An approach to decision making based on intuitionistic fuzzy rough sets over two universes

Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach.     

Properties of graphical regression models for multidimensional categorical data

We propose a two-component graphical chain model, the discrete regression distribution, where a set of discrete random variables is modeled as a response to a set of categorical and continuous covariates. The proposed model is useful for modeling a set of discrete variables measured at multiple sites along with a set of continuous and/or discrete covariates. The proposed model allows for joint examination of the dependence structure of the discrete response and observed covariates and also accommodates site-to-site variability. We develop the graphical model properties and theoretical justifications of this model. Our model has several advantages over the traditional logistic normal model used to analyze similar compositional data, including site-specific random effect terms and the incorporation of discrete and continuous covariates.     

Global convergence of a kinetic model of chemotaxis to a perturbed Keller–Segel model

We consider a class of kinetic models of chemotaxis with two positive non-dimensional parameters coupled to a parabolic equation of the chemo-attractant. If both parameters are set equal zero, we have the classical Keller–Segel model for chemotaxis. We prove global existence of solutions of this two-parameters kinetic model and prove convergence of this model to models of chemotaxis with global existence when one of these two parameters is set equal zero. In one case, we find as a limit model a kinetic model of chemotaxis while in the other case we find a perturbed Keller–Segel model with global existence of solutions.     

Maximising entropy on the nonparametric predictive inference model for multinomial data

The combination of mathematical models and uncertainty measures can be applied in the area of data mining for diverse objectives with as final aim to support decision making. The maximum entropy function is an excellent measure of uncertainty when the information is represented by a mathematical model based on imprecise probabilities. In this paper, we present algorithms to obtain the maximum entropy value when the information available is represented by a new model based on imprecise probabilities: the nonparametric predictive inference model for multinomial data (NPI-M), which represents a type of entropy-linear program. To reduce the complexity of the model, we prove that the NPI-M lower and upper probabilities for any general event can be expressed as a combination of the lower and upper probabilities for the singleton events, and that this model can not be associated with a closed polyhedral set of probabilities. An algorithm to obtain the maximum entropy probability distribution on the set associated with NPI-M is presented. We also consider a model which uses the closed and convex set of probability distributions generated by the NPI-M singleton probabilities, a closed polyhedral set. We call this model A-NPI-M. A-NPI-M can be seen as an approximation of NPI-M, this approximation being simpler to use because it is not necessary to consider the set of constraints associated with the exact model.     

A two-objective mathematical model without cutting patterns for one-dimensional assortment problems

This paper considers a one-dimensional cutting stock and assortment problem. One of the main difficulties in formulating and solving these kinds of problems is the use of the set of cutting patterns as a parameter set in the mathematical model. Since the total number of cutting patterns to be generated may be very huge, both the generation and the use of such a set lead to computational difficulties in solution process. The purpose of this paper is therefore to develop a mathematical model without the use of cutting patterns as model parameters. We propose a new, two-objective linear integer programming model in the form of simultaneous minimization of two contradicting objectives related to the total trim loss amount and the total number of different lengths of stock rolls to be maintained as inventory, in order to fulfill a given set of cutting orders. The model does not require pre-specification of cutting patterns. We suggest a special heuristic algorithm for solving the presented model. The superiority of both the mathematical model and the solution approach is demonstrated on test problems.     

Resampling-based information criteria for best-subset regression

When a linear model is chosen by searching for the best subset among a set of candidate predictors, a fixed penalty such as that imposed by the Akaike information criterion may penalize model complexity inadequately, leading to biased model selection. We study resampling-based information criteria that aim to overcome this problem through improved estimation of the effective model dimension. The first proposed approach builds upon previous work on bootstrap-based model selection. We then propose a more novel approach based on cross-validation. Simulations and analyses of a functional neuroimaging data set illustrate the strong performance of our resampling-based methods, which are implemented in a new R package.     

