A probabilistic neural network approach for modeling and classification of bacterial growth/no-growth data

In this paper, we propose to use probabilistic neural networks (PNNs) for classification of bacterial growth/no-growth data and modeling the probability of growth. The PNN approach combines both Bayes theorem of conditional probability and Parzen's method for estimating the probability density functions of the random variables. Unlike other neural network training paradigms, PNNs are characterized by high training speed and their ability to produce confidence levels for their classification decision. As a practical application of the proposed approach, PNNs were investigated for their ability in classification of growth/no-growth state of a pathogenic Escherichia coli R31 in response to temperature and water activity. A comparison with the most frequently used traditional statistical method based on logistic regression and multilayer feedforward artificial neural network (MFANN) trained by error backpropagation was also carried out. The PNN-based models were found to outperform linear and nonlinear logistic regression and MFANN in both the classification accuracy and ease by which PNN-based models are developed.     

Transportation Optimization with Fuzzy Trapezoidal Numbers Based on Possibility Theory

In this paper, a parametric method is introduced to solve fuzzy transportation problem. Considering that parameters of transportation problem have uncertainties, this paper develops a generalized fuzzy transportation problem with fuzzy supply, demand and cost. For simplicity, these parameters are assumed to be fuzzy trapezoidal numbers. Based on possibility theory and consistent with decision-makers'' subjectiveness and practical requirements, the fuzzy transportation problem is transformed to a crisp linear transportation problem by defuzzifying fuzzy constraints and objectives with application of fractile and modality approach. Finally, a numerical example is provided to exemplify the application of fuzzy transportation programming and to verify the validity of the proposed methods.     

On the Application of Fuzzy Decision Theory in Chemotherapy

1IntreductionTheliteratUreonmulti-Criteriondecisionmaking(MCDM)problemshas~tremendouslyintherecentpast.TwomajorareashaveevolvedwhiChbothconcentrateondecisionmakingwithseveralcriteria:multiobjectivedecisionmaking(MODM)andmulti-attributedecisionmaking(MADM).TheformerconcentratesoncontinuousdecisionspaceandthelatterfocusesonproblemswithdiscreteSPace.FuzzysettheoryhascontributedtoMODMproblemsaswellastheMADMProblems.ThegeneralMODMproblemcanbedeft.edLllasfollows:Twostagescangenerallybe…     

新疆区域水资源对产业生态系统与经济增长的动态关联——基于VAR模型

新疆正面临"五化同步"对水资源的需求不断增长与水资源开发利用过度的矛盾。水资源瓶颈制约已成为影响新疆经济可持续发展和长治久安的突出问题之一。运用VAR模型,通过ADF检验、脉冲响应函数和方差贡献度分解,对2000—2014年新疆耗水产业生态系统和经济增长的长期均衡关系进行实证分析。结果表明:(1)经济增长与总用水量、工业用水量和农业用水量之间均存在长期均衡关系;(2)经济发展对用水量产生负向冲击,工业用水量和农业用水量随着经济发展出现正向冲击效应。(3)新疆经济快速增长伴随着水资源的大力开发和过度利用。据此提出对策建议,通过实施严格的退地减水政策,明确用水总量控制和定额指标,加强跨流域调水工程建设,防止浪费等多途径维持新疆水资源可持续利用和耗水产业健康发展。     

Decision errors in evaluating tipping points for ecosystem resilience

When an ecosystem reaches tipping points for selected indicators, resilience to further changes in external drivers can decrease, regime shifts can occur that diminish the capacity of the ecosystem to provide ecosystem services, and the ecosystem is more vulnerable to collapse. Evaluating tipping points for resilience using crisp decision rules can result in decision errors about whether or not resilience has been compromised. The source and nature of those errors are described and a fuzzy decision rule is proposed for evaluating resilience. Decision errors are evaluated for four cases. Cases 1 through 3 (or case 4) derive conditions for evaluating decision errors when there is a single (or multiple) indicator(s). The primary sources of decision errors for the four cases are discrepancies between measured (or established) and true values of the indicators (or tipping points) and using a crisp decision rule to reach conclusions about whether or not resilience has been compromised. A fuzzy decision rule, based on fuzzy TOPSIS, is proposed that evaluates the extent to which an ecosystem is resilient. Although crisp decision rules provide unambiguous conclusions about resilience, those conclusions can be faulty, particularly when measured indicators and established tipping points deviate substantially from their true values. In contrast, the conclusions from the fuzzy decision rule are less susceptible to the decision errors and, hence, faulty decisions.     

