed method and comparison analysis is given to demonstrate the practicality and effectiveness.

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.

Xu Z, et al. Korean J Radiol. 2020 Feb;21:e55. https://doi.org/10.3348/kjr.2019.0853

Purpose: To translate a recombinant peptide containing the amino-terminal fragment (ATF) of urokinase plasminogen activator receptor-targeted magnetic iron oxide (IO) nanoparticles (uPAR-targeted human ATF-IONPs) into clinical applications, we conducted a pilot study to evaluate the toxicity and pharmacokinetics of this nanoparticle in normal rhesus monkeys. Methods: We assessed the changes in the following: magnetic resonance imaging (MRI) signals from pretreatment stage to 14 days posttreatment, serum iron concentrations from 5 minutes posttreatment to 12 weeks posttreatment, routine blood examination and serum chemistry analysis results from pretreatment stage to 12 weeks after administration, and results of staining of the liver with Perls’ Prussian Blue and hematoxylin–eosin at 24 hours and 3 months posttreatment in two rhesus monkeys following an intravenous administration of the targeted nanoparticles either with a polyethylene glycol (ATF-PEG-IONP) or without a PEG (ATF-IONP) coating. Results: The levels of alkaline phosphatase, alanine transaminase, and direct bilirubin in the two monkeys increased immediately after the administration of the IONPs but returned to normal within 20 days and stayed within the normal reference range 3 months after the injection. The creatinine levels of the two monkeys stayed within the normal range during the study. In addition, red blood cells, white blood cells, hemoglobin level, and platelets remained normal during the 3 months of the study. Conclusion: All of the results suggest that a transient injury in terms of normal organ functions, but no microscopic necrotic lesions, was observed at a systemic delivery dose of 5 mg/kg of iron equivalent concentration in the acute phase, and that no chronic toxicity was found 3 months after the injection. Therefore, we conclude that uPAR-targeted IONPs have the potential to be used as receptor-targeted MRI contrasts as well as theranostic agents for the detection and treatment of human cancers in future studies.