Image fusion using intuitionistic fuzzy sets

Image fusion is the process of combining one or more images which are obtained from different environment into a single image which is more useful for further image processing tasks. Image registration and image fusion are of great importance in defence and civilian sectors, particularly for recognizing a ground/air force vehicle and medical imaging. In this paper a new way is drawn to fuse two or more images by using maximum, minimum operations in intuitionistic fuzzy sets (IFSs). IFSs are more suitable for image processing since every digital image have lot of uncertainties. In processing phase, images are reformed into intuitionistic fuzzy images (IFIs). Entropy is employed to obtain the optimum value of the parameter in membership and non-membership function. Then the resulting IFIs are disintegrated into image blocks and the corresponding blocks of the images are reunioned by finding the count of blackness and whiteness of the blocks. This paper evaluates the performance of simple averaging (AVG), principal component analysis (PCA), discrete wavelet transform (DWT), stationary wavelet transform (SWT), dual tree complex wavelet transform (DTCWT), multi-resolution singular value decomposition (MSVD), nonsubsampled contourlet transform (NSCT) and IFS (proposed method) in terms of various performance measure. The experimental and comparison results show that luminance and contrast is of great importance for image processing and prove that the proposed method is better than all other methods.     

直觉模糊集的聚类方法研究

对基于直觉模糊集的聚类问题进行了研究．首先给出直觉模糊相似度的概念,并构建了直觉模糊相似矩阵和直觉模糊等价矩阵;然后定义了直觉模糊相似矩阵的合成运算法则．给出直觉模糊相似矩阵转化为直觉模糊等价矩阵的途径;此外．还分别定义了直觉模糊相似矩阵和直觉模糊等价矩阵的λ-截矩阵,进而给出了直觉模糊集的一种聚类方法;最后通过算例对该方法进行了说明和分析．     

基于直觉模糊三角模的直觉模糊粗糙集

提出一种基于直觉模糊三角模的直觉模糊粗糙集.首先,定义了直觉模糊集上的T模及其剩余蕴涵,研究了直觉模糊T模的剩余蕴涵的性质,并推导了通用计算表达式;然后,将模糊T粗糙集扩展成直觉模糊粗糙集,证明了模糊T粗糙集、粗糙模糊集和Pawlak粗糙集都是直觉模糊粗糙集的特殊情形;最后,证明了直觉模糊粗糙集的一些性质.     

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.     

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.     

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.     

Personnel selection based on intuitionistic fuzzy sets

One of the most important activities carried out by human resource management is personnel selection, concerned with identifying an individual from a pool of candidates suitable for a vacant position. Traditionally, personnel selection is a group decision‐making problem under multiple criteria containing subjectivity, imprecision, and vagueness, which are best represented with fuzzy data. In this article, the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS) method extended to intuitionistic fuzzy environments is proposed to select appropriate personnel among candidates. An intuitionistic fuzzy set (IFS), which is characterized by membership function, nonmembership function, and hesitation margin, is a more suitable way to deal with vagueness when compared to a fuzzy set. To demonstrate the applicability and effectiveness of the intuitionistic fuzzy TOPSIS method, a numerical example of personnel selection in a manufacturing company for a sales manager position is given. © 2011 Wiley Periodicals, Inc.     

一种基于直觉模糊集相似度的多属性决策方法

直觉模糊集（ＩＦＳ）是对模糊集理论的一种扩充,能更好地处理模糊概念．首先给出一种新的直觉模糊集相似度;然后提出基于直觉模糊集相似度的多属性决策方法;最后通过线性目标规划模型和直觉模糊集相似度,得到属性的最优权重和相应的方案排序．数值实例表明,该方法是有效而可行的．     

Segmentation of gray scale image based on intuitionistic fuzzy sets constructed from several membership functions

Segmentation is the process of extraction of objects from an image. This paper proposes a new algorithm to construct intuitionistic fuzzy set (IFS) from multiple fuzzy sets as an application to image segmentation. Hesitation degree in IFS is formulated as the degree of ignorance (due to the lack of knowledge) to determine whether the chosen membership function is best for image segmentation. By minimizing entropy of IFS generated from various fuzzy sets, an image is thresholded. Experimental results are provided to show the effectiveness of the proposed method.     

基于直觉模糊粗糙集的属性约简

针对Jensen下近似定义的局限性,提出一种新的等价类形式的近似算子表示,并将其推广到直觉模糊环境.在此基础上,将相对正域、相对约简、相对核等粗糙集的知识约简概念推广到直觉模糊环境,提出一种直觉模糊信息系统的启发式属性约筒算法.实例计算表明.该方法比Jensen的属性约简方法更为合理有效.     

