Optical flow estimation using the Fisher–Rao metric

The optical flow in an event camera is estimated using measurements in the address event representation (AER). Each measurement consists of a pixel address and the time at which a change in the pixel value equalled a given fixed threshold. The measurements in a small region of the pixel array and within a given window in time are approximated by a probability distribution defined on a finite set. The distributions obtained in this way form a three dimensional family parameterized by the pixel addresses and by time. Each parameter value has an associated Fisher–Rao matrix obtained from the Fisher–Rao metric for the parameterized family of distributions. The optical flow vector at a given pixel and at a given time is obtained from the eigenvector of the associated Fisher–Rao matrix with the least eigenvalue. The Fisher–Rao algorithm for estimating optical flow is tested on eight datasets, of which six have ground truth optical flow. It is shown that the Fisher–Rao algorithm performs well in comparison with two state of the art algorithms for estimating optical flow from AER measurements.

Multicriteria Decision-Making Approach for Aggregation Operators of Pythagorean Fuzzy Hypersoft Sets

The Pythagorean fuzzy hypersoft set (PFHSS) is the most advanced extension of the intuitionistic fuzzy hypersoft set (IFHSS) and a suitable extension of the Pythagorean fuzzy soft set. In it, we discuss the parameterized family that contracts with the multi-subattributes of the parameters. The PFHSS is used to correctly assess insufficiencies, anxiety, and hesitancy in decision-making (DM). It is the most substantial notion for relating fuzzy data in the DM procedure, which can accommodate more uncertainty compared to available techniques considering membership and nonmembership values of each subattribute of given parameters. In this paper, we will present the operational laws for Pythagorean fuzzy hypersoft numbers (PFHSNs) and also some fundamental properties such as idempotency, boundedness, shift-invariance, and homogeneity for Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators. Furthermore, a novel multicriteria decision-making (MCDM) approach has been established utilizing presented aggregation operators (AOs) to resolve decision-making complications. To validate the useability and pragmatism of the settled technique, a brief comparative analysis has been conducted with some existing approaches.

A Parametric Logarithmic Image Processing Framework Based on Fuzzy Graylevel Accumulation by the Hamacher T-Conorm

It has been proven that Logarithmic Image Processing (LIP) models provide a suitable framework for visualizing and enhancing digital images acquired by various sources. The most visible (although simplified) result of using such a model is that LIP allows the computation of graylevel addition, subtraction and multiplication with scalars within a fixed graylevel range without the use of clipping. It is claimed that a generalized LIP framework (i.e., a parameterized family of LIP models) can be constructed on the basis of the fuzzy modelling of gray level addition as an accumulation process described by the Hamacher conorm. All the existing LIP and LIP-like models are obtained as particular cases of the proposed framework in the range corresponding to real-world digital images.

Neutrosophic Hypersoft Matrices with Application to Solve Multiattributive Decision-Making Problems

The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The main objective of the follow-up study is to develop the theory of neutrosophic hypersoft matrix (NHSM). The NHSM is the generalized form of a neutrosophic soft matrix (NSM). Some fundamental operations and score function for NHSMs have been introduced with their desirable properties. Furthermore, we introduce the logical operators such as OR-operator and AND-operator with their fundamental properties in the following research. The necessity and possibility operations for NHSMs have been established. Utilizing the developed score function, a decision-making methodology has been developed to solve the multiattribute decision-making (MADM) problem. To ensure the validity of the proposed approach, a numerical illustration has been described for the selection of competent faculty member. The practicality and effectiveness of the current approach are proved through comparative analysis with the assistance of some existing studies.

Selection of an Effective Hand Sanitizer to Reduce COVID-19 Effects and Extension of TOPSIS Technique Based on Correlation Coefficient under Neutrosophic Hypersoft Set

Correlation coefficients are used to tackle many issues that include indistinct as well as blurred information excluding is not able to deal with the general fuzziness along with obscurity of the problems that have various information. The correlation coefficient (CC) between two variables plays an important role in statistics. Likewise, the accuracy of relevance assessment depends on the information in a set of discourses. The data collected for numerous statistical studies is full of exceptions. The concept of the neutrosophic hypersoft set (NHSS) is a parameterized family that deals with the subattributes of the parameters and is a proper extension of the neutrosophic soft set to accurately assess the deficiencies, anxiety, and uncertainty in decision-making. Compared with existing research, NHSS can accommodate more uncertainty, which is the most significant technique for describing fuzzy information in the decision-making process. The core objective of follow-up research is to develop the concept and characteristics of CC and the weighted correlation coefficient (WCC) of NHSS. We also introduced some aggregation operators in the considered environment, which can help us establish a prioritization technique for order preference by similarity to the ideal solution (TOPSIS) based on CC and WCC under NHSS. A decision-making strategy is established to solve multicriteria group decision-making (MCGDM) problems utilizing developed methodology. Moreover, the proposed method is utilized for the selection of an effective hand sanitizer during the COVID-19 pandemic to ensure the validity of the proposed approach. The practicality, effectivity, and flexibility of the current approach are proved through comparative analysis with the assistance of some existing studies.

