Modelling credit rating by fuzzy adaptive network

Human judgment plays an important role in the rating of enterprise financial conditions. The recently developed fuzzy adaptive network (FAN), which can handle systems whose behaviour is influenced by human judgment, appears to be ideally suited for the modelling of this credit rating problem. In this paper, FAN is used to model the credit rating of small financial enterprises. To illustrate the approach, the data of the credit rating problem is first represented by the use of fuzzy numbers. Then, the FAN network based on inference rules is constructed. And finally, the network is trained or learned by using the fuzzy number training data. The main advantages of the proposed network are the ability for linguistic representation, linguistic aggregation and the learning ability of the neural network.     

基于语义Choquet积分的知识服务能力测评方法

针对知识服务中考虑模糊语言关联性信息的知识服务能力评价与提升策略问题,提出了一种评价方法。为了解决该问题,首先构建了知识服务能力的评价指标体系和矩阵分析模型;然后,明晰了知识服务能力的语言评价指标会在不同程度上存在关联的问题特征及二元语义信息处理方法的特征,并进行了形式化描述;同时,提出并定义了二元语义Choquet积分算子,给出了一种基于二元语义Choquet积分算子评价知识服务能力的方法;最后,通过算例分析说明了本文给出方法的可行性和实用性。     

Distributed preference relations for multiple attribute decision analysis

In this paper, we propose a new pairwise comparison approach called distributed preference relation (DPR) to simultaneously signify preferred, non-preferred, indifferent, and uncertain degrees of one alternative over another on a set of grades, which is more versatile for elicitation of preference information from a decision maker than multiplicative preference relation, fuzzy preference relation (FPR) and intuitionistic FPR. In a DPR matrix on a set of alternatives, each element is a distribution recording the preferred, non-preferred, indifferent, and uncertain degrees of one alternative over another using a set of grades. To facilitate the comparison of alternatives, we define a score matrix based on a DPR matrix using the given score values of the grades. Its additive consistency is constructed, analysed, and compared with the additive consistency of FPRs between alternatives. A method for comparing two interval numbers is then employed to create a possibility matrix from the score matrix, which can generate a ranking order of alternatives with possibility degrees. A problem of evaluating strategic emerging industries is investigated using the approach to demonstrate the application of a DPR matrix to modelling and analysing a multiple attribute decision analysis problem.     

An integrated model-based interactive approach to FMAGDM with incomplete preference information

Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking, strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations, inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate the developed approach.     

Modelling class hierarchies in the fuzzy object-oriented data model

In this paper we describe a fuzzy logic based approach to modelling uncertainty in class hierarchies. It is shown that the traditional view of class hierarchies is subsumed in this model as a special case. The problem of multiple inheritance in class hierarchies is discussed and analyzed. The membership value derivations in the inheritance hierarchy reflects the degree of fuzziness existing in the data values and the semantics of the situation being modelled. Thus a more realistic modelling of the universe of discourse is possible through this approach. This model is compatible with existing object-oriented data models.     

Combining compound linguistic ordinal scale and cognitive pairwise comparison in the rectified fuzzy TOPSIS method for group decision making

Group decision making is the process to explore the best choice among the screened alternatives under predefined criteria with corresponding weights from assessment of a group of decision makers. The Fuzzy TOPSIS taking an evaluated fuzzy decision matrix as input is a popular tool to analyze the ideal alternative. This research, however, finds that the classical fuzzy TOPSIS produces a misleading result due to some inappropriate definitions, and proposes the rectified fuzzy TOPSIS addressing two technical problems. As the decision accuracy also depends on the evaluation quality of the fuzzy decision matrix comprising rating scores and weights, this research applies compound linguistic ordinal scale as the fuzzy rating scale for expert judgments, and cognitive pairwise comparison for determining the fuzzy weights. The numerical case of a robot selection problem demonstrates the hybrid approach leading to the much reliable result for decision making, comparing with the conventional fuzzy Analytic Hierarchy Process and TOPSIS.     

