基于区间值模糊集的理想化软BCK代数

将Zadeh提出的区间值模糊集概念应用于理想化软BCK代数问题的研究。借助于BCK代数的区间值模糊理想、区间值[(∈,∈∨q)]-模糊理想和区间值[(∈,∈∨q)]-模糊理想的概念,获得了一个给定的BCK代数上的几类特殊的理想化软BCK代数的若干等价刻画。     

Some results on information measures for complex intuitionistic fuzzy sets

Complex intuitionistic fuzzy sets (CIFSs), modeled by complex-valued membership and nonmembership functions with codomain the unit disc in a complex plane, handle two-dimensional information in a single set. Under this environment, the primary objective of the present study is to introduce some novel formulae of information measures (similarity measures, distance measures, entropies, and inclusion measures) and discuss the transformation relationships among them. To demonstrate the efficiency of the proposed similarity measures, we apply it to pattern recognition problem and a detailed comparative analysis is conducted with some of the existing measures. Further, algorithms based on proposed measures are developed for handing multicriteria decision-making problems and their working is illustrated with the help of an example. Besides this, the practicality of the proposed similarity measure is demonstrated by developing a clustering algorithm under CIFS environment.     

半环上生成模糊理想及其结构

给出了半环上生成模糊理想的概念并且讨论了生成模糊理想的与格相关性质,得到了令人满意的结果。     

New results about the centroid of an interval type-2 fuzzy set, including the centroid of a fuzzy granule

The centroid of an interval type-2 fuzzy set (IT2 FS) provides a measure of the uncertainty of such a FS. Its calculation is very widely used in interval type-2 fuzzy logic systems. In this paper, we present properties about the centroid of an IT2 FS. We also illustrate many of the general results for a T2 fuzzy granule (FG) in order to develop some understanding about the uncertainty of the FG in terms of its vertical and horizontal dimensions. At present, the T2 FG is the only IT2 FS for which it is possible to obtain closed-form formulas for the centroid, and those formulas are in this paper.     

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.     

Some remarks on fuzzy graphs

We show that a fuzzy group can be associated with a fuzzy graph in a natural way. Some properties of fuzzy graphs are considered and we introduce the notions of eccentricity and center. Our examples indicate that results from (crisp) graph theory do not always have analogs for fuzzy graphs.     

Goguen's contributions to fuzzy logic in retrospect

ABSTRACT

In the very early stage of the development of fuzzy logic, Joseph Goguen published profound work with lasting influence. Fifty years later, we provide an assessment of his contributions to fuzzy logic and thus pay tribute to Goguen, a former long-term member of the editorial board of this journal. We cover both Goguen's technical results, the research directions inspired by him, which have later been pursued, as well as his suggestions, which as yet remained explored to a lesser extent or practically unexplored.     

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.     

Soft rough fuzzy sets and soft fuzzy rough sets

Fuzzy set theory, soft set theory and rough set theory are mathematical tools for dealing with uncertainties and are closely related. Feng et al. introduced the notions of rough soft set, soft rough set and soft rough fuzzy set by combining fuzzy set, rough set and soft set all together. This paper is devoted to the further discussion of the combinations of fuzzy set, rough set and soft set. A new soft rough set model is proposed and its properties are derived. Furthermore, fuzzy soft set is employed to granulate the universe of discourse and a more general model called soft fuzzy rough set is established. The lower and upper approximation operators are presented and their related properties are surveyed.     

Lattice structure on some fuzzy algebraic systems

In this paper, we study the lattice structure of some fuzzy algebraic systems such as (G-)fuzzy groups, some fuzzy ordered algebras and fuzzy hyperstructures. We prove that under suitable conditions, these structures form a distributive or modular lattice. This research partially is supported by the “ Fuzzy Systems and its Applications Center of Excelence, Shahid Bahonar University of Kerman, Iran”.     

Comparison results for fuzzy differential equations

In this paper, we present several comparison results for the solutions of fuzzy differential equations, by using the Hukuhara derivative. These results constitute the extension to the fuzzy context of some comparison results for the solutions of linear differential equations. Besides, some side-results about the Hukuhara difference and the partial orderings are given. We illustrate the applicability of the new results by showing several examples.     

Alternative characterizations for the representation of families of sets by fuzzy sets

We investigate the representation of a given family of sets by a fuzzy set in such a way that the level sets of the fuzzy set are precisely the given sets. This concept of representation is widely used in the literature for the classification and study of fuzzy structures on the same underlying set. Negoita and Ralescu obtained two theorems, both giving necessary and sufficient conditions, one called the representation theorem and the second called the generalized representation theorem. Our aim in this paper is to take a closer look at both theorems, hence establishing some equivalent forms and several constructive remarks, including some directions for future investigations.     

