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This paper propose a topological logic model of approximate reasoning based on the type II topological logic $\mathbb{C}^2_\mathcal{T}$ and the structure of matching function $\mathcal{C}$ and $\mathcal{C}$-match neighborhood group. The type II topological algorithm of simple approximate reasoning and multiple approximate reasoning is given in type II topological logic $\mathbb{C}^2_\mathcal{T}$ with matching function $\mathcal{C}$. We also propose the structure of type II regular topological logic $\mathbb{C}^2_\mathcal{T}$ and regular matching function $\mathcal{C}$. The type II completeness and type II perfectness of knowledge base K is investigated in type II regular topological logic $\mathbb{C}^2_\mathcal{T}$ with regular matching function $\mathcal{C}$. [ABSTRACT FROM AUTHOR]

Typical description logics are limited to dealing with crisp concepts. It is necessary to add fuzzy features to description logics for management of the fuzzy information. In this paper, we propose extended fuzzy ALCN to enable representation and reasoning for complex fuzzy information. We define syntax structure, semantic interpretation and reasoning problems of the extended fuzzy ALCN, and discuss the reasoning properties inexistent in typical description logics. We also design tableau algorithms of reasoning problems for extended fuzzy ALCN. The tableau algorithms are developed in the style of so-called constraint propagation method. Extended fuzzy ALCN is more expressive than the existing fuzzy description logics and present more wide fuzzy information. [ABSTRACT FROM AUTHOR]

This paper proposes the formal description of nondeterministic information system based on tolerance rough set theory, analyzes six cases of approximate information system, and gives the concept of strong and weak similarity. After defining tolerance rough set, combining the theories of FCA and expanding non-definable concept into non-definable attributes, non-definable objects and non-definable context, we present optimal algorithm of formal concept of approximation system. Really emulation has illustrated that the algorithm obtains a satisfied approximate concept and a shorter time complexity. [ABSTRACT FROM AUTHOR]

In this paper, the selection of a data set from a universal set is carried out using a fuzzy entropy function. According to the definition of fuzzy entropy, the fuzzy entropy function is proposed and that function is proved through definitions. The proposed fuzzy entropy function calculates the certainty or uncertainty value of a data set; hence we can choose the data set that satisfies certain bounds or references. Therefore a reliable data set can be obtained using the proposed fuzzy entropy function. With a simple example we verify that the proposed fuzzy entropy function selects the reliable data set. [ABSTRACT FROM AUTHOR]

Automatic Summarization is need of the era. Mathematics is an important tool of nonfigurative thinking. A mathematic model of automatic summarization is established and discussed in the paper. The model makes use of meta-knowledge to describe the composition of the summary and help to calculate the semantic distance between summary and source document. It is proposed that how to get meta-knowledge aggregate and their weight are the key problems in the model. [ABSTRACT FROM AUTHOR]

As a kind of new uncertainty theory, the set pair analysis (SPA) researches certainties and uncertainties from the whole. The main idea of SPA is: (1) Every system is comprised of certainty knowledge and uncertainty knowledge; (2) Certainties and uncertainties are inter-related, inter-influenced, inter-restricted, and inter-transformed even under certain condition, in every system; (3) A computation formula (identity-discrepancy-contrary (IDC) connection degree formula) which can embody the above idea fully is used to depict uniformly all kinds of uncertainties such as fuzzy uncertainty, random uncertainty, indeterminate-known uncertainty, unknown and unexpected incident uncertainty, and uncertainty which is resulted from imperfective information. This paper introduces the concepts and provides the applications of IDC connection degree and IDC connection number in SPA. [ABSTRACT FROM AUTHOR]

This paper proposes an online self-organizing identification algorithm for TSK fuzzy model. The structure of TSK fuzzy model is identified using distance. Parameters of the piecewise linear function consisting consequent part are obtained using recursive version of combined learning method of global and local learning. Both input and output spaces are considered in the proposed algorithm to identify the structure of the TSK fuzzy model. By processing clustering both in input and output space, outliers are excluded in clustering effectively. The proposed algorithm is non-sensitive to noise not by using data itself as cluster centers. The proposed algorithm can obtain a TSK fuzzy model through one pass. By using the proposed combined learning method, the estimated function can have high accuracy. [ABSTRACT FROM AUTHOR]

