Informatica

Neutrosophic hesitant fuzzy set (NHFS) is a convincing tool that deals with uncertain information. In this paper, we propose an NH-MADM strategy for solving MADM with NHFSs based on extended GRA. We assume that the information of attributes is partially known or completely unknown. We develop two models to determine the weights of attributes. Then we rank the alternatives based on the strategy. Further, we extend the strategy into MADM in interval neutrosophic hesitant fuzzy set environment which we call INH-MADM strategy. Finally, we provide two illustrative examples to show the validity and effectiveness of the proposed strategies.

We propose a fast MATLAB implementation of the mini-element (i.e. $P1$-Bubble/$P1$) for the finite element approximation of the generalized Stokes equation in 2D and 3D. We use cell arrays to derive vectorized assembling functions. We also propose a Uzawa conjugate gradient method as an iterative solver for the global Stokes system. Numerical experiments show that our implementation has an (almost) optimal time-scaling. For 3D problems, the proposed Uzawa conjugate gradient algorithm outperforms MATLAB built-in linear solvers.

The 3D extensions of ordinary fuzzy sets such as intuitionistic fuzzy sets (IFS), Pythagorean fuzzy sets (PFS), and neutrosophic sets (NS) aim to describe experts’ judgments more informatively and explicitly. In this paper, generalized three dimensional spherical fuzzy sets are presented with their arithmetic, aggregation, and defuzzification operations. Weighted Aggregated Sum Product ASsessment (WASPAS) is a combination of two well-known multi-criteria decision-making (MCDM) methods, which are weighted sum model (WSM) and weighted product model (WPM). The aim of this paper is to extend traditional WASPAS method to spherical fuzzy WASPAS (SF-WASPAS) method and to show its application with an industrial robot selection problem. Additionally, we present comparative and sensitivity analyses to show the validity and robustness of the given decisions.

The Hamy mean (HM) operator, as a convenient mathematical aggregation tool, can deal with the interrelationship among multiple input parameters, and the power average (PA) operator can relieve the influence of awkward assessment values in the decision consequences. The interval neutrosophic sets (INSs) are a more powerful mathematical tool to handle insufficient, indeterminate and vague information that exists in real life problems. Yet, in some complicated decision-making situations, we require to consider the correlation between multi-input arguments and remove the influence of awkward data at the same time. To deal with such situations, in this paper, we combine the conventional HM operator to the traditional PA operator in interval neutrosophic settings and present two novel interval neutrosophic aggregation operators, that is, the interval neutrosophic power Hamy mean (INPHM) operator and the weighted interval neutrosophic power Hamy mean (WINPHM) operators. Then, some preferable properties of the developed aggregation operators are discussed. Moreover, based on these developed aggregation operators, we propose a new method for multiple attribute group decision making (MAGDM) under the INSs. Lastly, some examples are given to show the effectiveness of the developed method by comparing it with other existing methods.

In our previous paper we presented an offline e-cash system with observers. We have shown that the proposed system satisfies basic requirements for e-cash schemes. We also covered such security issues as chosen message attack resistance and forgery of protocols data. However, in that paper we focused more on the system itself, rather than its analysis.

The isometric mapping (Isomap) algorithm is often used for analysing hyperspectral images. Isomap allows to reduce such hyperspectral images from a high-dimensional space into a lower-dimensional space, keeping the critical original information. To achieve such objective, Isomap uses the state-of-the-art MultiDimensional Scaling method (MDS) for dimensionality reduction. In this work, we propose to use Isomap with SMACOF, since SMACOF is the most accurate MDS method. A deep comparison, in terms of accuracy, between Isomap based on an eigen-decomposition process and Isomap based on SMACOF has been carried out using three benchmark hyperspectral images. Moreover, for the hyperspectral image classification, three classifiers (support vector machine, k-nearest neighbour, and Random Forest) have been used to compare both Isomap approaches. The experimental investigation has shown that better classification accuracy is obtained by Isomap with SMACOF.

The multidimensional data model for kriging is developed using fractional Euclidean distance matrices (FEDM). The properties of FEDM are studied by means of the kernel matrix mehod. It has been shown that the factorization of kernel matrix enables us to create the embedded set being a nonsingular simplex. Using the properties of FEDM the Gaussian random field (GRF) is constructed doing it without positive definite correlation functions usually applied for such a purpose. Created GRF can be considered as a multidimensional analogue of the Wiener process, for instance, line realizations of this GRF are namely Wiener processes. Next, the kriging method is developed based on FEDM. The method is rather simple and depends on parameters that are simply estimated by the maximum likelihood method. Computer simulation of the developed kriging extrapolator has shown that it outperforms the well known Shepard inverse distance extrapolator. Practical application of the developed approach to surrogate modelling of wastewater treatment is discussed. Theoretical investigation, computer simulation, and a practical example demonstrate that the proposed kriging model, using FEDM, can be efficiently applied to multidimensional data modelling and processing.

Fermatean fuzzy sets (FFSs), proposed by Senapati and Yager (2019a), can handle uncertain information more easily in the process of decision making. They defined basic operations over the Fermatean fuzzy sets. Here we shall introduce three new operations: subtraction, division, and Fermatean arithmetic mean operations over Fermatean fuzzy sets. We discuss their properties in details. Later, we develop a Fermatean fuzzy weighted product model to solve the multi-criteria decision-making problem. Finally, an illustrative example of selecting a suitable bridge construction method is given to verify the approach developed by us and to demonstrate its practicability and effectiveness.

An extended TODIM is proposed in this paper to comprehensively reflect the psychological characteristics of decision makers (DMs) according to cumulative prospect theory (CPT). We replace the original weight with the weighting function of CPT and modify the perceived value of the dominance based on CPT, because the general psychological phenomena of DMs explained in CPT are verified by many experiments and recognized by researchers. Hence, the extended TODIM not only integrates the advantages of CPT in considering the psychological factors of DMs but also retains the superiority of the classical TODIM in relative dominance. Finally, the extended TODIM is demonstrated to capture the psychological factors of DMs well from the case study.