Fuzzy strongly pre-irresolute functions

We have introduced and studied a new class of fuzzy irresolute functions, called fuzzy strongly pre-irresolute functions, by using fuzzy preopen sets.     

效应代数的(η,γ]-模糊滤子

在Lu D L和Wang G J提出效应代数中模糊滤子(简称LW-模糊滤子)概念的富有成效的工作基础上,利用模糊点与模糊集的属于与重于关系给出了一种新的模糊滤子——(η,γ]-模糊滤子的定义,指出LW-模糊滤子、(∈,∈Vq)-模糊滤子和(∈,∈Vq)-模糊滤子是它的三个特例,获得了这些模糊滤子的等价刻画.     

小波分析与模糊系统分析的联系

讨论小波基函数与模糊集隶属函数之间的联系 ,证明模糊系统研究与应用中的隶属函数都可以由称之为简单小波的母函数表出 ,反之每一简单小波也可以由某一隶属函数表出 ,从而验证简单小波类与某一隶属函数类的一一对应关系。该结果进一步揭示模糊推理和模糊控制的实质 ,为在模糊系统辨识、模糊控制和模糊数据分析等诸多领域充分利用近代小波分析的成果提供新思路     

区间直觉模糊集多属性决策方法

定义了区间直觉模糊集的加权算子和加权几何集成算子,介绍了现有的区间直觉模糊集的得分函数和精确函数.定义了一个新的精确函数,此函数弥补了已有函数的不足和缺陷,应用新定义的精确函数,提出了对区间直觉模糊集多属性决策问题进行决策的方法.最后以应用实例对该方法进行说明和验证.     

On intutionistic fuzzy gpr-closed sets

In this paper, a new class of intuitionistic fuzzy closed sets called intuitionistic fuzzy generalized preregular closed sets (briefly intuitionistic fuzzy gpr-closed sets) and intuitionistic fuzzy generalized preregular open sets (briefly intuitionistic fuzzy gpr-open sets) are introduced and their properties are studied. Further the notion of intuitionistic fuzzy preregular T _1/2-spaces and intuitionistic fuzzy generalized preregular continuity (briefly intuitionistic fuzzy gpr-continuity) are introduced and studied.     

基于综合函数设计的模糊系统及其插值机理

分析现有模糊系统的数学表示形式,注意到模糊系统输出函数的构造常采用对规则后件模糊集峰点(中心)值加权平均的方法. 综合函数是因素空间理论中利用简单因素状态合成复杂因素状态的有效工具, 本文将综合函数用于构造规则后件模糊集峰点(中心)值的权重, 给出一种新的模糊系统设计方法, 并且证明了这种基于综合函数的模糊系统可归结为一种插值函数.     

Ranking fuzzy quantities based on the angle of the reference functions

Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, each proposed method may has some shortcoming. So we are going to present a novel method based on the angle of the reference functions to cover a wide range of fuzzy quantities by over coming the draw backs of some existing methods. In the mentioned firstly, the angle between the left and right membership functions (the reference functions) of every fuzzy set is called Angle of Fuzzy Set (AFS), and then in order to extend ranking of two fuzzy sets the angle of fuzzy sets and α-cuts is used. The method is illustrated by some numerical examples and in particular the results of ranking by the proposed method and some common and existing methods for ranking fuzzy sets is compared to verify the advantage of the new approach. In particular, based on the results of comparison of our method with well known methods which are exist in the literature, we will see that against of most existing ranking approaches, our proposed approach can rank fuzzy numbers that have the same mode and symmetric spreads. In fact, the proposed method in this paper can effectively rank symmetric fuzzy numbers as well as the effective methods which are appeared in the literature. Moreover, unlike of most existing ranking approaches, our proposed approach can rank non-normal fuzzy sets. Finally, we emphasize that the concept of fuzzy ordering is one of key role in establishing the numerical algorithms in operations research such as fuzzy primal simplex algorithms, fuzzy dual simplex algorithms and as well as discussed in the works of Ebrahimnejad and Nasseri and coworkers , , , , ,  and .     

