Granular fuzzy models: Analysis,design, and evaluation

The study is concerned with a design of granular fuzzy models. We exploit a concept of information granularity by developing a model coming as a network of intuitively structured collection of interval information granules described in the output space and a family of induced information granules (in the form of fuzzy sets) formed in the input space. In contrast to most fuzzy models encountered in the literature, the results produced by granular models are information granules rather than plain numeric entities. The design of the model concentrates on a construction of information granules that form a backbone of the overall construct. Interval information granules positioned in the output space are built by considering intervals of equal length, equal probability, and developing an optimized version of the intervals. The induced fuzzy information granules localized in the input space are realized by running a conditional Fuzzy C-Means (FCM). The performance of the model is assessed by considering criteria of coverage and information specificity (information granularity). Further optimization of the model is proposed along the line of an optimal re-distribution of input information granules induced by the individual interval information granules located in the output space. Experimental results involve some synthetic low-dimensional data and publicly available benchmark data sets.     

Structural modeling in a class of systems using fuzzy sets theory

On the basis of fuzzy sets theory, we propose a method for structuring hierarchy for the several complex problems, and call it Fuzzy Structural Modeling (FSM) method. An important requirement for structural modeling of complex systems is that the necessary data is acquired and organized into a form such that a structural model can be developed. The main purpose of this method is to describe and illustrate a formal procedure for constructing the graphic presentation of the hierarchical arrangement given the necessary information concerning the relation of each element to each other element. The procedure permits an automatic development of the graphic structure that portrays the hierarchy.     

Identification of fuzzy relation models using hierarchical fair competition-based parallel genetic algorithms and information granulation

The paper is concerned with a hybrid optimization of fuzzy inference systems based on hierarchical fair competition-based parallel genetic algorithms (HFCGA) and information granulation. The process of information granulation is realized with the aid of the C-Means clustering. HFCGA being a multi-population based parallel genetic algorithms (PGA) is exploited here to realize structure optimization and carry out parameter estimation of the fuzzy models. The HFCGA becomes helpful in the context of fuzzy models as it restricts a premature convergence encountered quite often in optimization problems. It concerns a set of parameters of the model including among others the number of input variables to be used, a specific subset of input variables, and the number of membership functions. In the hybrid optimization process, two general optimization mechanisms are explored. The structural development of the fuzzy model is realized via the HFCGA optimization and C-Means, whereas to deal with the parametric optimization we proceed with a standard least square method and the use of the HFCGA technique. A suite of comparative studies demonstrates that the proposed algorithm leads to the models whose performance is superior in comparison with some other constructs commonly used in fuzzy modeling.     

Allocation of information granularity in optimization and decision-making models: Towards building the foundations of Granular Computing

The highly diversified conceptual and algorithmic landscape of Granular Computing calls for the formation of sound fundamentals of the discipline, which cut across the diversity of formal frameworks (fuzzy sets, sets, rough sets) in which information granules are formed and processed. The study addresses this quest by introducing an idea of granular models – generalizations of numeric models that are formed as a result of an optimal allocation (distribution) of information granularity. Information granularity is regarded as a crucial design asset, which helps establish a better rapport of the resulting granular model with the system under modeling. A suite of modeling situations is elaborated on; they offer convincing examples behind the emergence of granular models. Pertinent problems showing how information granularity is distributed throughout the parameters of numeric functions (and resulting in granular mappings) are formulated as optimization tasks. A set of associated information granularity distribution protocols is discussed. We also provide a number of illustrative examples.     

Global statistical information in exponential experiments and selection of exponential models

The concept of global statistical information in the classical statistical experiment with independent exponentially distributed samples is investigated. Explicit formulas are evaluated for common exponential families. It is shown that the generalized likelihood ratio test procedure of model selection can be replaced by a generalized information procedure. Simulations in a classical regression model are used to compare this procedure with that based on the Akaike criterion.     

