On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces

Recently, the concept of statistical convergence of double sequences has been studied in intuitionistic fuzzy normed spaces by Mursaleen and Mohiuddine [Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, Solitons Fractals, 41 (2009) pp. 2414–2421]. We know that ideal convergence is more general than statistical convergence for single or double sequences. This has motivated us to study the ideal convergence of double sequences in a more general setting. That is, in this paper, we study the concept of ideal convergence and ideal Cauchy for double sequences in intuitionistic fuzzy normed spaces.     

Some fixed point theorems in fuzzy normed linear spaces

In this paper, the concepts of sectional fuzzy continuous mappings, l-fuzzy compact sets, asymptotic fuzzy normal structure and strong uniformly convex fuzzy normed linear spaces have been introduced. Schauder-type and other fixed point theorems have been established in fuzzy normed linear spaces.     

Fixed point theorems on fuzzy normed linear spaces

In this paper, definitions of strongly fuzzy convergent sequence, l-fuzzy weakly convergent sequence and l-fuzzy weakly compact set are given in a fuzzy normed linear space. The concepts of fuzzy normal structure, fuzzy non-expansive mapping, uniformly convex fuzzy normed linear space are introduced and fixed point theorems for fuzzy non-expansive mappings are proved.     

Nets and filters in intuitionistic fuzzy topological spaces

The basic concept of intuitionistic fuzzy point has been defined by Çoker and Demirci. Also, Çoker constructed the fundamental theory on intuitionistic fuzzy topological spaces. In this paper, we define the notions of net and filter in the intuitionistic fuzzy sense, and obtain some results on convergence, in particular we establish the correspondence between net convergence and filter convergence in the intuitionistic fuzzy sense.     

Schauder bases and approximation property in fuzzy normed spaces

Our aim in this article is to introduce and study the notion of weak and strong Schauder bases in fuzzy normed spaces. Further, we introduce strong and weak fuzzy approximation properties and set a relationship between these two new notions which may provide an acceleration to the structural analysis of fuzzy normed spaces.     

Stability of mixed type functional equation in normed spaces using fuzzy concept

S. M. Ulam once addressed the problem ‘when is it true that a mathematical object satisfying a certain property approximately must be close to an object satisfying the property exactly?’. This problem was solved by D. H. Hyers in 1941 using the functional equation and thereafter numerous research papers and monographs have been published for various types of functional equations in different spaces. The solution proposed by D. H. Hyers (1941) later developed into the famous generalized Hyers-Ulam-Rassias stability of functional equations. In this paper, we intend to attain the general solution to a new mixed type functional equation and interrogate the generalized Hyers–Ulam–Rassias stability in fuzzy normed spaces. Also, we seek to provide its application for generating secret keys in client–server environment.     

一类直觉模糊线性规划的求解及其应用

研究一类直觉模糊线性规划及其应用.首先,定义直觉模糊不等式,给出直觉模糊线性规划模型;然后,提出一种基于总精确函数的直觉模糊线性规划求解方法,并给出其求解步骤;最后,建立证劵投资组合的直觉模糊线性规划模型.数值算例表明了所提出理论是合理有效的.     

On the ideal convergence of sequences of fuzzy numbers

In this paper we introduce and study the concepts of I-convergence, I^∗-convergence and I-Cauchy sequence for sequences of fuzzy numbers where I denotes the ideal of subsets of N, the set of positive integers.     

Stability of Cauchy–Jensen type functional equation in generalized fuzzy normed spaces

In this paper, we establish some stability results concerning the Cauchy–Jensen functional equation in generalized fuzzy normed spaces. The results of the present paper improve and extend some recent results.     

基于直觉模糊线性方程组的IFTS 预测方法

针对模糊时间序列预测理论对不确定性数据集的实时模糊变化趋势研究存在的不足, 规范了直觉模糊时间序列的定义, 提出了基于直觉模糊线性方程组的直觉模糊时间序列预测方法. 所提出的算法将模型的求解转化为一系列带有约束的线性规划问题, 准确地反映了序列数据随时间发展变化的模糊关联规律, 简化了预测模型的复杂度, 提高了时间序列预测的精度, 扩展了直觉模糊时间序列预测理论的应用范围. 最后, 通过仿真实验验证了所提出方法的有效性和优越性.

     

基于直觉模糊Petri网的加权直觉模糊推理

利用直觉模糊集合较好地表现不确定信息的能力和Petri网的并行处理能力,构建了直觉模糊Petri网模型。给出了输入权值、变迁阈值等多种约束条件下的直觉模糊推理算法。该算法将直觉模糊推理过程转化为矩阵的运算过程可充分利用直觉模糊Petri网的并行推理能力,有效地避免同一变迁不必要地重复激发从而节省推理时间。实例分析表明所给出的直觉模糊推理算法较已有算法更加合理并且高效。     