Equilibrium and perfection in discounted supergames

In this paper, we discuss equilibrium and perfect equilibrium in a simplified model of the supergame. We assume that players can observe the mixed moves employed by all players at each previous stage. For this model, we obtain a complete characterization of the set of equilibrium outcomes, and a fairly weak sufficient condition for this set to coincide with the set of perfect equilibrium outcomes.Inter alia, simple proofs of the Folk Theorem and the result that the requirement of perfection does not eliminate any equilibrium outcomes for the undiscounted supergame are presented.     

基于小波多分辨率分析和改进窄带法的C-V水平集图像分割模型

本文研究了基于小波分析改进的C-V模型图像分割问题.利用小波多分辨率分析和改进的窄带水平集方法,获得了比传统C-V模型分割速度更快、准确度更高、算法复杂度更低的分割结果.推广了C-V水平集模型如何快速准确地分割灰度不均匀的图像和窄带水平集法等结果.     

Nonuniqueness of a Gibbs measure for a model on the Cayley tree

We propose a model on the Cayley tree and prove that a uncountable set of Ĝ-periodic Gibbs measures exists for this model, in contrast to models studied previously.     

MILP models for the selection of a small set of well-distributed points

Motivated by the problem of fitting a surrogate model to a set of feasible points in the context of constrained derivative-free optimization, we consider the problem of selecting a small set of points with good space-filling and orthogonality properties from a larger set of feasible points. We propose four mixed-integer linear programming models for this task and we show that the corresponding optimization problems are NP-hard. Numerical experiments show that our models consistently yield well-distributed points that, on average, help reducing the variance of model fitting errors.     

Input–Output Identifiability of Continuous-Time Linear Systems

In time-domain identification of linear systems the aim is to estimate the impulse response or transfer function of a linear system to within a given tolerance using a finite number of noisy observations of the output. Whether this is possible depends on the model set, that is, a given set to which the system is assumed to belong a priori. We give necessary and sufficient conditions on the model set to ensure that such identification is possible in the continuous-time case.     

Homology with Models and Tor

We consider the extension of the notion of a projective module to that of a projective functor relative to a model set (as in Dold, MacLane, Oberst, 1967). Then taking projective resolutions of functors, we consider the usual associated homology.We show that in some cases, including the classical simplicial homology of topological spaces, the model set can be replaced by a model set having only one element. We show that when the model set consists of a single element the homology modules can be interpreted as values of the Torsion functor. In the case of simplicial homology of topological spaces these Tors will be shown to be analogous to the Tors which occur in group homology.     

一类多指标对象评价模型

以C2R模型为基础给出了一类多指标对象评价模型——C2RM模型.我们首先定义了决策单元的优势集,论证了C2RM模型比一类多目标规划模型在优化意义上更进一步——排除了此类多目标规划模型的一些优势集为空的Pareto有效解.我们建立的C2RM模型是线性规划模型,易于判定一个决策单元是否DEA有效.在优势集性质基础上我们进一步定义了C2RM模型下DEA有效决策单元的实际有效率,并给出了所有决策单元的一种排序,最后举例予以说明.     

Binary operations and lattice structure for a model of matching with contracts

We consider a restricted model of many-to-one matching with contracts and we order the set of stable allocations according both to the unanimous-for-doctors partial ordering and Blair’s partial ordering for hospitals. We define two binary operations to calculate the least upper bound and greatest lower bound for each pair of elements of this set in a simple way. By using these operations, we show that the set of stable allocations has dual lattice structures, thus reflecting an expected counterposition of interests between both sides of the market.     

一类稀疏约束非线性规划的约束规格

研究一类带有闭凸集约束的稀疏约束非线性规划问题,这类问题在变量选择、模式识别、投资组合等领域具有广泛的应用.首先引进了限制性Slater约束规格的概念,证明了该约束规格强于限制性M-F约束规格,然后在此约束规格成立的条件下,分析了其局部最优解成立的充分和必要条件.最后,对约束集合的两种具体形式,指出限制性Slater约束规格必满足,并给出了一阶必要性条件的具体表达形式.     