建模支持系统中模型类的管理与组织

面向对象技术具有封装性,抽象性,继承性及多态性,用这种方法表示模型可支持模型的共享与重用,尤其是支持渐近式构模,文章提出用面向对象方法表示模型,将管理科学的各种模型定义成模型类,实现模型与方法的封装,借助于模型装配语言（MAL）定义复合模型类,解决因模型部件,方法部件和数据部件的分离带来的特性不匹配。     

Inventory models with a mixture of backorders and lost sales under fuzzy cost

Continuous review and periodic review inventory models in which a fraction of demand is backordered and the remaining fraction is lost during the stockout period are considered under fuzzy environment. Fuzziness is introduced by allowing the cost components imprecise and vague to certain extent. Trapezoidal fuzzy numbers are used to represent these characteristics. The optimum policies of these models under fuzzy costs are derived. Numerical results highlighting the sensitivity in the decision variables are also described.     

On coordination of supply chain based on information asymmetry of effort level and fuzzy market environment

The agent’s private information contributes greatly to a person to make principal decision in the supply of a chain coordination. Therefore, it is a great issue for him to design an effective incentive mechanism in order to get the true information from the agent in his principle making. Assuming that the demand depend upon an agent’s effort level and the fuzzy market condition, the author in this paper researches and analyzes the principle-agent problem under fuzzy information asymmetry condition by using the theory of principal-agent as well as incentive mechanism.     

知识库中知识的信息表示及其上的粗动力系统

粗集理论对知识进行了形式化定义,它为处理不确定,不完整的海量数据知识提供了一套严密的数据分析处理工具．但粗集概念及运算的代数意义表示往往不易被人理解．本文针对于此。在知识库中提出了知识的信息熵问题,证明了知识的某些信息表示与其代数表示是等价的,最后还讨论了知识库上的粗动力系统的一些性质。     

On the use of fuzzy inference techniques in assessment models: part I—theoretical properties

An assessment model is a mathematical model that produces a measuring index, either in the form of a numerical score or a category to a situation/object, with respect to the subject of measure. From the numerical score, decision can be made and action can be taken. To allow valid and useful comparisons among various situations/objects according to their associated numerical scores to be made, the monotone output property and the output resolution property are essential in fuzzy inference-based assessment problems. We investigate the conditions for a fuzzy assessment model to fulfill the monotone output property using a derivative approach. A guideline on how the input membership functions should be tuned is also provided. Besides, the output resolution property is defined as the derivative of the output of the assessment model with respect to its input. This derivative should be greater than the minimum resolution required. From the derivative, we suggest improvements to the output resolution property by refining the fuzzy production rules.     

Information granulation and uncertainty measures in interval-valued intuitionistic fuzzy information systems

Information granulation and entropy are main approaches for investigating the uncertainty of information systems, which have been widely employed in many practical domains. In this paper, information granulation and uncertainty measures for interval-valued intuitionistic fuzzy binary granular structures are addressed. First, we propose the representation of interval-valued intuitionistic fuzzy information granules and examine some operations of interval-valued intuitionistic fuzzy granular structures. Second, the interval-valued intuitionistic fuzzy information granularity is introduced to depict the distinguishment ability of an interval-valued intuitionistic fuzzy granular structure (IIFGS), which is a natural extension of fuzzy information granularity. Third, we discuss how to scale the uncertainty of an IIFGS using the extended information entropy and the uncertainty among interval-valued intuitionistic fuzzy granular structures using the expanded mutual information derived from the presented intuitionistic fuzzy information entropy. Fourth, we discovery the relationship between the developed interval-valued intuitionistic fuzzy information entropy and the intuitionistic fuzzy information granularity presented in this paper.     

Analysis and prediction of hazard risks caused by tropical cyclones in Southern China with fuzzy mathematical and grey models

A hazard-risk assessment model and a grey hazard-year prediction model (GHYPM) are constructed by integrating recent advances in the fuzzy mathematics, grey theory and information spread technique, and then applied to 17-year tropical cyclones (TCs) hazards in Southern China. In constructing the models, a genetic fuzzy mathematical algorithm is first developed to calculate the categorical and ranking weights of TC hazard impact and cause indicators, from which their combined weights are obtained after optimization. The hazard impact and cause index series are then found by coupling the combined weights with their corresponding down-scaled indicators. A two-dimensional normal-spread technique is employed to create a primitive information matrix and a fuzzy relation matrix in order to make fuzzy rough inference of hazard risks with the factorial space theory. An exceeded probability model is developed to assess the possibility of exceeding any given hazard-year category. Results from the GHYPM show that the simulated hazard risk values are more or less consistent with the hazard-impact index series, with more than 60% probability of exceeding a moderate hazard year in Southern China. Results also show small relative errors of the GHYPM, indicating its applicability to the prediction of TC hazard-years up to 20 years.     