复Fuzzy级数及其收敛性的进一步讨论

给出复 Fuzzy数项级数与复 Fuzzy函数级数的概念 ,讨论它们的收敛性问题 ,给出它们收敛性的相应判别法则。     

Fuzzy adaptive network in presidential elections

Several scientific forecasting models for presidential elections have been suggested. However, most of these models are based on traditional statistics approaches. Since the system is linguistic, vague, and dynamic in nature, the traditional rigorous mathematical approaches are inappropriate for the modeling of this kind of humanistic system. This paper presents a combined neural fuzzy approach, namely a fuzzy adaptive network, to model and forecast the problem of a presidential election. The fuzzy adaptive network, which is ideally suited for the modeling of vaguely defined humanistic systems, combines the advantages of the representation ability of fuzzy sets and the learning ability of a neural network. To illustrate the approach, experiments were carried out by first formulating the problem, then training the network, and, finally, predicting the election results based on the trained network. The experimental results show that a fuzzy adaptive network is an ideal approach for the modeling and forecasting of national presidential elections.     

Solving generalized fuzzy data envelopment analysis model: a parametric approach

Data envelopment analysis (DEA) is a non-parametric technique to assess the performance of a set of homogeneous decision making units (DMUs) with common crisp inputs and outputs. Regarding the problems that are modelled out of the real world, the data cannot constantly be precise and sometimes they are vague or fluctuating. So in the modelling of such data, one of the best approaches is using the fuzzy numbers. Substituting the fuzzy numbers for the crisp numbers in DEA, the traditional DEA problem transforms into a fuzzy data envelopment analysis (FDEA) problem. Different methods have been suggested to compute the efficiency of DMUs in FDEA models so far but the most of them have limitations such as complexity in calculation, non-contribution of decision maker in decision making process, utilizable for a specific model of FDEA and using specific group of fuzzy numbers. In the present paper, to overcome the mentioned limitations, a new approach is proposed. In this approach, the generalized FDEA problem is transformed into a parametric programming, in which, parameter selection depends on the decision maker’s ideas. Two numerical examples are used to illustrate the approach and to compare it with some other approaches.     

Linguistic quantifiers based on Choquet integrals

The introduction of linguistic quantifiers has provided an important tool to model a large number of issues in intelligent systems. Ying [M.S. Ying, Linguistic quantifiers modeled by Sugeno integrals, Artificial Intelligence 170 (2006) 581–606] recently introduced a new framework for modeling quantifiers in natural languages in which each linguistic quantifier is represented by a family of fuzzy measures, and the truth value of a quantified proposition is evaluated by using Sugeno’s integral. Representing linguistic quantifiers by fuzzy measures, this paper evaluates linguistic quantified propositions by the Choquet integral. Some elegant logical properties of linguistic quantifiers are derived within this approach, including a prenex normal form theorem stronger than that in Ying’s model. In addition, our Choquet integral approach to the evaluation of quantified statements is compared with others, in particular with Ying’s Sugeno integral approach.     

模糊决策在航空维修工程中的应用

本文以模糊数学和规划论为工具，对航空维修工程中一类决策问题的决策方法进行了探讨，给出了具有普遍意义的建模思想，通过实例分析，证明了这种方法的可行性和先进性。     

基于VIKOR和关联系数的犹豫三角模糊语言多属性决策方法

针对属性评价值为犹豫三角模糊语言集的多属性决策问题,提出一种基于VIKOR方法的犹豫三角模糊语言多属性决策方法.首先定义了犹豫三角模糊语言集的相关概念.然后运用VIKOR和关联系数方法,在可接受优势和决策过程稳定的条件下对方案进行择优,在理论分析的基础上,提出了这种新方法的计算步骤.并构建了确定最优属性权重的非线性规划模型,研究了当专家权重和属性权重未知情况下的犹豫三角模糊语言多属性决策方法.最后通过实例说明了该方法的有效性和可行性.     

Model predictive control of nonlinear hybrid systems with discrete inputs employing a hybrid fuzzy model

The paper deals with model predictive control (MPC) of nonlinear hybrid systems with discrete inputs based on reachability analysis. In order to implement a MPC algorithm, a model of the process that we are dealing with is needed. In the paper, a hybrid fuzzy modelling approach is proposed. The hybrid system hierarchy is explained and the Takagi–Sugeno fuzzy formulation for hybrid fuzzy modelling purposes is tackled. An efficient method of identification of the hybrid fuzzy model is also discussed.

An algorithm that is–due to its MPC nature–suitable for controlling a wide spectrum of systems (provided that they have discrete inputs only) is presented.

The benefits of the algorithm employing a hybrid fuzzy model are verified on a batch reactor example. The results suggest that by suitably determining the cost function, satisfactory control can be attained, even when dealing with complex hybrid–nonlinear–stiff systems such as the batch reactor.

