Generalized fuzzy set systems and particularization

It is suggested that there exists many fuzzy set systems, each with its specific pointwise operations for union and intersection. A general law of compound possibilities is valid for all these systems, as well as a general law for representing marginal possibility distributions as unions of fuzzy sets. Max-min fuzzy sets are a special case of a fuzzy set system which uses the pointwise operations of max and min for union and intersection respectively. Probabilistic fuzzy sets are another special case which uses the operations of addition and multiplication. Probably there exists an infinite number of fuzzy set operations and systems. It is shown why the law of idempotency for intersection is not required for such systems. An essential difference between the meaning of the operations of union and intersection in traditional measure theory as compared with their meaning in the theory of possibility is pointed out. The operation of particularization is used to illustrate that the two distinct classical theories of nonfuzzy relations and of probability are merely two aspects of a more generalized theory of fuzzy sets. It is shown that we must distinguish between particularization of conditional fuzzy sets and of joint fuzzy sets. The concept of restriction of nonfuzzy relations is a special case of particularization of both conditional and joint fuzzy sets. The computation of joint probabilities from conditional and marginal ones is a special case of particularization of conditional probabilistic fuzzy sets. The difference between linguistic modifiers of type 1 and particulating modifiers is pointed out, as well as a general difference between nouns and adjectives.     

多值不确定型直觉模糊识别决策方法

基于模糊环境给出多值不确定型直觉模糊集的概念,定义了集合的交、并、包含等基本运算性质。通过刻画集合间的相似程度,提出八个新的相似度公式。最后将相似度应用于识别决策,说明公式的实用性和有效性。     

扰动模糊集的粗糙度

首先,将扰动模糊集和粗糙集理论相结合,提出了粗糙扰动模糊集的概念并研究了其基本性质.接着,通过引进扰动模糊集水平上、下边界区域的概念,克服了粗糙集理论中普遍存在的两个集合的上近似的交不等于两个集合的交的上近似(两个集合的下近似的并不等于两个集合的并的下近似)的缺陷.最后,定义了依参数的扰动模糊集的粗糙度的定义,讨论了其基本性质.     

双向S-粗模糊集及其性质

讨论模糊集与双向S-粗集的联系。首先给出双向S-粗模糊集的概念,接着讨论它们的并、交、补运算及其性质;特别地,证明双向S-粗模糊集对并、交、补运算构成完全可无限分配的软代数。     

On a general class of fuzzy connectives

A general class of conectives, intersection and union, are presented for fuzzy sets. The properties of this class are studied in comparison to the ordinary intersection and union.     

模糊有穷自动机的互模拟关系

互模拟是离散事件系统中的一个等价关系,它已经应用到概率、随机和加权自动机中.本文给出模糊有穷自动机(FFA)前向互模拟关系和后向互模拟关系的定义,并给出它们的一些性质,证明前向和后向互模拟关系对于模糊有穷自动机(FFA)的一些运算(并,连接,交)和模糊正则语言的表现定理是封闭的.另外文中还给出一个可在有限步计算极大前向互模拟关系的算法,最后指出前向和后向互模拟之间的区别.     

决策模糊集覆盖系数的实用计算方法

研究了经济学中广泛应用的决策模糊理论中模糊集覆盖系数的性质,并据此提出了无须通过繁杂的统计实验就能够计算覆盖系数的实用方法,进而提出了模糊集交并运算算子.用两个算例说明了该方法和算子与实际情形相符,具有可行性.     

加法与乘法下的模糊熵

由于模糊集关于普通加法与乘法运算构成的代数系统是分配格、布尔代数,这就使得模糊集的应用受到一定的限制,为了扩展模糊集的应用,本文引进了模糊集的加法与乘法运算,接着研究了模糊集关于加法与乘法的运算性质以及模糊熵,距离测度,相似性测度在集合关于加法运算,乘法运算下的一些性质,并且对加法与乘法下的模糊熵与普通模糊熵作了对比.     

清晰集构造模糊集的简易方法及其在模糊评判中的应用

运用清晰集合的交、并运算、模糊集的分解定理,本文提出了一个用多个清晰集合构造一个模糊集合的简易方法,并将这个方法应用于模糊综合评判.本方法能将模糊综合评判中取值范围不同的指标的取值范围归一化为区间(0,1).实例表明,本方法在模糊综合评判领域是有效的、且易于操作,可以广泛应用于工程、社科等领域.     

