布尔代数的Fuzzy子代数和Fuzzy理想

引入了布尔代数的Fuzzy子代数、Fuzzy理想和Fuzzy商布尔代数的概念,给出了布尔代数的Fuzzy集是Fuzzy子代数(Fuzzy理想)的充要条件,讨论了布尔代数的Fuzzy子代数(Fuzzy理想)在布尔代数同态下的像和逆像,得到了布尔代数的Fuzzy子代数的同态基本定理。     

Fuzzy概率空间的Fuzzy格刻划

本文研究了Fuzzy概率空间中Fuzzy事件及概率的代数性质.利用Fuzzy概率空间中的概率为集函数这一特征和Fuzzy格的相关理论，得到了Fuzzy概率空间中的概率是从一个Fuzzy格到某个区间的Fuzzy格模同态，并将概率分解成Fuzzy格同态与Fuzzy格模同态的乘积。     

Fuzzy粗糙半群的Fuzzy粗糙同态与同构

给出Fuzzy粗糙半群与Fuzzy粗糙同态的定义,并讨论Fuzzy粗糙半群的Fuzzy粗糙同态与Fuzzy粗糙商半群的Fuzzy粗糙同构。     

关于弱不可约的Fuzzy理想

给出弱不可约的Fuzzy 理想的定义,研究Fuzzy 理想是弱不可约的Fuzzy 理想的充分和必要条件。另外,讨论了弱不可约的Fuzzy 理想的同态象与同态原象的代数性质。     

Fuzzy HX环

引入Fuzzy HX环、正则Fuzzy HX环和一致Fuzzy HX环概念,讨论了它们结构和性质及其有关同态与同构关系。     

Fuzzy幂群的基数及表示

研究Fuzzy幂群^[2]中元素的基数,证明这种Fuzzy幂群并非Zadeh意义的Fuzzy子群,而且可以用一分明群表示,给出有限群上Fuzzy幂群的正则表示,并讨论Fuzzy幂群的同态性质。     

格的Fuzzy子集间F-同态性质探讨(2)

提出格的Fuzzy子集同F-同态等概念,对F-同态的性质进行了研究,得到一些重要而有趣的结果。     

R0代数的Fuzzy子代数与Fuzzy关联MP滤子

引入了R0代数的Fuzzy 子代数、Fuzzy关联MP滤子的概念,给出了R0代数的Fuzzy集是Fuzzy子代数的几个等价刻画,讨论了R0代数的Fuzzy关联MP滤子的若干性质,证明了Fuzzy子代数(Fuzzy关联MP滤子)在R0代数同态(同构)下的不变性.     

关于三角模的直觉模糊群及其同态像

本文在K．Atanassov引进的直觉模糊集概念的基础上,利用T模和S模,定义了两个直觉模糊集的乘积．给出了关于三角模的直觉模糊群的概念及其等价命题,最后在两个经典群同态与同构意义下,研究了这种直觉模糊群的同态像及原像等问题。     

关于基本可数生成子模的扩张性

称左R-模M是ecg-扩张模,如果M的任意基本可数生成子模是M的直和因子的基本子模.在研究了ecg-扩张模的基本性质的基础上,本文证明了对于非奇异环R,所有左R-模是ecg-扩张模当且仅当所有左R-模是扩张模.同时我们还用ecg-拟连续模刻画了Noether环和Artin半单环.     

关于BL-代数的模糊滤子与模糊理想

在BL-代数中引入模糊超滤子和模糊固执滤子的概念,证明了如下条件对于BL-代数的非常数模糊滤子f来说是等价的:(1)f是布尔的和素的,(2)f是蕴涵的和素的,(3)f是超的,(4)f是固执的。应用模糊正蕴涵滤子给出G-代数的若干特征性质。提出BL-代数模糊理想的概念,给出一些重要例子,并通过例子说明在BL-代数中模糊理想一般不能由模糊滤子导出。同时,从模糊理想出发构造了商BL-代数,并建立了相应的同态基本定理。最后,研究了BL-代数的几类模糊理想及其相互关系,给出模糊布尔理想、模糊素理想、模糊超理想的特征性质。     

Construction of quotient BCI(BCK)-algebra via a fuzzy ideal

The present paper gives a new construction of a quotient BCI(BCK)-algebraX/μ by a fuzzy ideal μ inX and establishes the Fuzzy Homomorphism Fundamental Theorem. We show that if μ is a fuzzy ideal (closed fuzzy ideal) ofX, thenX/μ is a commutative (resp. positive implicative, implicative) BCK (BCI)-algebra if and only if μ is a fuzzy commutative (resp positive implicative, implicative) ideal ofX. Moreover we prove that a fuzzy ideal of a BCI-algebra is closed if and only if it is a fuzzy subalgebra ofX. We show that if the period of every element in a BCI-algebraX is finite, then any fuzzy ideal ofX is closed. Especially, in a well (resp, finite, associative, quasi-associative, simple) BCI-algebra, any fuzzy ideal must be closed.     

