General Chebyshev type inequalities for universal integral

A new inequality for the universal integral on abstract spaces is obtained in a rather general form. As two corollaries, Minkowski’s and Chebyshev’s type inequalities for the universal integral are obtained. The main results of this paper generalize some previous results obtained for special fuzzy integrals, e.g., Choquet and Sugeno integrals. Furthermore, related inequalities for seminormed integral are obtained.     

On equivalence classes of fuzzy connectives-the case of fuzzyintegrals

An equivalence relation between connectives (or operators) in the framework of multiple criteria decision-making is introduced. Two operators are said to be equivalent if they lead to the same ranking of alternatives. Some general results to find equivalence classes of operators are given through the concept of level surfaces. In a second part, these results are applied to the case of discrete fuzzy integrals, which are considered here as n-place operators. First, some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals     

Non-dominance and attitudinal prioritisation methods for intuitionistic and interval-valued intuitionistic fuzzy preference relations

A novel intuitionistic fuzzy set (IFS) score function and an intuitionistic fuzzy preference relation (IFPR) quantifier guided non-dominance based prioritisation method are introduced. Based on Yager’s continuous OWA (COWA) operator, the interval-valued intuitionistic fuzzy COWA (IVIF-COWA) operator is defined, and a new attitudinal expected score function for interval-valued intuitionistic fuzzy numbers (IVIFNs) is introduced. The novelty of this attitudinal expected score function is that it allows the comparison of IVIFNs by taking into account of the decision makers’ attitudinal character. Moreover, we show that the new attitudinal expected score function extends: (i) the IFS score function introduced in this paper, which is mathematically equivalent to Chen and Tan’s score function (Chen and Tan, 1994); and (ii) Xu and Chen’s score function for IVIFNs (Xu and Chen, 2007). Using the proposed score functions, a method is developed to construct FPRs from a given IFPR and IVIFPR, respectively. When the hesitancy degree function is null, we prove that the score FPRs coincide with their respective IFPR and IVIFPR. Finally, a ranking sensitivity analysis of the attitudinal expected score function with respect to the attitudinal parameter is provided.     

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.     

Simplified interval-valued intuitionistic fuzzy integrals and their use in park siting

The interval-valued intuitionistic fuzzy sets have received great attention of researchers because they can comprehensively depict the characters of things. In the past few years, some scholars have investigated the calculus of intuitionistic fuzzy information, but yet there is no research on the integrals in interval-valued intuitionistic fuzzy circumstance. To fill this vacancy, in this paper, we shall focus on investigating the integrals of simplified interval-valued intuitionistic fuzzy functions (SIVIFFs) and give their application in group decision making. We first develop the indefinite and definite integrals of SIVIFFs, and study their characteristics in detail. Then we establish the relationship between these two classes of integrals by giving two Newton–Leibniz formulas for SIVIFFs. Finally, a practical example concerning the park siting problem is given to illustrate the application of simplified interval-valued intuitionistic fuzzy integrals.     

On set-valued fuzzy measures

So far, there have been many discussions on Sugeno’s fuzzy measures and fuzzy integrals, but most of them are concentrated on single-valued functions. Motivated by Aumann’s set-valued integral [J. Math. Anal. Appl. 12 (1965) 1], we have introduced the fuzzy integral of set-valued functions [Fuzzy Sets Syst. 56 (1993) 237; Fuzzy Sets Syst. 76 (1995) 365; Fuzzy Sets Syst. 78 (1996) 341; Ph.D. Dissertation, Harbin Institute of Technology, 1998]. It is a well-behaved extension of fuzzy integrals of single-valued functions. It is well known that Arstein’s set-valued measure [Trans. Am. Math. Soc. 165 (1972) 103] is an important branch in set-valued analysis [Set-valued Analysis, Birkhauser, Berlin, 1990] or theory of correspondences [Theory of Correspondences, Wiley, New York, 1984]. Compared to it, the present paper will try to establish the basic idea of set-valued fuzzy measures, which are monotone set-valued set-functions. It is also a natural generalization of (single-valued) fuzzy measures, as well as an extension of set-valued measures in the case of one-dimension. These works include the concept of set-valued fuzzy measures, set-valued fuzzy measures defined by set-valued fuzzy integrals and set-valued pseudo-additive measures. It can be viewed as a continuation of previous work [Fuzzy Sets Syst. 56 (1993) 237; Fuzzy Sets Syst. 76 (1995) 365; Fuzzy Sets Syst. 78 (1996) 341].     