Sine-square embedded fuzzy sets versus type-2 fuzzy sets

The uncertainty is an inherent part of real-world applications. Type-2 fuzzy sets minimize the effects of uncertainties that cannot be modeled using type-1 fuzzy sets. However, the computational complexity of the type-2 fuzzy sets is very high and it is more difficult than type-1 fuzzy sets to use and understand. This paper proposes sine-square embedded fuzzy sets and gives a comparison with type-2 and nonstationary fuzzy sets. The sine-square embedded fuzzy sets consist of type-1 fuzzy sets and the sine function. The footprint of uncertainty in the type-2 fuzzy sets is provided with amplitude and frequency of sine-square function in the proposed algorithm. The proposed sine-square embedded fuzzy sets are much simpler than the type-2 fuzzy sets and the nonstationary fuzzy sets. Two control applications that are chosen as position control of a dc motor and simulation of human lifting motion using five-segment human model are carried out to demonstrate the effectiveness of the proposed approach.     

Improved method of multicriteria fuzzy decision-making based on vague sets

An improved method is presented, which provides improved score functions to measure the degree of suitability of each of a set of alternatives, with respect to a set of criteria presented with vague values. The improved algorithm for score functions is introduced by taking into account the effect of an unknown degree (hesitancy degree) of the vague values on the degree of suitability to which each alternative satisfies the decision-maker’s requirement. The meaning of the proposed function is more transparent than that of other existing functions, which are not reasonable in some cases. The proposed function illustrates that it has stronger discrimination in comparison with previous functions. The applicability of this improved multicriteria fuzzy decision-making approach is also demonstrated by means of examples. The improved method can be used to rank the decision alternatives according to the decision criteria. The functions proposed in this paper can provide a more useful technique than previous functions, in order to efficiently help the decision-maker.     

一种扩展的条件模糊C-均值聚类算法

在综合分析标准的模糊C-均值聚类算法和条件模糊C-均值聚类算法基础上,对模糊划分空间进行修改,进一步弱化模糊划分矩阵的约束,给出一种扩展的条件模糊C-均值聚类算法。算法的划分矩阵和原型不依赖于背景约束及模糊划分矩阵的隶属度总和。实验结果表明：该算法可以得到不同的聚类原型,并具有很好的聚类效果。     

Intuitionistic fuzzy soft modules

Molodtsov (1999) initiated the concept of soft sets in [1]. Maji et al. (2003) defined some operations on soft sets in [22]. Akta? and Ça?man (2007) generalized soft sets by defining the concept of soft groups in [16]. After them, Sun et al. (2008) gave soft modules in [21]. In this paper, the concept of an intuitionistic fuzzy soft module is introduced and some operations on intuitionistic fuzzy soft sets are given. Finally, some of its basic properties are studied.     

Robustness of interval-valued fuzzy inference

Since interval-valued fuzzy set intuitively addresses not only vagueness (lack of sharp class boundaries) but also a feature of uncertainty (lack of information), interval-valued fuzzy reasoning plays a vital role in intelligent systems including fuzzy control, classification, expert systems, and so on. To utilize interval-valued fuzzy inference better, it is very important to study the fundamental properties of interval-valued fuzzy inference such as robustness. In this paper, we first discuss the robustness of interval-valued fuzzy connectives. And then investigate the robustness of interval-valued fuzzy reasoning in terms of the sensitivity of interval-valued fuzzy connectives and maximum perturbation of interval-valued fuzzy sets. These results reveal that the robustness of interval-valued fuzzy reasoning is directly linked to the selection of interval-valued fuzzy connectives.     

Lattice-valued approach to closed sets under fuzzy relations: Theory and applications

Motivated by fuzzy control problems and by some investigations of eigen fuzzy sets, we deal with a closedness of fuzzy sets under fuzzy relations in two ways: in one sense by directly analyzing fuzzy concepts and in the other by investigating the corresponding crisp problems in the cutworthy framework. Our main task is to investigate particular fuzzy functional equations and inequations appearing in this context, which turn out to be essentially connected with fuzzy control problems. We analyze procedures and find solutions of these equations and inequations, pointing to important applications.     

模糊多准则决策方法研究综述

模糊多准则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.为此,介绍了基于模糊数、直觉模糊集和Vague集的多准则决策方法和语言多准则决策方法的研究现状,定义了直觉梯形模糊数和区间直觉梯形模糊数,扩展了模糊数和直觉模糊集.最后探讨了目前模糊多准则决策要解决的问题和发展方向.