几类广义模糊集的关系

经过近五十年的发展,模糊集在理论与应用两个领域的研究都已经取得长足的进展,特别地,在模糊决策等应用领域,涌现了几类重要的广义模糊集,包括区间值模糊集,直觉模糊集,区间值直觉模糊集,II型模糊集,Vague集,灰集等。本文简要介绍关于这些广义模糊集之间关系的研究成果,以及国外关于直觉模糊集术语问题的争议。     

Robust fuzzy rough classifiers

Fuzzy rough sets, generalized from Pawlak's rough sets, were introduced for dealing with continuous or fuzzy data. This model has been widely discussed and applied these years. It is shown that the model of fuzzy rough sets is sensitive to noisy samples, especially sensitive to mislabeled samples. As data are usually contaminated with noise in practice, a robust model is desirable. We introduce a new model of fuzzy rough set model, called soft fuzzy rough sets, and design a robust classification algorithm based on the model. Experimental results show the effectiveness of the proposed algorithm.     

New operations over hesitant fuzzy sets

Hesitant fuzzy sets are considered to be the way to characterize vague phenomenon. Their study has opened a new area of research and applications. Set operations on them lead to a number of properties of these sets which are not evident in classical (crisp) sets make the area mathematically also very productive. Since these sets are defined in terms of functions and set of functions, which is not the case when the sets are crisp, it is possible to define several set operations. Such a study enriches the use of these sets. In this paper, four new operations are envisaged, defined and taken up to study a score of new identities on hesitant fuzzy sets.     

Convex-cone-based comparisons of and difference evaluations for fuzzy sets

Abstract

This paper focuses on how to compare two fuzzy sets and, from the viewpoint of set optimization, proposes eight types of fuzzy-set relations based on a convex cone as new comparison criteria of fuzzy sets. Then, difference evaluation functions for fuzzy sets are introduced. Under suitable assumptions of certain compactness and stability of fuzzy sets, we show that these functions correspond well to the fuzzy-set relations. In addition, through transforming these functions stepwise, we deal with numerical calculation methods of them in particular cases. Consequently, we can judge whether each fuzzy-set relation holds or not for given two fuzzy sets with the aid of computers.     

几种新的截集及其应用

本文从“邻域”和“重域”的观点出发引入了三种新的截集：下截集，下重截集和上重截集。我们给出这些截集的性质及相应的分解定理，表现定理和扩展原理，作为应用，我们讨论了两方面的内容；一是利用落影表现理论，将一个模糊集看作“重云”的落影，然后用下生截集和落影表现理论来定义模糊集的运算，得到了与“２”一致的结果。     

Multifactorial fuzzy sets and multifactorial degree of nearness

Two new concepts, Multifactorial fuzzy sets and multifactorial degree of nearness, are advanced. First, an axiomatic definition for multifactorial functions is given, and multifactorial fuzzy sets and multifactorial degree of nearness are defined by using the multifactorial function. Second, three direct methods of multifactorial pattern recognition and two methods for fuzzy clustering with fuzzy characteristics are given. Last, we advance an interesting open problem.     

Additive fuzzy measures and integrals I

A point of view concerning “fuzzy measures” is explained. To this end, a new concept of “disjointness” for fuzzy is introduced and studied. Also, a concept of an “additive class of fuzzy sets” is defined to be a class of fuzzy sets closed under some “additive operations.” The fuzzy measures are defined to be sum-preserving real functions over such additive classes. Some basic properties of the fuzzy measures are derived. In contrast with other homonymous concepts studied in literature, our fuzzy measures lead to an additive fuzzy integral (see the part II of the paper).     

Derivatives and differentials for multiplicative intuitionistic fuzzy information

By using the unsymmetrical scale instead of the symmetrical scale, the multiplicative intuitionistic fuzzy sets (MIFSs) reflect our intuition more objectively. Each element in a MIFS is expressed by an ordered pair which is called a multiplicative intuitionistic fuzzy number (MIFN) and is based on the unbalanced scale (i.e., Saaty’s 1-9 scale). In order to describe the derivatives and differentials for multiplicative intuitionistic fuzzy information more comprehensively, in this paper, we firstly propose two new basic operational laws for MIFNs, which are the subtraction law and the division law. Secondly, we describe the change values of MIFNs when considering them as variables, classify these change values based on the basic operational laws for MIFNs, and depict the convergences of sequences of MIFNs by the subtraction and division laws. Finally, we focus on the multiplicative intuitionistic fuzzy functions and derive some basic results related to their continuities, derivatives and differentials, and also give their application in selecting the configuration of a computer.     