Neuro-fuzzy decision trees

Fuzzy decision trees are powerful, top-down, hierarchical search methodology to extract human interpretable classification rules. However, they are often criticized to result in poor learning accuracy. In this paper, we propose Neuro-Fuzzy Decision Trees (N-FDTs); a fuzzy decision tree structure with neural like parameter adaptation strategy. In the forward cycle, we construct fuzzy decision trees using any of the standard induction algorithms like fuzzy ID3. In the feedback cycle, parameters of fuzzy decision trees have been adapted using stochastic gradient descent algorithm by traversing back from leaf to root nodes. With this strategy, during the parameter adaptation stage, we keep the hierarchical structure of fuzzy decision trees intact. The proposed approach of applying backpropagation algorithm directly on the structure of fuzzy decision trees improves its learning accuracy without compromising the comprehensibility (interpretability). The proposed methodology has been validated using computational experiments on real-world datasets.     

Optimum Design in Multivariate Stratified Sampling

The procedure of determining the optimum sample size in each stratum in stratified sampling for several variables is expressed and solved as a multistage decision process through dynamic programming. Using data published elsewhere, the dynamic programming approach was shown to give results identical to those obtained by some other already suggested approaches. The advantage is that dynamic programming can more easily handle problems involving several strata and/or variables.     

A biologically inspired neural network for dynamic programming

An artificial neural network with a two-layer feedback topology and generalized recurrent neurons, for solving nonlinear discrete dynamic optimization problems, is developed. A direct method to assign the weights of neural networks is presented. The method is based on Bellmann's Optimality Principle and on the interchange of information which occurs during the synaptic chemical processing among neurons. The neural network based algorithm is an advantageous approach for dynamic programming due to the inherent parallelism of the neural networks; further it reduces the severity of computational problems that can occur in methods like conventional methods. Some illustrative application examples are presented to show how this approach works out including the shortest path and fuzzy decision making problems.     

Two-dimensional grey cloud clustering-fuzzy entropy comprehensive assessment model for river health evaluation

Abstract

The river health evaluation is typically complex non-linear system with characteristics of fuzziness and randomness. However, conventional gray clustering method has difficult to effectively describe fuzzy and random information simultaneously. For this purpose, the cloud model and fuzzy entropy theory are introduced to establish 2D gray cloud clustering-fuzzy entropy comprehensive evaluation model. Different with health level models, it reflects river health situation from aspects of health level and corresponding water body complexity simultaneously. The health level is obtained by gray cloud whitened weight function (first sub-system) and fuzzy entropy represents complexity and fuzziness of river health situation (second sub-system). Moreover, multi-level river health evaluation indicator system is constructed with dividing indicators into common and distinct sections according to differences on river characteristics. Meanwhile, indicator weights are determined by renewed combined weighting method based on minimum deviation principle. Finally, we conduct health evaluation work for rivers in the Taihu basin. The evaluation health levels and fuzzy entropy for river A–G are H3 (0.4888, relatively significant); H2 (0.5476, relatively fuzzy); H2 (0.7526, fuzzy); H2 (0.4731, relatively significant); H2 (05138, relatively fuzzy); H3 (0.5822, relatively fuzzy), and H2 (0.4064, relatively significant), respectively. Results are consistent with current river health situation and more intuitive than compared models. Furthermore, evaluation results with four different weighting methods are compared to further demonstrate rationality of the weighting method and evaluation model. Hence, the model proposed is demonstrated to provide new insight for solving river health assessment problem effectively.     

模糊数学在研究定西地区胡麻产量预报中的应用

目前,不少科学领域中,模糊数学方法已愈来愈受到重视。例如在气象、地震预报等方面已获得较好的效果。鉴于农作物产量预报的研究,现在尚处于经验估测阶段。但它考虑的模型与识别的对象在很大程度上往往都还是模糊的,因此,采用模糊数学方法来探测农作物产量预报就具有一定的可能性和优越性。近年来,我们在农作物产量预报方面做了一些探索,取得了一些初步结果。这些初步结果表明,模糊数学方法与技巧的应用,具有十分诱人的前景。本文在广义Fuzzy运算的综合决策模型的基础上,提出了一个改进的“综合决策模型”,并给出了其在产量预报中的具体实例。此法意义直观易懂,简便易行,便于群众掌握。最后又采用了逐步回归及逐段回归方法,建立了一个定量的预报模型与综合决策模型以作相互弥补,取得了较好的效果。它们不仅对历史资料模拟率可达88.2％,而且其可靠性也被1983年的大丰收所证实。经各方面探讨,认为采用这两种方法综合对产量趋势预报,其结果是令人满意的。     

