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In block encryption algorithms the only nonlinear component, which creates confusion and diffusion, is substitution box (S-Box). Therefore, carefully selection of S-Box is an important task. In this article, an algorithm is presented for the construction of 8 × 8 S-Box based on all subfields of Galois Field G F 2 16 and linear fractional transformation. Proposed algorithm is easy and simple but significantly complex for the attackers as it utilizes all subfields of G F (2 16) corresponding to all primitive irreducible polynomials for making G F (2 16) . An illustrating S-Box is also developed which is showing good structural characteristics such as it has no fixed point with 108.5 nonlinearity and 0.5020 strict avalanche. In the last, illustrated S-Box is applied on images for checking the performance under various criteria available in the literature. Obtained results of analyses are compared to well-known S-Boxes and found better in the comparison. [ABSTRACT FROM AUTHOR]

When it comes to solving dynamic programming challenges, it is essential to have a well-structured decision theory. As a result, the decision-makers must operate in a dynamically complicated environment where appropriate and rapid reaction in a cooperative way is the fundamental key to effectively completing the task. We express a theory of decision modeling and axiomatizing a decision-making process. The payoffs and probabilities are represented with simplified neutrosophic sets. We therefore, provide the theory of choice with the implementation of simplified neutrosophic sets. By exploiting the idea of pure strategy, we introduce two steps: in the first step, for each attractive point, some particular event is selected that can bring about a relatively neutrosophic upper payoff with a relatively neutrosophic upper probability or a relatively neutrosophic lower payoff with a relatively neutrosophic upper probability. A decision-maker selects the most favored attractive point in the second stage, based on the focus on all attractive points. Neutrosophic focus theory has been introduced to improve overall performance with more flexibility in complex decision-making. The approach suggested in this work has been implemented in a real-life example to determine its effectiveness. The proposed method is shown to be the most useful for ranking scenarios and addressing dynamic programming problems in decision-making. [ABSTRACT FROM AUTHOR]

Metric-based parameters aided the study of the structural properties of graph network space like complexity, central tendency, connectivity, robustness, accessibility, and vulnerability. At the same time, these parameters played a pivotal role in rectifying problems in navigation, integer programming, optimization, pattern recognition and avoidance, combinatoric detection, backtracking in geographical routing, etc. In this paper, we considered the fractional edge dimension, a metric-based parameter in local environment by initiating the study of the fractional local edge dimensions of a graph (FLED). We define the aforesaid concept and give its bounds. We discussed the characterization problem for FLED equal to 1 , the realization problem, and its relation with the fractional metric dimensions. We also calculated the FLED of the Petersen graph, Coxeter graph, the families of cycle, complete, wheel, grid and complete r -partite graphs. [ABSTRACT FROM AUTHOR]

The problem of ordered clustering in the context of decision-making with multiple criteria has garnered significant interest from researchers in the field of management science and operational research. In real-world scenarios, the datasets often exhibit imprecision or uncertainty, which can lead to suboptimal ordered-clustering outcomes. However, the intuitionistic fuzzy c-means (IFCM) clustering algorithm enhances the accuracy and effectiveness of decision-making processes by effectively handling uncertain dataset information for clustering. Therefore, we propose a new clustering algorithm, called the generalized ordered intuitionistic fuzzy c-means (G-OIFCM), based on PROMETHEE and the IFCM clustering algorithm. Different from the classical IFCM clustering algorithm, we use positive flow ( φ + s i ∈ 0 , 1 ) and negative flow ( φ − s i ∈ 0 , 1 ) of PROMETHEE to generate ordered clusters within the intuitionistic environment. We define a new objective function based on the positive and negative flow of the PROMETHEE and IFCM clustering algorithm, whose properties are mathematically justified in terms of convergence and optimization. The performance of the proposed algorithm is evaluated using two different real-world datasets to assess both the ordered clustering and the quality of partitioning. To demonstrate the effectiveness of G-OIFCM, a comparison is conducted with three other algorithms: fuzzy c-means (FCM), ordered fuzzy c-means (OFCM), and an adaptive generalized intuitionistic fuzzy c-means (G-IFCM). The results demonstrate the effectiveness of G-OIFCM in enhancing optimal ordered clustering and utility when dealing with uncertainty in datasets. [ABSTRACT FROM AUTHOR]