Multi-attribute decision-making (MADM) is usually used to aggregate fuzzy data successfully. Choosing the best option regarding data is not generally symmetric on the grounds that it does not provide complete information. Since Aczel-Alsina aggregation operators (AOs) have great impact due to their parameter variableness, they have been well applied in MADM under fuzzy construction. Recently, the Aczel-Alsina AOs on intuitionistic fuzzy sets (IFSs), interval-valued IFSs and T-spherical fuzzy sets have been proposed in the literature. In this article, we develop new types of Pythagorean fuzzy AOs by using Aczel-Alsina t-norm and Aczel-Alsina t-conorm. Thus, we give these new operations Aczel-Alsina sum and Aczel-Alsina product on Pythagorean fuzzy sets based on Aczel-Alsina t-norm and Aczel-Alsina t-conorm. We also develop new types of Pythagorean fuzzy AOs including Pythagorean fuzzy Aczel-Alsina weighted averaging and Pythagorean fuzzy Aczel-Alsina weighted geometric operators. We elaborate some characteristics of these proposed Aczel-Alsina AOs on Pythagorean fuzzy sets, such as idempotency, monotonicity, and boundedness. By utilizing the proposed works, we solve an example of MADM in the information of the multinational company under the evaluation of impacts in MADM. We also illustrate the comparisons of the proposed works with previously existing AOs in different fuzzy environments. These comparison results demonstrate the effectiveness of the proposed Aczel-Alsina AOs on Pythagorean fuzzy sets.

This work consists of developing shrinkage estimation strategies for the multivariate normal mean when the covariance matrix is diagonal and known. The domination of the positive part of James–Stein estimator (PPJSE) over James–Stein estimator (JSE) relative to the balanced loss function (BLF) is analytically proved. We introduce a new class of shrinkage estimators which ameliorate the PPJSE, and then we construct a series of polynomial shrinkage estimators which improve the PPJSE; also, any estimator of this series can be ameliorated by adding to it a new term of higher degree. We end this paper by simulation studies which confirm the performance of the suggested estimators.

In the present paper, we offer a novel three-parameter model called the weighted Weibull inverse exponential (WW-IE) distribution. We compute some basic statistical properties such as quantile function (QuF), inverse moments (INMO), harmonic mean (HM) and different measures of entropy. The WW-IE distribution parameters were estimated using the maximum likelihood (ML) method. The WW-IE distribution compared to six known distributions such as new double-weighted-Weibull, weighted-transmuted Weibull, Weibull, transmuted-Weibull, double-weighted-exponential (DWE) and weighted-Weibull distributions employing one real medical dataset. The numerical results illustrate the superiority of the WW-IE distribution other than the six competitive distributions. Received: July 2, 2023 Accepted: August 8, 2023