The resource-constrained project scheduling model of Bianco and Caramia: clarifications and an alternative model formulation

Recently, Bianco and Caramia (Flex Serv Manuf J 25(1–2), 6–24, 2013) proposed a new model for the resource-constrained project scheduling problem. Despite its potential, the presentation of the mixed-integer programming model contains some ambiguity which may create misunderstanding in the implementation phase. Here, we clarify the definitions of the decision variables and illustrate their corresponding values using a numerical example. Furthermore, we propose a different interpretation of two decision variables which gives rise to an alternative model formulation also presented using the same numerical example.     

An Efficacious Multi-Objective Fuzzy Linear Programming Approach for Optimal Power Flow Considering Distributed Generation

This paper proposes a new formulation for the multi-objective optimal power flow (MOOPF) problem for meshed power networks considering distributed generation. An efficacious multi-objective fuzzy linear programming optimization (MFLP) algorithm is proposed to solve the aforementioned problem with and without considering the distributed generation (DG) effect. A variant combination of objectives is considered for simultaneous optimization, including power loss, voltage stability, and shunt capacitors MVAR reserve. Fuzzy membership functions for these objectives are designed with extreme targets, whereas the inequality constraints are treated as hard constraints. The multi-objective fuzzy optimal power flow (OPF) formulation was converted into a crisp OPF in a successive linear programming (SLP) framework and solved using an efficient interior point method (IPM). To test the efficacy of the proposed approach, simulations are performed on the IEEE 30-busand IEEE 118-bus test systems. The MFLP optimization is solved for several optimization cases. The obtained results are compared with those presented in the literature. A unique solution with a high satisfaction for the assigned targets is gained. Results demonstrate the effectiveness of the proposed MFLP technique in terms of solution optimality and rapid convergence. Moreover, the results indicate that using the optimal DG location with the MFLP algorithm provides the solution with the highest quality.     

APPLICATION OF FUZZY SETS AND NEURAL NETWORKS IN SENSORY ANALYSIS

This paper describes an initial but fundamental attempt to lay some groundwork for a fuzzy-set-based paradigm for sensory analysis and to demonstrate how fuzzy set and neural network techniques may lead to a natural way for sensory data interpretation. Sensory scales are described as fuzzy sets, sensory attributes as fuzzy variables, and sensory responses as sample membership grades. Multi-judge responses are formulated as a fuzzy membership vector or fuzzy histogram of response, which gives an overall panel response free of the unverifiable assumptions implied in conventional approaches. Neural networks are used to provide an effective tool for modeling and analysis of sensory responses in their naturally fuzzy and complex forms. A maximum method of defuzzification is proposed to give a crisp grade of the majority opinion. Two applications in meat quality evaluation are used to demonstrate the use of the paradigm and procedure. It is hoped that this work will bring up some new ideas and generate interest in research on application of fuzzy sets and neural networks in sensory analysis.     

F-IND: A framework to design fuzzy indices of environmental conditions

Multivariable indices of environmental conditions summarize the information provided by several biotic or abiotic variables into a single value of immediate interpretability. Thus they are important instruments for monitoring. Developing new indices that combine different variables is not a trivial task: variables may be qualitative, or measured in different units, and the relationship between primitive components and quality may be ambiguous. Fuzzy logic has been repeatedly proposed as an effective technique to cope with such problems; however, the variety of choices that exist at each stage of the development of fuzzy models may present a problem for the index designer. In this paper we present F-IND, a framework to create fuzzy indices by means of a simplified and intuitive procedure. It allows to capture the expert knowledge of the system under study (air, soil, water) to easily generate a multivariable index of environmental conditions. F-IND is implemented in Java, to achieve an optimal portability on any operating system.     

