The security of a chaos-based image encryption (IE) systems is based upon chaotic map’s performance and the encryption algorithm’s permutation and diffusion strategies. Nevertheless, existing IE schemes exhibit different drawbacks, such as limited disordering capabilities, inadequate dynamic performance, and the chaotic maps’ insensitivity. To address these limitations, this study presents an octal-based shuffling and multilayer rotational diffusing IE (OSMRD-IE) utilizing a 2-D hybrid Michalewicz–Ackley (2-D-HMA) map. The 2-D-HMA map has the capability to generate new hyperchaotic maps by integrating hybrid functions using different encapsulation functions. The integration of a map generator could lead to dynamic nature, chaotic perturbations, and parameter control mechanisms. To enhance the algorithm’s resilience against cyberthreats, the 2-D-HMA map-based OSMRD-IE scheme shuffles the pixels using octal-base scrambling and manipulates pixel values through multilayer rotation. By means of comparisons with existing techniques, the OSMRD-IE scheme’s reliability and 2-D-HMA map’s dynamic performance are validated independently. The superior chaotic properties of the 2-D-HMA map are evident in the experimental results, establishing OSMRD-IE as the more reliable scheme in both visual and quantitative comparisons.

Sustainable supplier selection (SSS) is an essential part of the decision-making process in sustainable supply chains. Numerous research studies have been conducted using various decision-making methods to attend to this research-worthy issue. This literature review presents a comprehensive SSS analysis focusing on social, economic, and environmental aspects. The present study spans five years (2018–2022) and considers 101 papers. It provides a detailed breakdown of the papers based on their dates of publication, the countries of the writers, application fields, and journals, and it categorizes them based on their approaches. In addition, this review examines the use of single- or hybrid-form methodologies in the papers reviewed. It also identifies that the TOPSIS, AHP, VIKOR, BWM, DEA, DEMATEL, and MULTIMOORA methods and their extensions are the most frequently used methods in SSS studies. It is concluded that hybrid approaches and their rough, grey, and fuzzy extensions are used to solve real-world problems. However, state-of-the-art mathematical tools, such as soft sets and their hybrid versions with fuzzy sets, have not been utilized in SSS studies. Therefore, this study inspires and encourages the use of such tools in SSS research.

In this paper, we first define eight pseudo-metrics and eight pseudo-similarities based on these pseudo-metrics over fpfs -matrices. We then propose a new classification algorithm, i.e. Fuzzy Parameterized Fuzzy Soft Euclidean Classifier (FPFS-EC), based on Euclidean pseudo-similarity. After that, we compare FPFS-EC with Support Vector Machines (SVM), Fuzzy k-Nearest Neighbor (Fuzzy kNN), Fuzzy Soft Set Classifier (FSSC), FussCyier, Fuzzy Soft Set Classification Using Hamming Distance (HDFSSC), and Fuzzy kNN Based on the Bonferroni Mean (BM-Fuzzy kNN) in terms of the performance criteria - namely accuracy, precision, recall, macro F-score, and micro F-score - and running time by using 18 real-world datasets in the UCI machine learning repository. The results show that FPFS-EC performs better in the occurrence of the 13 of 18 datasets in question than SVM, Fuzzy kNN, FSSC, FussCyier, HDFSSC, and BM-Fuzzy kNN.

Cuong [Picture Fuzzy Sets, Journal of Computer Science and Cybernetics 30 (4) (2014) 409–420] has introduced the concept of picture fuzzy soft sets (pfs-sets) relying on his definition and operations of picture fuzzy sets (pf -sets), in which there exist some inconsistencies. Yang et al. [Adjustable Soft Discernibility Matrix Based on Picture Fuzzy Soft Sets and Its Applications in Decision Making, Journal of Intelligent & Fuzzy Systems 29 (4) (2015) 1711–1722] have claimed that they have introduced the concept of pfs-sets with the inconsistencies in Cuong’s definition of pf -sets. Therefore, this study redefines the concept of pfs-sets to deal with the inconsistencies therein. Moreover, it investigates some of the properties of pfs-sets and their product operations and proposes a soft decision-making method via pfs-sets. Finally, pfs-sets, their product operations, and the proposed method are discussed for further research.