广义多值直觉模糊软集及其在多属性决策中的应用

软集理论作为一种处理不确定问题的数学新工具弥补了传统模糊理论在参数工具上的不足。本文将广义模糊软集与多值直觉模糊集相结合,提出了广义多值直觉模糊软集的概念,给出了广义多值直觉模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,还将广义多值直觉模糊软集应用到多属性决策问题中去,给出相应的算法。并进行实例分析说明该决策方法的可行性和有效性。     

单向奇异粗糙模糊集合的结构

用模糊集合与模糊等价关系对单向奇异粗集进行了研究,并给出了单向奇异粗糙模糊集合的数学结构及其并、交、补运算和性质.同时证明了单向奇异粗糙模糊集合对并、交、补运算构成完全可无限分配的软代数.     

广义对偶犹豫模糊软集及其在决策中的应用

犹豫模糊软集作为一种处理不确定问题的工具受到了广泛关注。本文将广义模糊软集与对偶犹豫模糊集相结合,提出了广义对偶犹豫模糊软集的概念,给出了广义对偶犹豫模糊软集的交、并、补、“且”、“或”运算的概念,并基于这些概念研究其若干相关性质。此外,定义了广义对偶犹豫模糊软集的信息能量、相关性和相关系数的概念并讨论了它的性质。最后,给出了基于广义对偶犹豫模糊软集的多属性决策方法,并通过实例说明了该方法的的可行性和有效性。     

R-模糊正规子群

给出了R-模糊正规子群与基于蕴涵的模糊正规子群的定义,得到了R-模糊正规子群的交、并、同态像以及同态原像的相关性质;另外还讨论了它与不同的模糊正规子群的区别与联系,并且给出了具体的蕴涵算子厦它的等价形式.     

依零测度的Fuzzy集运算

给出了Fuzzy集合依零测度的包含,依零测度的相等。依零测度的并．交,补运算等。并补充地研究了这些基本运算,获得了若干好的性质。Fuzzy集依零测度的基本运算比标准fuzzy集合论的相应运算更有人情味,更为接近人的智能机理。有望在智能信息处理和软计算领域取得好的应用。     

G-fuzzy topologies on algebraic structures

Considering complete Boolean algebras as sets of truth values the structure of a fuzzy topological group, fuzzy topological ring, etc., is specified. The probabilistic completion of ordinary topological algebraic structures shows the applicability of these concepts to the theory of stochastic processes, e.g., a new definition of the stochastic integral is presented in Section 5.     

External Ellipsoidal Estimation of the Union of Two Concentric Ellipsoids and Its Applications

For an arbitrary set representable as the convex hull formed by the union of two concentric ellipsoids we propose a method to construct a family of external undominated ellipsoidal approximations and represent the estimated set as the intersection of all estimates from a given family. A sufficient condition of undominated guaranteed ellipsoidal approximation of a convex compactum is derived. A method is described that for certain classes of sets (such as the intersection of an ellipsoid or a cone with two halfspaces) constructs a family of internal undominated ellipsoidal approximations using the previous formulas for the external estimates of the union of concentric ellipsoids.     

Some aspects of synthesis of probabilistic fuzzy controllers

This paper deals with some aspects of analysis and design problems of a class of control algorithms called probabilistic fuzzy controllers.The notion of random intersection coefficient is proposed here.The decomposition of a multi-dimensional probabilistic fuzzy controller is discussed as well. Such decomposition provides uniform expressions for both single-input, single-output and multi-dimensional probabilistic fuzzy controllers and it improves the computational efficiency.As an example, a two-input and two-output control system is presented as well.     

Fuzzy nilpotent algebras

We define the concept of fuzzy nilpotent algebra, prove that the homomorphic inverse image of a fuzzy nilpotent algebra is also nilpotent and study the intersection and union of fuzzy nilpotent algebras.     

基于相似度和改进雷达图的概率犹豫模糊多属性决策方法

为了解决属性权重未知的概率犹豫模糊多属性决策问题,构建基于相似度和改进雷达图的多属性决策方法。首先基于概率犹豫模糊元的信息完全度构建概率犹豫模糊集的距离测度和灰色关联系数,然后基于灰色关联理想解法定义了概率犹豫模糊集的相似度,最后根据概率犹豫模糊集的相似度和改进雷达图构建多属性决策模型,并通过案例进行了验证分析。     

基于“直觉模糊集的距离测度”的联想

直觉模糊集不同于模糊集的最重要指标是犹豫度.在直觉模糊集的距离定义和公式中应突出体现犹豫度;在直觉模糊集的距离定义中也应包含经典距离的性质—三角不等式.基于论文"直觉模糊集的距离测度",提出直觉模糊集的新距离定义和新公式.应用实例表明,新提出的直觉模糊集的距离公式是实用的.