One of the fundamental goals of artificial intelligence (AI) is to build artificially computer-based systems which make computer simulate, extend and expand human's intelligence and empower computers to perform tasks which are routinely performed by human beings. Without effective reasoning mechanism, it is impossible to make computer think and reason. Research on reasoning is an interesting and meaningful problem. Case-based reasoning is a branch of reasoning research. There are a lot of research results and successful application on Case-based reasoning. How to index and retrieve similar cases is one of key issue in Case-based reasoning research hotspots in CBR research works. In addition, there is a lot of uncertainty information in daily work and everyday life. So how to deal with uncertainty information in Case-based Reasoning effectively becomes more and more important. In this paper, a new case indexing and retrieval model which can deal with both fuzzy information and accurate information is presented. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the fuzzy constraints linear programming. First we discuss the properties of an optimal solution vector and of an optimal value in the corresponding parametric programming, and propose a method to the critical values. Then we present a new algorithm to the fuzzy constraint linear programming by associating an object function with the optimal value of parametric programming. [ABSTRACT FROM AUTHOR]

Dubois and Prade defined an interval-valued expectation of fuzzy numbers, viewing them as consonant random sets. Fullér and Majlender then proposed an weighted possibility mean value, variance and covariance of fuzzy numbers, viewing them as weighted possibility distributions. In this paper, we define a new weighted possibilistic variance and covariance of fuzzy numbers based on Fullér and Majlenders' notations. Some properties of these notations are obtained in a similar manner as in probability theory. We also consider the weighted possibilistic mean-variance model of portfolio selection and introduce the notations of the weighted possibilistic efficient portfolio and efficient frontier. Moreover, a simple example is presented to show the application of our results in security market. [ABSTRACT FROM AUTHOR]

Fuzzy set theory has grown to become a major scientific domain collectively referred to as fuzzy systems. In this paper, the fuzzy variation coefficients programming and its application are discussed. The proposed fuzzy variation coefficients programming has found application in operations management and it will find various application in other areas. [ABSTRACT FROM AUTHOR]

This paper presents a method for consensus measures and adjusting inconsistency of linguistic preference relations in group decision-making (GDM). Several consensus measures are defined by comparing positions of alternatives between individual ordered vectors and a collective ordered vector. In such a way, the consensus situation is evaluated in each moment in a more realistic way. Feedback mechanism would be applied if the consensus degree of all experts does not reach the required consensus level. This feedback mechanism is simple and easy computing process to help experts change their opinions in order to obtain the consensus level. It is based on the use of individual linguistic preferences, collective and individual ordered vectors of alternatives. It is also based on the use of fuzzy majority of consensus, represented by means of a linguistic quantifier. Keywords: Group decision making (GDM); Linguistic preference relation; Consensus degree; Feedback mechanism. [ABSTRACT FROM AUTHOR]

Passenger satisfaction index (PSI) is one of the most important indexes in comprehensive evaluation of management performance and service quality of passenger transport corporations. Based on the investigations in China, the authors introduced the notion and method for passenger group division and the concept of index weight matrix, and made successful application for passenger satisfaction evaluation. Index weight matrix developed by applying AHP and Delphi methods gives satisfactory results. The paper ends with examples of using a fuzzy inference system for passenger satisfaction evaluation in Beijing railway station. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the multiple attribute decision making problems under fuzzy linguistic environment. We introduce the concept of trapezoid fuzzy linguistic variable and some operational laws of trapezoid fuzzy linguistic variables. We develop a similarity measure between two trapezoid fuzzy linguistic variables. Based on the similarity measure and the ideal point of attribute values, we develop an approach to ranking the decision alternatives in multiple attribute decision making with trapezoid fuzzy linguistic variables. We finally illustrate the developed approach with a practical example. [ABSTRACT FROM AUTHOR]

This paper deals with interval regression analysis using support vector machine and quantile regression method. The algorithm consists of two phases - the identification of the main trend of the data and the interval regression based on acquired main trend. Using the principle of support vector machine the linear interval regression can be extended to the nonlinear interval regression. Numerical studies are then presented which indicate the performance of this algorithm. [ABSTRACT FROM AUTHOR]