Clustering algorithm for intuitionistic fuzzy sets

The intuitionistic fuzzy set (IFS) theory, originated by Atanassov [K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986) 87-96], has been used in a wide range of applications, such as logic programming, medical diagnosis, pattern recognition, and decision making, etc. However, so far there has been little investigation of the clustering techniques of IFSs. In this paper, we define the concepts of association matrix and equivalent association matrix, and introduce some methods for calculating the association coefficients of IFSs. Then, we propose a clustering algorithm for IFSs. The algorithm uses the association coefficients of IFSs to construct an association matrix, and utilizes a procedure to transform it into an equivalent association matrix. The λ-cutting matrix of the equivalent association matrix is used to cluster the given IFSs. Moreover, we extend the algorithm to cluster interval-valued intuitionistic fuzzy sets (IVIFSs), and finally, demonstrate the effectiveness of our clustering algorithm by experimental results.     

A novel approach to multi-attribute decision making based on intuitionistic fuzzy sets

In this paper we present a new approach to solve multi-attribute decision making problems in intuitionistic fuzzy environment. This approach is based on a new ranking method of intuitionistic fuzzy sets, in which the evaluated values (in the form of intervals) of the same alternative with different attributes are considered as one unified entity. According to people’s intuition, the ranking method proposed in this paper is mainly grounded on a revised score function and a revised accuracy function of intuitionistic fuzzy sets. Different from the traditional methods, in this new approach, the degree of membership, the degree of nonmembership and the degree of hesitation are considered with various importance in reflecting the true image of the respective alternative. Furthermore, an optimization model is established to estimate the relative degree of importance of each quantity. Finally, two practical examples are provided to illustrate our approach.     

On the J-divergence of intuitionistic fuzzy sets with its application to pattern recognition

The importance of suitable distance measures between intuitionistic fuzzy sets (IFSs) arises because of the role they play in the inference problem. A concept closely related to one of distance measures is a divergence measure based on the idea of information-theoretic entropy that was first introduced in communication theory by Shannon (1949). It is known that J-divergence is an important family of divergences. In this paper, we construct J-divergence between IFSs. The proposed J-divergence can induce some useful distance and similarity measures between IFSs. Numerical examples demonstrate that the proposed measures perform well in clustering and pattern recognition.     

On possible and necessary inclusion of intuitionistic fuzzy sets

The problem of measuring the degree of inclusion for two intuitionistic fuzzy sets (IF-sets) is considered. Since the nature of IF-sets includes uncertainty expressed both by the membership and nonmembership functions, this very feature should be also regarded in the construction of the subsethood measures. Therefore, we suggest not a single coefficient measuring the grade of subsethood but two indicators that leave some space to the mentioned uncertainty and correspond rather to necessary and possible inclusion.     

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.     

Choquet integrals of weighted intuitionistic fuzzy information

The Choquet integral is a very useful way of measuring the expected utility of an uncertain event [G. Choquet, Theory of capacities, Annales de l’institut Fourier 5 (1953) 131-295]. In this paper, we use the Choquet integral to propose some intuitionistic fuzzy aggregation operators. The operators not only consider the importance of the elements or their ordered positions, but also can reflect the correlations among the elements or their ordered positions. It is worth pointing out that most of the existing intuitionistic fuzzy aggregation operators are special cases of our operators. Moreover, we propose the interval-valued intuitionistic fuzzy correlated averaging operator and the interval-valued intuitionistic fuzzy correlated geometric operator to aggregate interval-valued intuitionistic fuzzy information, and apply them to a practical decision-making problem involving the prioritization of information technology improvement projects.     

基于加权直觉模糊集合的聚类模型

针对已有基于直觉模糊集的聚类方法的局限性,提出了一种基于加权直觉模糊集合的聚类模型——WIFSCM。在该模型中,提出了特定特征空间下的等价样本和加权直觉模糊集合的概念;并推导出基于等价样本和加权直觉模糊集合的直觉模糊聚类算法的目标函数,利用该目标函数推导出直觉模糊聚类中心迭代算法和隶属度矩阵迭代算法;定义了基于加权直觉模糊集合的密度函数,确定了初始聚类中心,减少了迭代次数。通过灰度图像分割实验,证明了该模型的有效性,同时与普通直觉模糊集FCM聚类算法(IFCM)相比,聚类速度提高近百倍。     

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).     

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。     

Generalized intuitionistic fuzzy soft sets with applications in decision-making

The concept of intuitionistic fuzzy soft set (IFSS) arising from intuitionistic fuzzy set (IFS) is generalized by including a parameter reflecting a moderator's opinion about the validity of the information provided. The resulting generalized intuitionistic fuzzy soft set (GIFSS) finds a special role in the decision making applications. It can evaluate the given criteria along with the moderator's assessment of the furnished data. The properties of GIFSS are investigated and the associated relations called generalized intuitionistic fuzzy soft relations (GIFSR) are given. A similarity measure is given to compare two GIFSSs. As this is not applicable to fuzzy numbers, a new score function is devised to compare two intuitionistic fuzzy numbers (IFNs), the components of IFS. The effectiveness of the proposed GIFSS in decision making is demonstrated on four case studies.