A New Kind of Generalized Pythagorean Fuzzy Soft Set and Its Application in Decision-Making

The aim of this paper is to introduce the concept of a generalized Pythagorean fuzzy soft set(GPFSS),which is a combination of the generalized fuzzy soft sets and Pythagorean fuzzy sets.Several of important operations of GPFSS including complement,restricted union,and extended intersection are discussed.The basic properties of GPFSS are presented.Further,an algorithm of GPFSSs is given to solve the fuzzy soft decision-making.Finally,a comparative analysis between the GPFSS approach and some existing approaches is provided to show their reliability over them.

Generalized Soft Expert Set and Its Applications

The expert set theory performs an important part in making decisions. It can successfully convey the opinions of every expert since it includes several experts. In this study, generalizations and soft expert sets are combined. First, the generalized soft expert set notion is presented, then follows the definition of operation approaches and characteristics as the complement, union, intersection, AND and OR. The application of the generalized soft expert set concept to decision issues is then presented with an example. The study also introduces the idea of a generalized soft expert matrix and demonstrates how it may be used to solve decision-making issues. The most striking aspect of this paper is to present the concepts of generalized soft expert sets and generalized soft expert matrices and to apply them to the same decision-making scenario.

Dynamic weighted voting for multiple classifier fusion:a generalized rough set method

To improve the performance of multiple classifier system, a knowledge discovery based dynamic weighted voting （KD-DWV） is proposed based on knowledge discovery. In the method, all base classifiers may be allowed to operate in different measurement/feature spaces to make the most of diverse classification information. The weights assigned to each output of a base classifier are estimated by the separability of training sample sets in relevant feature space. For this purpose, some decision tables （DTs） are established in terms of the diverse feature sets. And then the uncertainty measures of the separability are induced, in the form of mass functions in Dempster-Shafer theory （DST）, from each DTs based on generalized rough set model. From the mass functions, all the weights are calculated by a modified heuristic fusion function and assigned dynamically to each classifier varying with its output. The comparison experiment is performed on the hyperspectral remote sensing images. And the experimental results show that the performance of the classification can be improved by using the proposed method compared with the plurality voting （PV）.

The Structure and the Sufficent and Necessary Conditions for Generalized Statistically Self-Similar Sets

We constructed a class of generalized statistically self-similar set.S and give the necessary and sufficent conditions to ensure a random recursive set being a generalized statistically self-similar set. The statistically self-similar sets defined by Hutchinson,Falconer,Graf are the special cases of ours.

α-Input and α-Unit Resolution Methods for Generalized Horn Clause Set in L_(V(n×2))F(X)

α-Input resolution and α-unit resolution for generalized Horn clause set are discussed in linguistic truth-valued lattice-valued first-order logic (LV(n×2)F(X)), which can represent and handle uncertain linguistic values-based information. Firstly the concepts of α-input resolution and α-unit resolution are presented, and the equivalence of them is shown. Then α-input (α-unit) resolution is equivalently transformed from LV(n×2)F(X) into that of LnP(X), and their soundness and completeness are also established. Finally an algorithm for α-unit resolution is contrived in LnP(X).

Arithmetic Operations of Generalized Trapezoidal Picture Fuzzy Numbers by Vertex Method

In this article, we define the arithmetic operations of generalized trapezoidal picture fuzzy numbers by vertex method which is assembled on a combination of the (α, γ, β)-cut concept and standard interval analysis. Various related properties are explored. Finally, some computations of picture fuzzy functions over generalized picture fuzzy variables are illustrated by using our proposed technique.

Federated Learning Model for Auto Insurance Rate Setting Based on Tweedie Distribution

In the assessment of car insurance claims,the claim rate for car insurance presents a highly skewed probability distribution,which is typically modeled using Tweedie distribution.The traditional approach to obtaining the Tweedie regression model involves training on a centralized dataset,when the data is provided by multiple parties,training a privacy-preserving Tweedie regression model without exchanging raw data becomes a challenge.To address this issue,this study introduces a novel vertical federated learning-based Tweedie regression algorithm for multi-party auto insurance rate setting in data silos.The algorithm can keep sensitive data locally and uses privacy-preserving techniques to achieve intersection operations between the two parties holding the data.After determining which entities are shared,the participants train the model locally using the shared entity data to obtain the local generalized linear model intermediate parameters.The homomorphic encryption algorithms are introduced to interact with and update the model intermediate parameters to collaboratively complete the joint training of the car insurance rate-setting model.Performance tests on two publicly available datasets show that the proposed federated Tweedie regression algorithm can effectively generate Tweedie regression models that leverage the value of data fromboth partieswithout exchanging data.The assessment results of the scheme approach those of the Tweedie regressionmodel learned fromcentralized data,and outperformthe Tweedie regressionmodel learned independently by a single party.

