Intuitionistic fuzzy recognizers and intuitionistic fuzzy finite automata

Intuitionistic fuzzy recognizers and intuitionistic fuzzy finite automata are discussed. The notions of intuitionistic fuzzy recognizer, complete accessible intuitionistic fuzzy recognizer, intuitionistic fuzzy finite automata, deterministic intuitionistic fuzzy finite automata, and intuitionistic fuzzy language are introduced. It is shown that the languages recognized by intuitionistic fuzzy recognizer are regular, and the intuitionistic fuzzy languages recognized by the intuitionistic fuzzy finite automaton and the intuitionistic fuzzy languages recognized by deterministic intuitionistic fuzzy finite automaton are equivalent. This work is supported by National Science Foundation of China (Grant No.10571112), “TRAPOYT” of China and National 973 Foundation Research Program(Grant No.2002CB312200).     

On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators

This paper presents a general framework for the study of relation-based (I,T)-intuitionistic fuzzy rough sets by using constructive and axiomatic approaches. In the constructive approach, by employing an intuitionistic fuzzy implicator I and an intuitionistic fuzzy triangle norm T, lower and upper approximations of intuitionistic fuzzy sets with respect to an intuitionistic fuzzy approximation space are first defined. Properties of (I,T)-intuitionistic fuzzy rough approximation operators are examined. The connections between special types of intuitionistic fuzzy relations and properties of intuitionistic fuzzy approximation operators are established. In the axiomatic approach, an operator-oriented characterization of (I,T)-intuitionistic fuzzy rough sets is proposed. Different axiom sets characterizing the essential properties of intuitionistic fuzzy approximation operators associated with various intuitionistic fuzzy relations are explored.     

直觉模糊逻辑算子研究’

模糊逻辑算子是模糊信息融合、模糊推理及模糊决策的重要工具。针对作为模糊逻辑算子重要扩展的直觉模糊逻辑算子,首先引入了直觉模糊集在特殊格上的等价定义。其次,验证了直觉模糊t-模与s-模的若干重要性质。在此基础上,对两种常用的蕴涵算子：直觉模糊孓蕴涵与直觉模糊R-蕴涵所具有的新性质进行讨论和证明,从而便于直觉模糊逻辑算子的进一步应用。     

基于覆盖的直觉模糊粗糙集

通过直觉模糊覆盖概念将覆盖粗糙集模型进行推广,提出一种基于直觉模糊覆盖的直觉模糊粗糙集模型.首先,介绍了直觉模糊集、直觉模糊覆盖和直觉模糊逻辑算子等概念;然后,利用直觉模糊三角模和直觉模糊蕴涵,构建两对基于直觉模糊覆盖的下直觉模糊粗糙近似算子和上直觉模糊粗糙近似算子;最后,给出了这些算子的基本性质并研究了它们之间的对偶性.     

广义的直觉模糊蕴涵及剩余格

根据交通流的动态变化情况,实时优化交通信号配时,是减少交通延误,提高交通效率的有效方法。为减少信号优化时间,提高时效性,提出一种并行化的交通信号对比分析算法,该算法首先根据专家经验和交通管理常识设定一定的信号变化区间,然后针对该区间给定变化区间Δ,依次给定相应的信号配时策略,将每一种信号配时策略分配给集群系统中的一个计算节点,由各个计算节点分别进行仿真运算,最后由主节点聚合分析,对比给出最优信号控制方案。以微观交通仿真系统Paramics进行了仿真实验,结果表明,在4个节点组成的并行网络中,加速比为1.75,其提高了仿真效率,且能较好地遴选出最优控制方案。     

BL-代数上的几种直觉模糊滤子

结合直觉模糊集和滤子理论,对BL-代数上的直觉模糊滤子进行了研究。首先回顾了BL-代数和直觉模糊集的有关基础知识。然后引入BL-代数上的直觉模糊滤子、直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子的概念,讨论了它们的一系列重要性质,证明了直觉模糊滤子与直觉模糊格滤子、直觉模糊布尔滤子和直觉模糊蕴涵滤子是等价的,并用实例进行了验证。最后探讨了直觉模糊滤子和模糊滤子的关系。     

Some geometric aggregation operators based on intuitionistic fuzzy sets

The weighted geometric (WG) operator and the ordered weighted geometric (OWG) operator are two common aggregation operators in the field of information fusion. But these two aggregation operators are usually used in situations where the given arguments are expressed as crisp numbers or linguistic values. In this paper, we develop some new geometric aggregation operators, such as the intuitionistic fuzzy weighted geometric (IFWG) operator, the intuitionistic fuzzy ordered weighted geometric (IFOWG) operator, and the intuitionistic fuzzy hybrid geometric (IFHG) operator, which extend the WG and OWG operators to accommodate the environment in which the given arguments are intuitionistic fuzzy sets which are characterized by a membership function and a non-membership function. Some numerical examples are given to illustrate the developed operators. Finally, we give an application of the IFHG operator to multiple attribute decision making based on intuitionistic fuzzy sets.     

直觉模糊S-粗决策模型及应用

基于直觉模糊S-粗集理论,提出双向直觉模糊S-粗决策模型.首先给出指标值的量化方法,将目标矩阵进行标准化处理.其次,建立直觉模糊S-粗决策的上一决策和下一决策优化模型,并给出直觉模糊S-粗决策算法及详细步骤.最后,以空袭目标为例,详细研究了目标威胁程度评估过程.结果表明,直觉模糊S-粗决策模型能够综合处理决策因素的定性与定量因素,得到的决策结果综合性能最优.所得的排序结果真实、准确地反映了实际情况.     