Multi-attribute decision making based on a novel IF point operator

Intuitionistic fuzzy (IF) point operators transform an intuitionistic fuzzy set to a fuzzy set, or an intuitionistic fuzzy set with a smaller degree of hesitance. The purpose of which is to empower the operations of intuitionistic fuzzy sets with traditional fuzzy set methodologies. In the present paper, a new IF point operator is proposed. Different from the existing IF point operators, the new approach includes two parametric functions with respect to the number of iterations. It is proved that the newly proposed method could be degenerated to the traditional IF point operators. Meanwhile, the new IF point operator can extend our horizons in the exploration of the relationship between fuzzy sets and intuitionistic fuzzy sets. Specifically, a special case of the new IF point operator would be entitled as the memoryless multi-stage voting method, with which the decision makers are assumed to be affected only by the outcomes of the latest round of voting. It is proved that the memoryless multi-stage voting method converges to the limit produced by the infinite number of iterations much faster than the traditional voting method. Furthermore, a numerical example is employed to demonstrate the validity and performance of the memoryless multi-stage voting approach.     

Different generalizations of bags

We consider four different generalizations of bags (alias multisets). We first discuss Yager’s fuzzy bags having different sets of operations. It is shown that one is not a generalization of fuzzy sets but a mapping of them into fuzzy bags, since operations are inconsistent between the two, while the other includes fuzzy sets as particular cases. Third type is called real-valued bags which is simpler than the former two and is a kind of the reduction of fuzzy bags. Finally, the fourth generalization called G-bags includes all three except the first type. It is a minimal extension of the second and the third generalizations. Bag relations are defined for the third type of real-valued bags, which can further be generalized for G-bags.     

A family of skew Hadamard difference sets

In 1933 a family of skew Hadamard difference sets was described by Paley using matrix language and was called the Paley-Hadamard difference sets in the literature. During the last 70 years, no new skew Hadamard difference sets were found. It was conjectured that there are no further examples of skew Hadamard difference sets. This conjecture was proved to be true for the cyclic case in 1954, and further progress in favor of this conjecture was made in the past 50 years. However, the conjecture remains open until today. In this paper, we present a family of new perfect nonlinear (also called planar) functions, and construct a family of skew Hadamard difference sets using these perfect nonlinear functions. We show that some of the skew Hadamard difference sets presented in this paper are inequivalent to the Paley-Hadamard difference sets. These new examples of skew Hadamard difference sets discovered 70 years after the Paley construction disprove the longstanding conjecture on skew Hadamard difference sets. The class of new perfect nonlinear functions has applications in cryptography, coding theory, and combinatorics.     

模糊集单调型分解定理

模糊集的分解集定理有两种形式，第一种形式与模糊集的λ—截集有关：Ａ＝其中Ａ＿λ是的λ—截集￣［１］．第二种形式与集合套有关：其中Ｈ（λ）为集合套￣［２］或者Ａ＝其中Ｈ（λ）为集合套，Ｑ为（０，１）的可列稠密子集＿［３］，．其实，这两种形式在本文提出的基本模糊集的概念下，可以统一起来成为任何模糊集可以分解为一些（可数或不可数）基本模糊集的和。不仅如此，本文还提出简单模糊集的概念，并证明了任何模糊集都可以表示成为可数个单调上升的简单模糊集的和，或等价地，可以表示成可数个单调上升的简单模糊集的极限，所用的证明方法是构造性的，所以对模糊集的结构也得出了一个清晰的认识．     

模糊软P-超群

把模糊软集理论应用到P-超群,引入了(∈γ,∈γVqδ)-模糊软P-超群和正规(∈γ,∈γVqδ)-模糊软P-超群的概念,并研究了其性质.