直觉模糊集的扩展原理

基于文[1]给出的直觉模糊集的截集、分解定理和表现定理,利用模糊集的扩展原理,本文建立了直觉模糊集的扩展原理.首先,给出了直觉模糊集的扩展原理及其等价形式;其次,讨论了直党模糊集的扩展原理的有关性质;最后,研究了复合函数的直觉模糊集扩展原理及其性质.     

直觉模糊群与它的同态像

在Ｋ,Ａｔａｎａｓｓｏｖ引进直觉模糊集的基础上,给出它的扩展原理,进而定义了直觉模糊群,并讨论了它的简单性质,最后在两个经典群同态与同构意义下,研究了这咱直觉模糊群的像、前像与逆映射等问题。     

基于极小扩展原理的表现外延及其性质

讨论因素空间理论中基于极小扩展原理的概念表现外延,给出了表现外延的投影与柱体扩张的性质.     

一阶线性模糊微分方程的解

利用文[8]中的扩展原理求解了一阶线性模糊微分方程,给出了解可表示的条件,讨论了同其他求解方法之间的关系,最后给出了具体算例。     

综合函数与扩展原理

本文首先对合情扩展映射的公理化条件的完备性与独立性进行讨论,之后给出了扩展原理的一般形式及合情扩展映射的等价定义。最后,利用综合函数,特别是变维综合函数列,给出了扩展原理的一些具体形式     

语言值多属性决策问题研究

指出了目前已有的语言值综合决策模型的不足,建立了一个新的语言值综合决策模型.利用三角形模糊数和扩展原理以及格贴近度和择近原则,证明了所给模型的科学性,同时分析了它的几条良好性质.最后给出一个该模型的应用实例.     

扩展的(G'/G)展开法求量子Zakharov-Kuznetsov方程的精确解

为得到量子Zakharov-Kuznetsov方程的一些新精确解,借助行波解的思想,结合齐次平衡原理和一类非线性常微分方程解的结构,利用扩展的(G’/G)展开方法,研究了其相应的更加丰富的精确解表达形式.新精确解的表达式主要由双曲函数、三角函数和有理数函数构成,出现了某些怪波解的情形.通过对比不同情况下解的形式,利用Matlab软件给出数值模拟图形,并根据图形的特点分析了一些怪波现象形成的机理.     

简易插值模糊推理方法

从函数扩充的角度将模糊推理视为两个论域语言值与语言值之间的对应关系,将一条规则视为一个由前提和结论组成的模糊数据对,将规则集视为一组已知的模糊数据节点集,将它们作为模糊插值节点,给出了一种插值推理函数的建立方法.然后利用扩展原理给出插值推理结果,推理的过程简化为一个求复合函数的过程.无论是对稀疏规则集还是对完备规则集,只要具有有序交叠互补性,该推理方法就能保证还原性,语气单调性,属性介值性和保正规性.     

一类扩展线性规划问题的推广

研究文［１］的扩展线性规划问题的更一般的情形：ｍｉｎｚ＝∑ｎｊ＝１ｃｊ｜ｘｊ｜，ｓ．ｔＡｘ＝ｂ，ｘｊ≥０，ｊ∈Ｉ｛１，２，…，ｎ｝。给出其不扩展单纯形表的单纯形算法。     

基本概念格的数据扩展及相容性判定问题

数据分析在计算机数据处理中占有重要地位.概念格理论是数据分析有力工具,本文以概念格为工具,讨论数据扩展而引起的相容性问题.主要是将数据作为概念格中的对象,在给定数据基本集并假设数据特征一定的条件下,考虑数据扩展相容性问题,解决了数据扩展的相容性判定问题并给出了相应的判定定理.目的是使在特征一定的情况下,数据对象达到最大化.     

模糊集范畴及集合范畴上的模

本文构造了在完备格上模糊集范畴.利用极小扩展原则和范畴的性质,获得了函子Uα构成集合范畴上的模结构,推广了P.Eklund的结论.     

Construction of periodic wavelet frames with dilation matrix

An important tool for the construction of periodic wavelet frame with the help of extension principles was presented in the Fourier domain by Zhang and Saito [Appl. Comput. Harmon. Anal., 2008, 125： 68-186]. We extend their results to the dilation matrix cases in two aspects. We first show that the periodization of any wavelet frame constructed by the unitary extension principle formulated by Ron and Shen is still a periodic wavelet frame under weaker conditions than that given by Zhang and Saito, and then prove that the periodization of those generated by the mixed extension principle is also a periodic wavelet frame if the scaling functions have compact supports.     