基于模糊决策的临床科室主任绩效考核的研究

通过研究临床科室主任绩效考核指标,调动科室主任管理的积极性,增强科室员工质量管理意识和医疗安全意识,促进医院的发展。在分析传统临床科室绩效考核方法不足的基础上,结合模糊决策的概念,提出了一种基于模糊决策的临床科室主任综合评判方法。该方法充分利用了模糊逻辑中模糊决策的概念,对医院临床科室主任进行了模糊意见集中决策和模糊综合评判决策。最后通过具体的数值实验对该方法进行了性能分析,结果证明该方法具有良好的性能。     

Fuzzy p-values in latent variable problems

We consider the problem of testing a statistical hypothesiswhere the scientifically meaningful test statistic is a functionof latent variables. In particular, we consider detection ofgenetic linkage, where the latent variables are patterns ofinheritance at specific genome locations. Introduced by Geyer& Meeden (2005), fuzzy p-values are random variables, describedby their probability distributions, that are interpreted asp-values. For latent variable problems, we introduce the notionof a fuzzy p-value as having the conditional distribution ofthe latent p-value given the observed data, where the latentp-value is the random variable that would be the p-value ifthe latent variables were observed. The fuzzy p-value provides an exact test using two sets of simulationsof the latent variables under the null hypothesis, one unconditionaland the other conditional on the observed data. It providesnot only an expression of the strength of the evidence againstthe null hypothesis but also an expression of the uncertaintyin that expression owing to lack of knowledge of the latentvariables. We illustrate these features with an example of simulateddata mimicking a real example of the detection of genetic linkage.     

Backpropagation through time training of a neuro-fuzzy controller

The paper considers gradient training of fuzzy logic controller (FLC) presented in the form of neural network structure. The proposed neuro-fuzzy structure allows keeping linguistic meaning of fuzzy rule base. Its main adjustable parameters are shape determining parameters of the linguistic variables fuzzy values as well as that of the used as intersection operator parameterized T-norm. The backpropagation through time method was applied to train neuro-FLC for a highly non-linear plant (a biotechnological process). The obtained results are discussed with respect to adjustable parameters rationality. Conclusions are made with respect to the appropriate intersection operations too.     

Computer simulation of different types of evolutionary process

The computer model of two alternative variants of biological evolution is proposed. The first variant supposes random while the second--directed change of individual features, thus corresponding to the Darwinian and non-Darwinian evolution. The evolution of fish communities in fresh waters serves as a particular example. The model is executed using object-oriented method of programming and mathematical apparatus of fuzzy logics. The investigation of the model showed that process of Darwinian evolution is connected with significantly greater species diversity and variability of evolutionary process trajectories than non-Darwinian one. On the other hand, non-Darwinian type of evolution provides fast achievement of high individual fitness, especially under conditions of constant environment. Non-Darwinian type evolution failed in big evolutionary alteration (for example, transition to predation); while the Darwinian evolution under the same conditions can produce such alterations though it took more time and many extinct species. Phylogenetic tree of Darwinian evolution is always more complex than of non-Darwinian one under the same conditions.     

Exact and Metaheuristic Approaches for a Bi-Objective School Bus Scheduling Problem

As a class of hard combinatorial optimization problems, the school bus routing problem has received considerable attention in the last decades. For a multi-school system, given the bus trips for each school, the school bus scheduling problem aims at optimizing bus schedules to serve all the trips within the school time windows. In this paper, we propose two approaches for solving the bi-objective school bus scheduling problem: an exact method of mixed integer programming (MIP) and a metaheuristic method which combines simulated annealing with local search. We develop MIP formulations for homogenous and heterogeneous fleet problems respectively and solve the models by MIP solver CPLEX. The bus type-based formulation for heterogeneous fleet problem reduces the model complexity in terms of the number of decision variables and constraints. The metaheuristic method is a two-stage framework for minimizing the number of buses to be used as well as the total travel distance of buses. We evaluate the proposed MIP and the metaheuristic method on two benchmark datasets, showing that on both instances, our metaheuristic method significantly outperforms the respective state-of-the-art methods.     

Analytical fuzzy approach to biological data analysis

The assessment of the physiological state of an individual requires an objective evaluation of biological data while taking into account both measurement noise and uncertainties arising from individual factors. We suggest to represent multi-dimensional medical data by means of an optimal fuzzy membership function. A carefully designed data model is introduced in a completely deterministic framework where uncertain variables are characterized by fuzzy membership functions. The study derives the analytical expressions of fuzzy membership functions on variables of the multivariate data model by maximizing the over-uncertainties-averaged-log-membership values of data samples around an initial guess. The analytical solution lends itself to a practical modeling algorithm facilitating the data classification. The experiments performed on the heartbeat interval data of 20 subjects verified that the proposed method is competing alternative to typically used pattern recognition and machine learning algorithms.