Cournot–Walras equilibrium as a subgame perfect equilibrium

In this paper, we investigate the problem of the strategic foundation of the Cournot–Walras equilibrium approach. To this end, we respecify à la Cournot–Walras the mixed version of a model of simultaneous, noncooperative exchange, originally proposed by Lloyd S. Shapley. We show, through an example, that the set of the Cournot–Walras equilibrium allocations of this respecification does not coincide with the set of the Cournot–Nash equilibrium allocations of the mixed version of the original Shapley’s model. As the nonequivalence, in a one-stage setting, can be explained by the intrinsic two-stage nature of the Cournot–Walras equilibrium concept, we are led to consider a further reformulation of the Shapley’s model as a two-stage game, where the atoms move in the first stage and the atomless sector moves in the second stage. Our main result shows that the set of the Cournot–Walras equilibrium allocations coincides with a specific set of subgame perfect equilibrium allocations of this two-stage game, which we call the set of the Pseudo–Markov perfect equilibrium allocations. We would like to thank Pierpaolo Battigalli, Marcellino Gaudenzi, and an anonymous referee for their comments and suggestions.     

A general model for matroids and the greedy algorithm

We present a general model for set systems to be independence families with respect to set families which determine classes of proper weight functions on a ground set. Within this model, matroids arise from a natural subclass and can be characterized by the optimality of the greedy algorithm. This model includes and extends many of the models for generalized matroid-type greedy algorithms proposed in the literature and, in particular, integral polymatroids. We discuss the relationship between these general matroids and classical matroids and provide a Dilworth embedding that allows us to represent matroids with underlying partial order structures within classical matroids. Whether a similar representation is possible for matroids on convex geometries is an open question. S. Fujishige’s research was supported by a Grant-in-Aid for Scientific Research of the Ministry of Education, Culture, Sports, Science and Technology of Japan.     

A fuzzy rough set approach to emergency material demand prediction over two universes

Emergency decision-making is still an important issue of unconventional emergency events management. Although many studies are developed on this topic, they remain political and qualitative, and it is difficult to make them operational in practice. Therefore, this article considers a fuzzy rough set over two universes model and approach for solving such a difficulty. As is well known, an exact and scientific emergency material demand prediction can make a quick and efficient emergency rescue and realize the optimal effect. Considering the main characteristics of emergency decision-making with insufficient risk identification, incomplete and inaccuracy of available information and uncertainty of decision-making environment, the fuzzy rough set theory over two universes is used to emergency material demand prediction. We propose a model and approach to emergency material demand prediction, i.e., the fuzzy rough set model of emergency material demand prediction over two universes. We present decision rules and computing methods for the proposed model by using the risk decision-making principle of classical operational research. Finally, the validity of the approach and the applied process of the proposed model is tested by a numerical example with the background of earthquake emergency material demand forecasting.     

Primal and dual algorithms for optimization over the efficient set

ABSTRACT

Optimization over the efficient set of a multi-objective optimization problem is a mathematical model for the problem of selecting a most preferred solution that arises in multiple criteria decision-making to account for trade-offs between objectives within the set of efficient solutions. In this paper, we consider a particular case of this problem, namely that of optimizing a linear function over the image of the efficient set in objective space of a convex multi-objective optimization problem. We present both primal and dual algorithms for this task. The algorithms are based on recent algorithms for solving convex multi-objective optimization problems in objective space with suitable modifications to exploit specific properties of the problem of optimization over the efficient set. We first present the algorithms for the case that the underlying problem is a multi-objective linear programme. We then extend them to be able to solve problems with an underlying convex multi-objective optimization problem. We compare the new algorithms with several state of the art algorithms from the literature on a set of randomly generated instances to demonstrate that they are considerably faster than the competitors.