On a class of weak nonhomogeneous affine bi-frames for reducing subspaces of <Emphasis Type="Italic">L</Emphasis><Superscript>2</Superscript>(ℝ<Superscript><Emphasis Type="Italic">d</Emphasis></Superscript>)

For refinable function-based affine bi-frames, nonhomogeneous ones admit fast algorithms and have extension principles as homogeneous ones. But all extension principles are based on some restrictions on refinable functions. So it is natural to ask what are expected from general refinable functions. In this paper, we introduce the notion of weak nonhomogeneous affine bi-frame (WNABF). Under the setting of reducing subspaces of L ²(R ^d ), we characterize WNABFs and obtain a mixed oblique extension principle for WNABFs based on general refinable functions.     

解决矛盾问题的可拓模型与可拓知识的研究

可拓学是解决矛盾问题的学科,在可拓学的可拓模型原型的基础上,明确了计算机解决矛盾问题的可拓模型,它包括三部分:关联函数、可拓知识和推理算法,其中关联函数和可拓知识对不同的问题需要利用不同的原理,且它们是逐步变化的.在可拓知识中,关联函数的可拓变换需要通过计算证明其值是逐步增加的.这样,矛盾问题在计算机中才能得到解决.本文通过多个实例来说明解决矛盾问题的可拓模型及可拓知识的建立和实现.     

The Cauchy-Kovalevskaya extension theorem in Hermitian Clifford analysis

Hermitian Clifford analysis is a higher dimensional function theory centered around the simultaneous null solutions, called Hermitian monogenic functions, of two Hermitian conjugate complex Dirac operators. As an essential step towards the construction of an orthogonal basis of Hermitian monogenic polynomials, in this paper a Cauchy-Kovalevskaya extension theorem is established for such polynomials. The minimal number of initial polynomials needed to obtain a unique Hermitian monogenic extension is determined, along with the compatibility conditions they have to satisfy. The Cauchy-Kovalevskaya extension principle then allows for a dimensional analysis of the spaces of spherical Hermitian monogenics, i.e. homogeneous Hermitian monogenic polynomials. A version of this extension theorem for specific real-analytic functions is also obtained.     

A deteriorating multi-item inventory model with fuzzy costs and resources based on two different defuzzification techniques

Normally inventory models of deteriorating items, such as food products, vegetables, etc. involve imprecise parameters, like imprecise inventory costs, fuzzy storage area, fuzzy budget allocation, etc. In this paper, we aim to provide two defuzzification techniques for two fuzzy inventory models using (i) extension principle and duality theory of non-linear programming and (ii) interval arithmetic. On the basis of Zadeh’s extension principle, two non-linear programs parameterized by the possibility level α are formulated to calculate the lower and upper bounds of the minimum average cost at α-level, through which the membership function of the objective function is constructed. In interval arithmetic technique the interval objective function has been transformed into an equivalent deterministic multi-objective problem defined by the left and right limits of the interval. This formulation corresponds to the possibility level, α = 0.5. Finally, the multi-objective problem is solved by a multi-objective genetic algorithm (MOGA). The model has been illustrated through a numerical example and solved for different values of possibility level, α through extension principle and for α = 0.5 via MOGA. As a particular case, the results have been obtained for the inventory model without deterioration. Results from two methods for α = 0.5 are compared.     

A-调和方程很弱解的比较原理

应用McShane扩张定理证明了A-调和方程很弱解的比较原理.这个结果可以看作经典弱解比较原理的一个扩展.     

A-调和方程很弱解的比较原理

应用McShane扩张定理证明了A-调和方程很弱解的比较原理.这个结果可以看作经典弱解比较原理的一个扩展.     

An Extension of the Contraction Principle

The concept of quasi-continuity and the new concept of almost compactness for a function are the basis for the extension of the contraction principle in large deviations presented here. Important equivalences for quasi-continuity are proved in the case of metric spaces. The relation between the exponential tightness of a sequence of stochastic processes and the exponential tightness of its transform (via an almost compact function) is studied here in metric spaces. Counterexamples are given to the nonmetric case. Relations between almost compactness of a function and the goodness of a rate function are studied. Applications of the main theorem are given, including to an approximation of the stochastic integral.