On generalized intuitionistic fuzzy rough approximation operators

In rough set theory, the lower and upper approximation operators defined by binary relations satisfy many interesting properties. Various generalizations of Pawlak’s rough approximations have been made in the literature over the years. This paper proposes a general framework for the study of relation-based intuitionistic fuzzy rough approximation operators within which both constructive and axiomatic approaches are used. In the constructive approach, a pair of lower and upper intuitionistic fuzzy rough approximation operators induced from an arbitrary intuitionistic fuzzy relation are defined. Basic properties of the intuitionistic fuzzy rough approximation operators are then examined. By introducing cut sets of intuitionistic fuzzy sets, classical representations of intuitionistic fuzzy rough approximation operators are presented. The connections between special intuitionistic fuzzy relations and intuitionistic fuzzy rough approximation operators are further established. Finally, an operator-oriented characterization of intuitionistic fuzzy rough sets is proposed, that is, intuitionistic fuzzy rough approximation operators are defined by axioms. Different axiom sets of lower and upper intuitionistic fuzzy set-theoretic operators guarantee the existence of different types of intuitionistic fuzzy relations which produce the same operators.     

Intuitionistic fuzzy semiregularization spaces

We introduce the intuitionistic fuzzy semiregularization space induced by an intuitionistic fuzzy topological space. We also investigate some properties of intuitionistic fuzzy semiregularization spaces.     

直觉模糊粗糙推理的规则库完备性研究

针对规则库检验问题,提出了直觉模糊粗糙规则库的完备性检验方法.首先,引入直觉模糊粗糙集的概念,给出了直觉模糊粗糙规则库的完备性定义;其次,针对直觉模糊粗糙规则库的完备性,提出了完备性检验算法,指出如何设计规则库才能满足完备性要求;最后,通过实例验证了算法的合理性和有效性.     

Intuitionistic nil radicals of intuitionistic fuzzy ideals and Euclidean intuitionistic fuzzy ideals in rings

The notion of intuitionistic nil radicals of intuitionistic fuzzy ideals in rings is introduced, and related properties are investigated. The notion of semiprime intuitionistic fuzzy ideals is provided, and its characterization is established. The concept of Euclidean intuitionistic fuzzy ideals is also introduced, and its characterization is established.     

一般等价关系下直觉模糊粗糙集模型及其性质的研究

系统研究了一般等价关系下直觉模糊粗糙集模型,给出该模型多种定义形式,详细阐述了上下近似的性质,定义了直觉模糊粗糙集截集的概念,最后给出了该直觉模糊粗糙集模型的分解定理和表现定理,并证明定理的正确性。     

直觉模糊三角模的剩余蕴涵及其性质

研究了直觉模糊三角模的剩余蕴涵及其性质。首先,定义了直觉模糊三角模的剩余蕴涵;其次,推导了直觉模糊三角模的剩余蕴涵与三角模的剩余蕴涵的关系;最后,证明了直觉模糊三角模的剩余蕴涵的16条性质。直觉模糊三角模的剩余蕴涵及其性质在直觉模糊推理、群决策等领域具有广阔的应用前景。     

Intuitionistic preference relations and their application in group decision making

Intuitionistic fuzzy set, characterized by a membership function and a non-membership function, was introduced by Atanassov [Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96]. In this paper, we define the concepts of intuitionistic preference relation, consistent intuitionistic preference relation, incomplete intuitionistic preference relation and acceptable intuitionistic preference relation, and study their various properties. We develop an approach to group decision making based on intuitionistic preference relations and an approach to group decision making based on incomplete intuitionistic preference relations respectively, in which the intuitionistic fuzzy arithmetic averaging operator and intuitionistic fuzzy weighted arithmetic averaging operator are used to aggregate intuitionistic preference information, and the score function and accuracy function are applied to the ranking and selection of alternatives. Finally, a practical example is provided to illustrate the developed approaches.     

直觉模糊多属性决策方法综述

直觉模糊多属性决策是当前决策领域的一个研究热点,在实际决策中有着广泛的应用.按照直觉模糊集的发展形式:直觉模糊集、区间直觉模糊集、直觉三角模糊数和直觉梯形模糊数,分别介绍它们在多属性决策与群决策中的研究现状,并对其未来的发展方向进行了探讨与展望.     

Quotient structures of intuitionistic fuzzy finite state machines

Quotient structures of intuitionistic fuzzy finite state machines are discussed. We give congruence relations which can be naturally introduced in such a way that each associates a semigroup with an intuitionistic fuzzy finite state machine. We also introduce the notion of intuitionistic admissible relation, and give its characterization. An isomorphism between an intuitionistic fuzzy finite state machine and the quotient structure of another intuitionistic fuzzy finite state machine is established.     

基于组合模型的直觉模糊集多属性决策方法

针对直觉模糊集是对模糊集理论的一种扩充,能够更好地处理模糊概念,研究了基于直觉模糊集的多属性决策问题.提出了直觉指数加权平均最大化和最小化组合模型,通过线性规划模型得到了属性的最优权重和相应的方案排序.数值例子表明,该方法是可行而有效的.     

直觉模糊神经网络的函数逼近能力

运用直觉模糊集理论,建立了自适应神经-直觉模糊推理系统（ANIFIS）的控制模型,并证明了该模型具有全局逼近性质.首先将Zadeh模糊推理神经网络变为直觉模糊推理网络,建立一个多输入单输出的T-S型ANIFIS模型;然后设计了系统变量的属性函数和推理规则,确定了各层的输入输出计算关系,以及系统输出结果的合成计算表达式;最后通过证明所建模型的输出结果计算式满足Stone-Weirstrass定理的3个假设条件,完成了该模型的全局逼近性证明.