The paper defines a fuzzy time Petri net (FTPN) which adopts four fuzzy set theoretic functions of time called fuzzy timestamp, fuzzy enabling time, fuzzy occurrence time and fuzzy delay, to deal with temporal uncertainty of train group operation and we also present different firing strategies for the net to give prominence to key events. The application instance shows that the method based on FTPN can efficiently analyze trains converging time, the possibility of converging and train terminal time in adjustment of train operation plan. Compared with time interval method, this method has some outstanding characteristics such as accurate analysis, simple computation, system simplifying and convenience for system integrating. [ABSTRACT FROM AUTHOR]

This paper presents a new kind of Evolutionary Fuzzy System (EFS) based on the Least Squares (LS) method and a hybrid learning algorithm: Adaptive Evolutionary-programming and Particle-swarm-optimization (AEPPSO). The structure of the Extended Fuzzy Basis Function Network (EFBFN) is firstly proposed, and the LS method is used to design it with presetting the widths of the hidden units in EFBFN. Then, to enhance the performance of the obtained EFBFN ulteriorly, a novel learning algorithm based on least squares and the hybrid of evolutionary programming and particle swarm optimization (AEPPSO) is proposed, in which we use EPPSO to tune the parameters of the premise part in EFBFN, and the LS algorithm to decide the consequent parameters in it simultaneously. In the simulation part, the proposed method is employed to predict a chaotic time series. Comparisons with some typical fuzzy modeling methods and artificial neural networks are presented and discussed. [ABSTRACT FROM AUTHOR]

An approach to identify data-driven interpretable and accurate fuzzy models is presented in this paper. Firstly, Gustafson-Kessel fuzzy clustering algorithm is used to identify initial fuzzy model, and cluster validity indices are adopted to determine the number of rules. Secondly, orthogonal least square method and similarity measure of fuzzy sets are utilized to reduce the initial fuzzy model and improve its interpretability. Thirdly, constraint Levenberg-Marquardt algorithm is used to optimize the reduced fuzzy model to improve its accuracy. The proposed approach is applied to PH neutralization process, and results show its validity. [ABSTRACT FROM AUTHOR]

This paper presents a general framework for the study of fuzzy rough sets in which constructive approach is used. In the approach, a pair of lower and upper general fuzzy rough approximation operator in the lattice L is defined. Furthermore, the entire property and connection between the set of logical operator and the set of its corresponding general fuzzy rough approximation operator are examined, and we prove that they are 1-1 mapping. In addition, the structural theorem of negator operator is given. At last, the decomposition and synthesize theorem of general fuzzy rough approximation operator are proved. That for how to promote general rough approximation operator to suitable general fuzzy rough approximation operator, that is, how to select logical operator, provides theory foundation. [ABSTRACT FROM AUTHOR]

In this paper, we mainly extend entropy and subsethood from intuitionistic fuzzy sets to general interval-valued intuitionistic fuzzy sets, propose a definition of entropy and subsethood , offer a function of entropy and construct a class of subsethood function. Then from discussing the relationship between entropy and subsethood, we know that while choosing the subsethood, we can get some kinds of function of entropy based on subsethood. Our work is also applicable to practical fields such as: neural networks, expert systems, and other. [ABSTRACT FROM AUTHOR]

A fuzzy evaluation based multi-objective optimization model for reactive power optimization in power distribution networks is presented in this paper. The two objectives, reducing active power losses and improving voltage profiles, are evaluated by membership functions respectively, so that the objectives can be compared in a single scale. To facilitate the solving process, a compromised objective is formed by the weighted sum approach. The weights are decided according to the preferences and importance of the objectives. The reactive tabu search algorithm is employed to get global optimization solutions. Simulation results of a practical power distribution network, greatly improved voltage profiles and reduced power losses, demonstrated that the proposed method is effective. [ABSTRACT FROM AUTHOR]

As a generalization of fuzzy sets, the concept of interval-valued fuzzy sets was introduced by Gorzalczany [Fuzzy Sets and Systems 21 (1987) 1]. In this paper, we shall extend the concept of "fuzzy inclusion", introduced by Šostak [Supp. Rend. Circ. Mat. Palermo (Ser. II) 11 (1985) 89], to the interval-valued fuzzy setting and study its fundamental properties for some extent. [ABSTRACT FROM AUTHOR]