Hierarchical TS fuzzy system and its universal approximation

An efficient tool to deal with the ‘rule explosion’ problem is the hierarchical system by which a fuzzy system can be decomposed into a number of hierarchically connected low-dimensional systems. In this paper a generalized hierarchical Tagaki–Sugeno (TS) system is built. It is shown that the input–output (I/O) relationship of this generalized hierarchical system can be represented as one of a standard TS fuzzy system. And the system approximation capability is analyzed by taking piecewise linear functions as a bridge. By constructive method it is proven that the hierarchical fuzzy systems (HFS’s) can be universal approximators. For the given approximation accuracy, an estimation formula about the number of the rules needed in the HFS is established. Finally some simulation examples confirm that the HFS’s with smaller size rule base can approximate the given functions with high accuracy. The results obtained here provide us with the theoretical basis for various applications of HFS’s.     

Comparing expressibility of normed BPA and normed BPP processes

We present an exact characterization of those transition systems which can be equivalently (up to bisimilarity) defined by the syntax of normed BPA and normed BPP processes. We give such a characterization for the subclasses of normed BPA and normed BPP processes as well. Next we demonstrate the decidability of the problem whether for a given normed BPA process there is some unspecified normed BPP process such that and are bisimilar. The algorithm is polynomial. Furthermore, we show that if the answer to the previous question is positive, then (an example of) the process is effectively constructible. Analogous algorithms are provided for normed BPP processes. Simplified versions of the mentioned algorithms which work for normed BPA and normed BPP are given too. As a simple consequence we obtain the decidability of bisimilarity in the union of normed BPA and normed BPP processes. Received: 3 June 1997     

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.     

改进径向基函数神经网及其在手写体字符识别中的应用

提出一种基于半模型矢量量化（ＳＦＶＱ）技术的改进径向基函数神经网（ＩＲＢＦＮＮ）分类器,并且用于无约束手写体数字的识别。作者在模糊聚类和矢量量化的基础上利用半模糊的思想提出了半模糊矢量量化算法,并在其中加入了有监督的控制,从而使系统在聚类过程中可以确定比较合适的类别数并使聚类结果能更好地反映训练集的概率分布。以半模糊矢量量化作为预处理的改进ＲＢＦ网,应用了多尺度补偿等办法,能够充分利用训练样本集的     

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.     

赋范格H蕴涵代数和模糊格H蕴涵代数

在范数的条件下扩充了格H蕴涵代数的概念,即赋范格H蕴涵代数,并讨论一些性质。然后将模糊集合论运用于赋范格H蕴涵代数,给出了模糊赋范格H蕴涵代数的定义,得到了一些基本性质。通过使用两个赋范格H蕴涵代数之间的映射定义了赋范格H蕴涵代数同态,且得到了一些性质。最后得到了在赋范格H蕴涵代数中的数列对于蕴涵距离是有界的结论。     

A model of human evaluation process using fuzzy measure

This paper presents a mathematical model for the human subjective evaluation process using fuzzy integrals based on the general fuzzy measure. First, the concept of overlap coefficient is introduced to describe the properties of a given fuzzy measure and to characterize the human evaluation process. Further, a new algorithm is developed to identify the fuzzy measure with full degrees of freedom. Lastly, the model and the identification scheme are applied to two practical examples: prediction of wood strength by an experienced inspector and trouble evasive actions taken by a computer game player.     

Ranking of System Elements Based on Fuzzy Relation of Influence and Transitive Closure

The author proposes a method of elements ranking in multi-functional system using the fuzzy relations theory. The problem is formulated as an automatic classification based on the transitive closure of the fuzzy similarity relation. The original information about the system is given as a fuzzy relation of influence of elements’ failures on the performance of system’s functions. To calculate the degrees of element’s influence on the functions performance, we use the comparison of all influences with the least influence by 9-point Saaty scale. The proposed method relaxes the assumption about the independence and the binary-state (up-down) of elements. The possible fields of application are multi-functional systems with ill-defined structures such as organizational, ergatic, military, etc.     