A linear ordering on the class of Trapezoidal intuitionistic fuzzy numbers

Fuzzy numbers and intuitionistic fuzzy numbers are introduced in the literature to model problems involving incomplete and imprecise information in expert and intelligent systems. Ranking of TrIFNs plays an important role in an information system (Decision Making) with imprecise and inadequate information and the complete ranking on the class of trapezoidal intuitionistic fuzzy number is an open problem worldwide. Researchers from all over the world have been working in ranking of intuitionistic fuzzy numbers since 1985, but till date there is no common methodology that ranks any two arbitrary intuitionistic fuzzy numbers due to the partial ordering of TraIFNs. Different algorithms are available in the literature for solving intuitionistic fuzzy decision (or information system) problem, but each and every algorithm failed to give better result in some places due to the ranking procedure of TrIFNs. Intuitionistic fuzzy decision algorithm works better when it have a complete ranking procedure that ranks arbitrary intuitionistic fuzzy numbers. In this paper a linear (total) ordering on the class of trapezoidal intuitionistic fuzzy numbers using axiomatic set of eight different scores is introduced. The main idea of this paper is to classify and study the properties of eight different sub classes of the set of TrIFNs. Further new total order relations are defined on each of the subclasses of TrIFNs and they are extended to a complete ranking procedure on the set of TrIFNs. Finally the significance of the proposed method over existing methods is studied by illustrative examples.     

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.     

On intuitionistic fuzzy topologies based on intuitionistic fuzzy reflexive and transitive relations

Topologies and rough set theory are widely used in the research field of machine learning and cybernetics. An intuitionistic fuzzy rough set, which is the result of approximation of an intuitionistic fuzzy set with respect to an intuitionistic fuzzy approximation space, is an extension of fuzzy rough sets. For further studying the theories and applications of intuitionistic fuzzy rough sets, in this paper, we investigate the topological structures of intuitionistic fuzzy rough sets. We show that an intuitionistic fuzzy rough approximation space can induce an intuitionistic fuzzy topological space in the sense of Lowen if and only if the intuitionistic fuzzy relation in the approximation space is reflexive and transitive. We also examine the sufficient and necessary conditions that an intuitionistic fuzzy topological space can be associated with an intuitionistic fuzzy reflexive and transitive relation such that the induced lower and upper intuitionistic fuzzy rough approximation operators are, respectively, the intuitionistic fuzzy interior and closure operators of the given topology.     

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.     

软直觉模糊集

直觉模糊集是在模糊集上增加了一个新的属性参数：非隶属度函数,成为描述“非此非彼”的“模糊概念”的工具。为了提高决策的精确性,将软集与直觉模糊集相结合,构造了一种新的数学模型,即直觉模糊软集,对其性质进行了一些讨论。     

Prioritized intuitionistic fuzzy aggregation operators

In some multi-attribute decision making problems, distorted conclusions will be generated due to the lack of considering various relationships among the attributes of decision making. In this paper, we investigate the prioritization relationship of attributes in multi-attribute decision making with intuitionistic fuzzy information (i.e., partial or all decision information, like attribute values and weights, etc., is represented by intuitionistic fuzzy values (IFVs)). Firstly, we develop a new method for comparing two IFVs, based on which the basic intuitionistic fuzzy operations satisfy monotonicities. In addition, we devise a method to derive the weights with intuitionistic fuzzy forms, which can indicate the importance degrees of the corresponding attributes. Then we develop a prioritized intuitionistic fuzzy aggregation operator, which is motivated by the idea of the prioritized aggregation operators [R.R. Yager, Prioritized aggregation operators, International Journal of Approximate Reasoning 48 (2008) 263–274]. Furthermore, we propose an intuitionistic fuzzy basic unit monotonic (IF-BUM) function to transform the derived intuitionistic fuzzy weights into the normalized weights belonging to the unit interval. Finally, we develop a prioritized intuitionistic fuzzy ordered weighted averaging operator on the basis of the IF-BUM function and the transformed weights.     

单向S-粗直觉模糊集

针对系统具有的模糊、不确定及动态特性,基于直觉模糊集和单向S-粗集理论,提出单向S-粗直觉模糊集,给出它的结构、性质、存在背景和意义解释。分析了单向S-粗直觉模糊集与Pawlak粗集,单向S-粗模糊集以及单向S-粗集等之间的关系。     

Generalized intuitionistic fuzzy Bonferroni means

Intuitionistic fuzzy set is a widely used tool to express the membership, nonmembership, and hesitancy information of an element to a set. To aggregate the intuitionistic fuzzy information, a lot of aggregation techniques have been developed, especially, the ones which reflect the correlations of the aggregated arguments are the hot research topics, among which Bonferroni mean (BM) is an important aggregation technique. However, the classical BM ignores some aggregation information and the weight vector of the aggregated arguments. In this paper, we introduce the generalized weighted BM and the generalized intuitionistic fuzzy weighted BM, both of which focus on the group opinion. Paying more attention to the individual opinions, we further define the generalized weighted Bonferroni geometric mean and the generalized intuitionistic fuzzy weighted Bonferroni geometric mean. Various families of the existing operators can be obtained when the parameters of the developed aggregation techniques are assigned different values. Finally, we propose an approach to multicriteria decision making on the basis of the proposed aggregation techniques and an example is also given to illustrate our results. © 2011 Wiley Periodicals, Inc.