幺半环上模糊有限状态机的一些性质

状态机的很多性质在计算机等方面有着广泛的应用,因此对状态机的研究具有重要的意义.本文给出了幺半环上模糊有限状态机的概念,对状态之间的等价进行了定义,引入了同态的概念,得到同态定理和满同态分解定理,讨论了幺半环上模糊有限状态机在同态下的交换性质和连通性以及子状态机的可分离性.     

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.     

模糊质量设计的数学模型及解法

本文给出了模糊质量设计的数学模型 ,并给出了具有模糊约束、模糊约束函数值及双目标两层次的模糊质量设计模型的解法 .     

Fuzzy coefficient volatility (FCV) models with applications

Recently, Carlsson and Fuller [C. Carlsson, R. Fuller, On possibilistic mean value and variance of fuzzy numbers, Fuzzy Sets and Systems 122 (2001) 315–326] have introduced possibilistic mean, variance and covariance of fuzzy numbers and Fuller and Majlender [R. Fuller, P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers, Fuzzy Sets and Systems 136 (2003) 363–374] have introduced the notion of crisp weighted possibilistic moments of fuzzy numbers. In this paper, we propose a class of FCV (Fuzzy Coefficient Volatility) models and study the moment properties. The method used here is very similar to the method used in Appadoo et al. [S.S. Appadoo, M. Ghahramani, A. Thavaneswaran, Moment properties of some time series models, Math. Sci. 30 (1) (2005) 50–63]. The proposed models incorporate fuzziness, subjectivity, arbitrariness and uncertainty observed in most financial time series. The usual forecasting method does not incorporate parameter variability. Fuzzy numbers are used to model the parameters to incorporate parameter variability.     

特征0无穷维单Novikov代数的非奇异模

本文证明了每一个A-模是一个平凡模和一个非奇异模的直和;给出了两类特征0无穷维单Novikov代数的非奇异模的结构定理.     

RM approach for ranking of generalized trapezoidal fuzzy numbers

Ranking of fuzzy numbers play an important role in decision making, optimization and forecasting etc. Fuzzy numbers must be ranked before an action is taken by a decision maker. In this paper, with the help of several counter examples, it is proved that ranking method proposed by Chen and Chen (Expert Systems with Applications 36 (3): 6833) is incorrect. The main aim of this paper is to propose a new approach for the ranking of generalized trapezoidal fuzzy numbers. The proposed ranking approach is based on rank and mode so it is named as an RM approach. The main advantage of the proposed approach is that the proposed approach provides the correct ordering of generalized and normal trapezoidal fuzzy numbers and also the proposed approach is very simple and easy to apply in the real life problems. It is shown that proposed ranking function satisfies all the reasonable properties of fuzzy quantities proposed by Wang and Kerre (Fuzzy Sets and Systems 118 (3): 375).     

Fuzzy system reliability analysis by the use of Tω (the weakest t-norm) on fuzzy number arithmetic operations

In general, the sup-min convolution has been used for fuzzy arithmetic to analyze fuzzy system reliability, where the reliability of each system component is represented by fuzzy numbers. It is well known that T_ω-based addition preserves the shape of L-R type fuzzy numbers. In this paper, we show T_ω-based multiplication also preserves the shape of L-R type fuzzy numbers. We then apply T_ω-based arithmetic operations to fuzzy system reliability analysis. In fact, we show that we can simplify fuzzy arithmetic operations and even get the exact solutions for L-R type fuzzy system reliability, while others [Singer, Fuzzy Sets Syst. 34 (1990) 145; Cheng and Mon, Fuzzy Sets Syst. 56 (1993) 29; Chen, Fuzzy Sets Syst. 64 (1994) 31] have got the approximate solutions using sup-min convolution for evaluating fuzzy system reliability.