Fuzzy measures and integrals defined on algebras of fuzzy subsets over complete residuated lattices

This paper presents basic notions about fuzzy measures over algebras of fuzzy subsets of a fuzzy set. It also presents basic ideas on fuzzy integrals defined using these fuzzy measures. Definitions of new types of fuzzy measures and integrals are motivated by our research on generalized quantifiers. Several useful properties of fuzzy measures and fuzzy integrals are stated and proved. Definitions presented in this paper and its results will be employed in subsequent papers on generalized quantifiers defined using this type of fuzzy integral.     

Sugeno integral generalization applied to improve adaptive image binarization

Classic adaptive binarization methodologies threshold pixels intensity with respect to adjacent pixels exploiting integral images. In turn, integral images are generally computed optimally by using the summed-area-table algorithm (SAT). This document presents a new adaptive binarization technique based on fuzzy integral images. Which, in turn, this technique is supported by an efficient design of a modified SAT for generalized Sugeno fuzzy integrals. We define this methodology as FLAT (Fuzzy Local Adaptive Thresholding). Experimental results show that the proposed methodology produced a better image quality thresholding than well-known global and local thresholding algorithms. We proposed new generalizations of different fuzzy integrals to improve existing results and reaching an accuracy $\approx 0.94$ on a wide dataset. Moreover, due to high performances, these new generalized Sugeno fuzzy integrals created ad hoc for adaptive binarization, can be used as tools for grayscale processing and more complex real-time thresholding applications.     

Extremal fuzzy integrals

Fuzzy integral is a monotone idempotent functional on a fuzzy measure. The extremal fuzzy integrals are introduced. Regular fuzzy integrals do not distinguish functions not distinguishable by the underlying fuzzy measures. These integrals include Choquet, Sugeno, Shilkret and several other well known integrals.     

A Universal Integral as Common Frame for Choquet and Sugeno Integral

The Choquet and the Sugeno integral provide a useful tool in many problems in engineering and social choice where the aggregation of data is required. However, their applicability is restricted because of the special operations used in the construction of these integrals. Therefore, we provide a concept of integrals generalizing both the Choquet and the Sugeno case. For functions with values in the nonnegative real numbers, universal integrals are introduced and investigated, which can be defined on arbitrary measurable spaces and for arbitrary monotone measures. For a fixed pseudomultiplication on the nonnegative real numbers, the smallest and the greatest universal integrals are given. Finally, another construction method for obtaining universal integrals is introduced, and the restriction to the unit interval, i.e., to fuzzy integrals, is considered.      

Fuzzy collision avoidance system for ships

The paper discusses the problem of maritime traffic control. A model of the relative motion of two vessels is considered. An algorithm for the generation of alarms of various types in accordance with the verbal ship–ship danger level is considered. Navigation situations are separated into levels based on the ship’s maneuvering intensity and time to collision. A fuzzy decision-making system about the motion’s danger level that combines Mamdani and Sugeno fuzzy inference systems is proposed. The results of the numerical experiment that demonstrates the system’s operation under standard conditions and the results of the system’s field tests based on real ship traffic data in the waters adjacent to the port of Vladivostok are given.     

改进的半监督聚类在MEG脑机接口中的应用

脑磁信号(MEG)作为一种新的脑机接口(BCI)输入信号,含有手运动方向的模式信息。鉴于半监督聚类融合了训练数据先验知识的优势,提出一种基于训练中心的半监督模糊聚类算法。该算法分为降维和改进的半监督聚类,采用主成分分析和线性判别分析将高维数据降到低维,改进的半监督聚类在对训练数据进行模糊聚类的基础上,将得到的聚类中心加权到测试数据聚类过程中,以增加测试数据聚类中心的鲁棒性。结果表明,该算法识别率较高,平均识别率达到了55.1%,优于BCI竞赛Ⅳ的最好结果46.9%。