Modeling the role of information and optimal control on an SEIR epidemic model with infectivity in latent period

The outbreak of a disease can lead to behavioral changes in the healthy to avert infection. We first establish a nonlinear SEIR epidemic model that incorporates the impact of individuals' behavioral response owe to information of the disease prevalence. Both the existence of equilibria and sharp sufficient conditions on stable equilibria are verified. Whereafter, the local and global sensitivity analyses are carried out to assess the relative effects of parameters on the basic reproduction number. Therewith the optimal control problem is considered to provide a theoretical basis for disease prevention and control, and the existence and uniqueness consequences for optimal control paths are demonstrated. Some numerical examples and discussions are given to support and visualize our analytical results, which can be derived that the combined use of three control measures is more effective than any single adopted control strategy to curb the spread of diseases. We also find that the information plays a crucial role in controlling infection.     

A normal form which preserves tautologies and contradictions in a class of fuzzy logics

Most of the normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve tautologies and contradictions which is important, for example, for automated theorem provers based on refutation methods.De Morgan implicative systems are triples like the De Morgan systems, which consider fuzzy implications instead of t-conorms. These systems can be used to evaluate the formulas of a propositional language based on the logical connectives of negation, conjunction and implication. Therefore, they determine different fuzzy logics, called implicative De Morgan fuzzy logics.In this paper, we will introduce a normal form for implicative De Morgan systems and we will show that for implicative De Morgan fuzzy logics whose t-norms are strict, this normal form preserves contradictions as well as tautologies.     

On rates of convergence of information theoretic criterion in rank determination of one-way random effects models

In this paper, upper bounds on the probabilities of wrong determination of the rank of covariance matrix of random effects in one-way random effects models are given, based on the information theoretic criterion. Under weak conditions, the bounds are shown of exponential-type.The work was partially supported by Natural Sciences and Engineering Research Council of Canada and Faculty Research Grant, Faculty of Arts, York University.     

ARMA-GARCH模型对上海铜期货市场收益率的建模与分析

本文首先对沪铜期货收益率序列的进行了分析,在单位根检验中克服了观察等价性的影响,并得到为该收益率服从ARIMA（0,1,1）-GARCH（1,1）模型.在此基础上,利用TARCH和EGARCH模型对收益率的杠杆效应进行了检验.     

The effect of information in separable Bayesian semi-Markov control models and its application to investment planning

We consider a separable Bayesian semi-Markov control model to describe economic decisions under uncertainty. Our main interest is to examine the influence of the possibility of learning on the economic decisions and on the total expected return in a multi-period framework. We make use of the concept of Blackwell-sufficiency and apply the results to multi-period investment planing under uncertainty.     

Optimal advertising and pricing in a class of general new-product adoption models

In [21], Sethi et al. introduced a particular new-product adoption model. They determine optimal advertising and pricing policies of an associated deterministic infinite horizon discounted control problem. Their analysis is based on the fact that the corresponding Hamilton–Jacobi–Bellman (HJB) equation is an ordinary non-linear differential equation which has an analytical solution. In this paper, generalizations of their model are considered. We take arbitrary adoption and saturation effects into account, and solve finite and infinite horizon discounted variations of associated control problems. If the horizon is finite, the HJB-equation is a 1st order non-linear partial differential equation with specific boundary conditions. For a fairly general class of models we show that these partial differential equations have analytical solutions. Explicit formulas of the value function and the optimal policies are derived. The controlled Bass model with isoelastic demand is a special example of the class of controlled adoption models to be examined and will be analyzed in some detail.