Finally, a comparison between MPC employing a hybrid linear model and a hybrid fuzzy model is carried out. It has been established that the latter approach clearly outperforms the approach where a linear model is used.     

An intuitionistic fuzzy projection-based approach for partner selection

The partner selection is an important decision problem in the formation of a new virtual enterprise. Using the projection technique, this study introduces an approach to partner selection with linguistic values and intuitionistic fuzzy information under a group decision-making environment. To avoid information loss, there is no aggregations of decision information in this model except ideal decisions as auxiliary decision tools. Comparisons of the suggested methodology with other methods are also made. A numerical example and an experimental analysis are proposed to illustrate the application of the proposed model.     

模糊均衡问题的求解及应用

根据实际均衡问题研究的需要,给出了模糊向量、模糊值函数、模糊矩阵等新概念,建立了模糊均衡问题的数学模型,即模糊线性互补问题。在引入新的模糊期望的基础上,研究了其性质,并据此给出了模糊线性互补问题的一种确定型等价式及此类问题的均衡解的概念。用实例说明了所提模型和方法的合理性及应用前景。     

Regression-fuzzy approach to land valuation

In this paper, we demonstrate that the fuzzy pricing model can improve regression analysis in applications where non-smoothness appears. Combining the fuzzy and regression approaches it is capable of modelling complex non-linearities. The application of this approach describes an effort to design a regression-fuzzy system to estimate real estate market values, especially for vacant urban plots. The results are compared with those obtained using a traditional multiple regression model only. The changes of parameters in the domain of independent variables of the regression function are determined by the analysis of membership functions defining the terms of the fuzzy model. The paper also describes possible future research. The suggested method is interesting for real estate appraisers, real estate companies, and bureaus because it provides a better overview of location prices. The suggested approach could be also used in various other economic and business analyses.     

基于对偶犹豫模糊语言变量的多属性决策方法

首先定义了对偶犹豫模糊语言变量,然后给出其运算规则、得分值函数、精确值函数、比较规则以及对偶犹豫模糊语言变量的加权算术平均算子、有序加权算术平均算子和混合平均算子。针对属性值为对偶犹豫模糊语言变量的多属性决策问题,提出了一种基于对偶犹豫模糊语言变量集结算子的多属性决策方法。最后,结合国家电网公司合作单位选择问题,验证了该方法的有效性和可行性。     

FUZZY IDENTIFIER WITH EXPONENTIAL RATE OF CONVERGENCE FOR NONLINEAR DYNAMIC SYSTEMS

1 IntroductionIn recent yearst there is a development in the use of fuzzy systems for modelling, identifyingand controlling nonlinear systems. The reason is that conventional identification methods canonly use input-output pairs, but ignore linguistic information about the behavior of nonlinearsystems. Therefore, developing identifiers and controllers Of nonlinear systems which can com-bine both linguistic knowledge and numerical information is an important task. Ill this repect,works on the …     

Fuzzy guaranteed cost controller for trajectory tracking in nonlinear systems

In this paper, we propose a fuzzy logic based guaranteed cost controller for trajectory tracking in nonlinear systems. Takagi–Sugeno (T–S) fuzzy model is used to represent the dynamics of a nonlinear system and the controller design is carried out using this fuzzy model. State feedback law is used for building the fuzzy controller whose performance is evaluated using a quadratic cost function. For designing the fuzzy logic based controller which satisfies guaranteed performance, linear matrix inequality (LMI) approach is used. Sufficient conditions are derived in terms of matrix inequalities for minimizing the performance function of the controller. The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs. This minimization problem can be solved easily and efficiently using the LMI optimization techniques. Our controller design method also ensures that the closed-loop system is asymptotically stable. Simulation study is carried out on a two-link robotic manipulator tracking a reference trajectory. From the results of the simulation study, it is observed that our proposed controller tracks the reference trajectory closely while maintaining a guaranteed minimum cost.     

A fuzzy-linguistic approach to a multi-criteria sequencing problem

In this paper, a fuzzy approach to a single machine scheduling problem is considered. In this approach, the system's variables are defined using linguistic terms. Each of these variables may take values described via fuzzy triangular numbers. The scheduling criteria are the common due date, the total earliness and tardiness and the controllable duration of the jobs' processing times. The aim is to determine the length of the processing times, to sequence the jobs in the machine and, finally, to determine the common due date in a near optimal way. The problem is solved using an algorithmic procedure, which is illustrated by means of an example.