Estimating the ultimate bound and positively invariant set for a generalized Lorenz system

A generalized Lyapunov function was employed to investigate the ultimate bound and positively invariant set of a generalized Lorenz system.We derived an ellipsoidal estimate of the ultimate bound and positively invariant set for the generalized Lorenz system,for all the positive values of system parameters a,b,and c.Our results extend the related result of Li,et al.[Li DM,Lu JA,Wu XQ,et al.,Estimating the ultimate bound and positively invariant set for the Lorenz system and a unified chaotic system,Journal of Mathematical Analysis and Application,2006,323(2):844-653].

Benson proper efficiency for vector optimization of generalized subconvexlike set-valued maps in ordered linear spaces

Several equivalent statements of generalized subconvexlike set-valued map are established in ordered linear spaces. Using vector closure, we introduce Benson proper efficient solution of vector optimization problem. Under the assumption of generalized subconvexlikeness, scalarization, multiplier and saddle point theorems are obtained in the sense of Benson proper efficiency.

Some Polar Sets for the Generalized Brownian Sheet

Let W^-（t）（t∈R＋^N） be the d-dimensional N-parameter generalized Brownian sheet. We study the polar sets for W^-（t）. It is proved that for any α∈ R^d, P{W^-（t） = α, for some t∈ R〉^N} = {1, if βd 〈 2N ,0 if αd〉 2N and the probability that W^-（t） has k-multiple points is 1 or 0 according as whether 2kN〉d（k-1）β or 2kN 〈 d（k - 1）α. These results contain and extend the results of the Brownian sheet, where R〉^N = （0,＋∞）U,R＋^N = [0,＋∞）^N,0〈 α ≤1and β〉1.

Upper and Lower Semicontinuity of Solution Sets for Parametric Generalized Vector Quasi-equilibrium Problems

In this paper, two kinds of parametric generalized vector quasi-equilibrium problems are introduced and the relations between them are studied. The upper and lower semicontinuity of their solution sets to parameters are investigated.

A NOTE ON GENERALIZED MORAN SET

Let E be a generallied Moran set. The authors determine the dim E and get the sufficient and necessary condition for E being a s-set.

Category of Generalized Intuitionistic Fuzzy Sets

In this paper, category GIFS of generalized intuitionistic fuzzy sets(GIF) is built up. Topoi properties of category GIFS axe studied. Firstly， it is proved that the category GIFS has all topoi properties except that it has no subobject classifiers， Secondly， it is proved that the category GIFS has middle object and consequently GIFS is a weak topos.Thirdly， by the use of theory of weak topos GIFS，the power object of an object in GIFS is studied.

DNA Sequences with Forbidden Words and the Generalized Cantor Set

In this work, we establish relations between DNA sequences with missing subsequences (the forbidden words) and the generalized Cantor sets. Various examples associated with some generalized Cantor sets, including Hao’s frame representation and the generalized Sierpinski Set, along with their fractal graphs, are also presented in this work.

Generalized cone-subconvexlike set-valued maps and applications to vector optimization

The definitions of cone-subconvexlike set-valued maps and generalized cone-subconvexlike set-valued maps in topological vector spaces are defined by using the relative interiors of ordering cone. The relationships between the two classes of set-valued maps are investigated, and some properties of them are shown. A Gordan type alternative theorem under the assumption of generalized cone-subconvexlikeness of set-valued maps is proved by applying convex separation theorems involving the relative interiors in infinite dimensional spaces. Finally a necessary optimality condition theorem is shown for a general kind of set-valued vector optimization in a sense of weak E-minimizer.

Generalized Quasi-Variational Inequalities on Paracompact Sets

Taking advantage of result in [1], this paper studied generalized quasi variational inequalities on paracompact sets, unified and extended corresponding results in [4-6].

MULTI-GRAY EDGE DETECTION BASED ON GENERALIZED FUZZY SET

In this letter, drawbacks of the classical algorithm to enhance the fuzzy contrast among adjacent regions are analyzed. Based on it, a new fuzzy enhancement algorithm and a linear fuzzy distribution that maps the gray images to corresponding generalized fuzzy set are proposed. Results of two examples illustrate that the algorithm is more effective and faster when used to detect the multi-level edges of images.

Sensitivity analysis of generalized set-valued quasi-variational inclusion in Banach spaces

The sensitivity analysis for a class of generalized set-valued quasi-variational inclusion problems is investigated in the setting of Banach spaces. By using the resolvent operator technique, without assuming the differentiability and monotonicity of the given data, equivalence of these problems to the class of generalized resolvent equations is established.