Multiple attribute group decision-making based on interval-valued q-rung orthopair uncertain linguistic power Muirhead mean operators and linguistic scale functions

Fuzzy set theory and its extended form have been widely used in multiple-attribute group decision-making (MAGDM) problems, among which the interval-valued q-rung orthopair fuzzy sets (IVq-ROFSs) got a lot of attention for its ability of capturing information denoted by interval values. Based on the previous studies, to find a better solution for fusing qualitative quantization information with fuzzy numbers, we propose a novel definition of interval-valued q-rung orthopair uncertain linguistic sets (IVq-ROULSs) based on the linguistic scale functions, as well as its corresponding properties, such as operational rules and the comparison method. Furthermore, we utilize the power Muirhead mean operators to construct the information fusion method, and provide a variety of aggregation operators based on the proposed information description environment. A model framework is constructed for solving the MAGDM problem utilizing the proposed method. Finally, we illustrate the performance of the new method and investigate its advantages and superiorities through comparative analysis.

Method for constructing the fundamental equation of state that takes into account the peculiarities of the substance behaviour in a wide vicinity of the critical point

On the basis of the phenomenological theory of the critical point and the Benedek hypothesis, an expression for the Helmholtz free energy F with scale functions in the density-temperature variables has been developed. The proposed free energy equation has been tested on the example of constructing the fundamental equation of state of 2,3,3,3-tetrafluoropropene (R1234yf). By comparison with the known experimental data on the equilibrium properties of R1234yf – density and pressure on the phase equilibrium line, p-ρ-T-data in the single-phase region, the second and third virial coefficients, isochoric heat capacity, isobaric heat capacity and the sound velocity – the operating range of the equation of state of R1234yf has been established according to temperature from 220 K to 420 K and pressure up to 20 MPa.

Machine learning on properties of multiscale multisource hydroxyapatite nanoparticles datasets with different morphologies and sizes

Machine learning models for exploring structure-property relation for hydroxyapatite nanoparticles (HANPs) are still lacking. A multiscale multisource dataset is presented, including both experimental data (TEM/SEM, XRD/crystallinity, ROS, anti-tumor effects, and zeta potential) and computation results (containing 41,976 data samples with up to 9768 atoms) of nanoparticles with different sizes and morphologies at density functional theory (DFT), semi-empirical DFTB, and force field, respectively. Three geometric descriptors are set for the explainable machine learning methods to predict surface energies and surface stress of HANPs with satisfactory performance. To avoid the pre-determination of features, we also developed a predictive deep learning model within the framework of graph convolution neural network with good generalizability. Energies with DFT accuracy are achievable for large-sized nanoparticles from the learned correlations and scale functions for mapping different theoretical levels and particle sizes. The simulated XRD spectra and crystallinity values are in good agreement with experiments.

A novel Picture fuzzy linguistic Muirhead Mean aggregation operators and their application to Multiple Attribute Decision Making

The Picture fuzzy linguistic set (PFLS) is an extension of intuitionistic fuzzy set (IFS) and linguistic variables (LVs), which has been applied successfully in the process of decision making. Considering the lack of closeness of extant PFLS operations and the interrelationship among input attributes do not considered. In this paper, for the sake of addressing those limitations, we firstly redefine some novel operational laws for PFLS by introducing linguistic scale functions and the related properties are studied. Then, new score function and accuracy function are also defined to compare PFLSs. Subsequently, in consideration of the superiority of Muirhead Mean (MM) operator in capturing the interaction relationship between the input parameters, we extend the MM operator to the picture fuzzy linguistic context, and then propose picture fuzzy linguistic weighted MM operator and its dual form in a new light. After that, we have adopted these operators to build two novel models to solve multiple attribute decision making (MADM) problems. Finally, a practical example for the selection of the innovative ``Mobike'' sharing bike design is provided to illustrate the practicality and effectiveness of our developed approaches.

Optimally Stopping at a Given Distance from the Ultimate Supremum of a Spectrally Negative Lévy Process

We consider the optimal prediction problem of stopping a spectrally negative Lévy process as close as possible to a given distance $b \geq 0$ from its ultimate supremum, under a squared-error penalty function. Under some mild conditions, the solution is fully and explicitly characterised in terms of scale functions. We find that the solution has an interesting non-trivial structure: if b is larger than a certain threshold then it is optimal to stop as soon as the difference between the running supremum and the position of the process exceeds a certain level (less than b), while if b is smaller than this threshold then it is optimal to stop immediately (independent of the running supremum and position of the process). We also present some examples.

Discussion & analysis: Spatial reasoning assessment

A complete Rasch multi-faceted analysis was performed on the draft Spatial Reasoning Assessment. While the psychometric report presents the complete analysis for the examination, this discussion proceeds step-by-step to understand the way in which the analysis proceeded, and the findings therein. The findings were that holistically, the instrument performed admirably. As a pretest, it is likely that students were not expected to demonstrate certain reasoning skills (e.g., GIS) as indeed they did not. The rating scale functions well to capture the examiner judgement. Overall, the instrument works together as a functional assessment, capturing the general construct of Spatial Reasoning.

Do generalized draw-down times lead to better dividends? A Pontryagin principle-based answer

In the context of maximizing cumulative dividends under barrier policies, generalized Azéma–Yor (draw-down) stopping times receive increasing attention during these past years. Based on Pontryagin’s maximality principle, we illustrate the necessity of such generalizations under the framework of spectrally negative Markov processes. Roughly speaking, starting from the explicit expression of the optimal value of discounted dividends in terms of the scale functions, we write down the optimality conditions (via Pontryagin’s principle). The use of generalized draw-downs is then quantified through a structure term (linked to the existence of non bang-bang optimal controls). We thoroughly study several classes of Lévy processes (Bertoin, Lévy Processes, vol. 121. Cambridge University Press, 1998; Kyprianou, Fluctuations of Lévy Processes with Applications: Introductory Lectures. Springer Science & Business Media, 2014) constituting the usual models of insurance claims and a particular piece-wise deterministic Markov model (extending the premium rate to reserve-dependent settings). In all these models, we disprove the consistency of the aforementioned structure equation, thus denying the necessity of such generalizations. We end the paper with some heuristics on possible non-trivial cases for general Markov models.