Development of TOPSIS Technique under Pythagorean Fuzzy Hypersoft Environment Based on Correlation Coefficient and Its Application towards the Selection of Antivirus Mask in COVID-19 Pandemic

The correlation coefficient between two variables plays an important role in statistics. Also, the accuracy of relevance assessment depends on information from a set of discourses. The data collected from numerous statistical studies are full of exceptions. The Pythagorean fuzzy hypersoft set (PFHSS) is a parameterized family that deals with the subattributes of the parameters and an appropriate extension of the Pythagorean fuzzy soft set. It is also the generalization of the intuitionistic fuzzy hypersoft set (IFHSS), which is used to accurately assess insufficiency, anxiety, and uncertainties in decision-making. The PFHSS can accommodate more uncertainties compared to the IFHSS, and it is the most substantial methodology to describe fuzzy information in the decision-making process. The core objective of the this study is to develop the notion and features of the correlation coefficient and the weighted correlation coefficient for PFHSS and to introduce the aggregation operators such as Pythagorean fuzzy hypersoft weighted average (PFHSWA) and Pythagorean fuzzy hypersoft weighted geometric (PFHSWG) operators under the PFHSS scenario. A prioritization technique for order preference by similarity to the ideal solution (TOPSIS) under PFHSS based on correlation coefficients and weighted correlation coefficients is presented. Through the developed methodology, a technique for solving multiattribute group decision-making (MAGDM) problem is planned. Also, the importance of the developed methodology and its application in indicating multipurpose antivirus mask throughout the COVID-19 pandemic period is presented. A brief comparative analysis is described with the advantages, effectiveness, and flexibility of numerous existing studies that demonstrate the effectiveness of the proposed method.

Spreading under shifting climate by a free boundary model: Invasion of deteriorated environment

In this paper, we consider a free boundary model in one space dimension which describes the spreading of a species subject to climate change, where favorable environment is shifting away with a constant speed [Formula: see text] and replaced by a deteriorated yet still favorable environment. We obtain two threshold speeds [Formula: see text] and a complete classification of the long-time dynamics of the model, which reveals significant differences between the cases [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. For example, when [Formula: see text], for a suitably parameterized family of initial functions [Formula: see text] increasing continuously in [Formula: see text], we show that there exists [Formula: see text] such that the species vanishes eventually when [Formula: see text], it spreads with asymptotic speed [Formula: see text] when [Formula: see text], it spreads with forced speed [Formula: see text] when [Formula: see text], and it spreads with speed [Formula: see text] when [Formula: see text]. Moreover, in the last case, while the spreading front propagates with asymptotic speed [Formula: see text], the profile of the population density function [Formula: see text] approaches a propagating pair consisting of a traveling wave with speed [Formula: see text] and a semi-wave with speed [Formula: see text].

Bifurcation Analysis in Planar Quadratic Differential Systems with Boundary

Given a planar quadratic differential system delimited by a straight line, we are interested in studying the bifurcation phenomena that can arise when the position on the boundary of two tangency points are considered as parameters of bifurcation. First, under generic conditions, we find a two-parametric family of quadratic differential systems with at least one tangency point. After that, we find a normal form for this parameterized family. Next, we study two subfamilies, one of them characterized by the existence of two fold points of different nature, and the other one, characterized by the existence of one fold point and one boundary equilibrium point. For the first family, we find sufficient conditions for the existence of stationary bifurcations: saddle-node, transcritical and pitchfork, while for the second family, the existence of the called transcritical Bogdanov–Takens bifurcation is proved. Finally, the results are illustrated with two examples.

The no‐upward‐crossing condition, comparative statics, and the moral‐hazard problem

We define and explore no‐upward‐crossing (NUC), a condition satisfied by every parameterized family of distributions commonly used in economic applications. Under smoothness assumptions, NUC is equivalent to log‐supermodularity of the negative of the derivative of the distribution with respect to the parameter. It is characterized by a natural monotone comparative static and is central in establishing quasi‐concavity in a family of decision problems. As an application, we revisit the first‐order approach to the moral‐hazard problem. NUC simplifies the relevant conditions for the validity of the first‐order approach and gives them an economic interpretation. We provide extensive analysis of sufficient conditions for the first‐order approach for exponential families.