Algebraic Computations with Hausdorff Continuous Functions

The paper has been presented at the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria, June, 2006.

Uncertainty and Fuzzy Sets: Classifying the Situation

The so called “Plural Uncertainty Model” is considered, in which statistical, maxmin, interval and Fuzzy model of uncertainty are embedded. For the last case external and internal contradictions of the theory are investigated and the modified definition of the Fuzzy Sets is proposed to overcome the troubles of the classical variant of Fuzzy Subsets by L. Zadeh. The general variants of logit- and probit- regression are the model of the modified Fuzzy Sets. It is possible to say about observations within the modification of the theory. The conception of the “situation” is proposed within modified Fuzzy Theory and the classifying problem is considered. The algorithm of the classification for the situation is proposed being the analogue of the statistical MLM(maximum likelihood method). The example related possible observing the distribution from the collection of distribution is considered.

Contradiction versus Selfcontradiction in Fuzzy Logic

* This work is partially supported by CICYT (Spain) under project TIN 2005-08943-C02-001 and by UPM-CAM (Spain) under project R05/11240.

A Geometrical Interpretation to Define Contradiction Degrees between Two Fuzzy Sets

For inference purposes in both classical and fuzzy logic, neither the information itself should be contradictory, nor should any of the items of available information contradict each other. In order to avoid these troubles in fuzzy logic, a study about contradiction was initiated by Trillas et al. in [5] and [6]. They introduced the concepts of both self-contradictory fuzzy set and contradiction between two fuzzy sets. Moreover, the need to study not only contradiction but also the degree of such contradiction is pointed out in [1] and [2], suggesting some measures for this purpose. Nevertheless, contradiction could have been measured in some other way. This paper focuses on the study of contradiction between two fuzzy sets dealing with the problem from a geometrical point of view that allow us to find out new ways to measure the contradiction degree. To do this, the two fuzzy sets are interpreted as a subset of the unit square, and the so called contradiction region is determined. Specially we tackle the case in which both sets represent a curve in [0,1]2. This new geometrical approach allows us to obtain different functions to measure contradiction throughout distances. Moreover, some properties of these contradiction measure functions are established and, in some particular case, the relations among these different functions are obtained.

On the Arithmetic of Errors

An approximate number is an ordered pair consisting of a (real) number and an error bound, briefly error, which is a (real) non-negative number. To compute with approximate numbers the arithmetic operations on errors should be well-known. To model computations with errors one should suitably define and study arithmetic operations and order relations over the set of non-negative numbers. In this work we discuss the algebraic properties of non-negative numbers starting from familiar properties of real numbers. We focus on certain operations of errors which seem not to have been sufficiently studied algebraically. In this work we restrict ourselves to arithmetic operations for errors related to addition and multiplication by scalars. We pay special attention to subtractability-like properties of errors and the induced “distance-like” operation. This operation is implicitly used under different names in several contemporary fields of applied mathematics (inner subtraction and inner addition in interval analysis, generalized Hukuhara difference in fuzzy set theory, etc.) Here we present some new results related to algebraic properties of this operation.

Partner selection for reverse logistics centres in green supply chains: a fuzzy artificial immune optimization approach

The design of reverse logistics networks has now emerged as a major issue for manufacturers, not only in developed countries where legislation and societal pressures are strong, but also in developing countries where the adoption of reverse logistics practices may offer a competitive advantage. This paper presents a new model for partner selection for reverse logistic centres in green supply chains. The model offers three advantages. Firstly, it enables economic, environment, and social factors to be considered simultaneously. Secondly, by integrating fuzzy set theory and artificial immune optimization technology, it enables both quantitative and qualitative criteria to be considered simultaneously throughout the whole decision-making process. Thirdly, it extends the flat criteria structure for partner selection evaluation for reverse logistics centres to the more suitable hierarchy structure. The applicability of the model is demonstrated by means of an empirical application based on data from a Chinese electronic equipment and instruments manufacturing company.

Instituições de Ensino Superior e movimentos migratórios em Portugal: uma aplicação do método fuzzy

As Instituições de Ensino Superior (IES) localizam-se ao longo de todo o território português, em cidades de dimensão distinta mas sempre âncoras dos territórios envolventes. Um dos efeitos mais imediatos, entre os “efeitos de procura”, relaciona-se com a dimensão populacional das cidades onde as IES estão instaladas. Logo que todos os agentes diretamente envolvidos com a IES chegam à (permanecem na) cidade – funcionários docentes e não docentes e estudantes – provocam efeitos vários, quer pela dimensão demográfica (quer em termos de volume quer de estrutura) quer pelos efeitos multiplicadores na atividade económica. O enquadramento teórico deste estudo prende-se com duas teorias fundamentais: os estudos acerca dos impactes das IES e a teoria das migrações jovens. Esta investigação visa estudar a existência de correlações entre as cidades que acolhem as IES, estas instituições e os movimentos migratórios ao longo do país. As questões de investigação são as seguintes: a dimensão das IES está relacionada com a dimensão da cidade onde está instalada e a capacidade de atração de ambas é proporcional? Podem as IES servir para inverter os fluxos migratórios que se verificam com destino às cidades onde existem IES? Os objectivos do trabalho são: - relacionar a dimensão das IES com as cidades de acolhimento, bem como os respectivos níveis de atração; - estudar os fluxos migratórios, destacando os jovens do conjunto do total da população que se desloca para as cidades / concelhos onde existem IES. Utilizar-se-ão dados relativos i) aos estabelecimentos da rede pública, universitária e politécnica; ii) às migrações internas em Portugal por grupos de idades e, iii) caracterização das cidades de acolhimento das IES. Os dados serão analisados com métodos de estatística descritiva, multivariada e com a metodologia fuzzy que visa conhecer as condições necessárias e/ou suficientes da atratividade das cidades relativamente aos fluxos migratórios jovens.

An assessment system for evaluation of driving competencies

Automobiles have deeply impacted the way in which we travel but they have also contributed to many deaths and injury due to crashes. A number of reasons for these crashes have been pointed out by researchers. Inexperience has been identified as a contributing factor to road crashes. Driver’s driving abilities also play a vital role in judging the road environment and reacting in-time to avoid any possible collision. Therefore driver’s perceptual and motor skills remain the key factors impacting on road safety. Our failure to understand what is really important for learners, in terms of competent driving, is one of the many challenges for building better training programs. Driver training is one of the interventions aimed at decreasing the number of crashes that involve young drivers. Currently, there is a need to develop comprehensive driver evaluation system that benefits from the advances in Driver Assistance Systems. A multidisciplinary approach is necessary to explain how driving abilities evolves with on-road driving experience. To our knowledge, driver assistance systems have never been comprehensively used in a driver training context to assess the safety aspect of driving. The aim and novelty of this thesis is to develop and evaluate an Intelligent Driver Training System (IDTS) as an automated assessment tool that will help drivers and their trainers to comprehensively view complex driving manoeuvres and potentially provide effective feedback by post processing the data recorded during driving. This system is designed to help driver trainers to accurately evaluate driver performance and has the potential to provide valuable feedback to the drivers. Since driving is dependent on fuzzy inputs from the driver (i.e. approximate distance calculation from the other vehicles, approximate assumption of the other vehicle speed), it is necessary that the evaluation system is based on criteria and rules that handles uncertain and fuzzy characteristics of the driving tasks. Therefore, the proposed IDTS utilizes fuzzy set theory for the assessment of driver performance. The proposed research program focuses on integrating the multi-sensory information acquired from the vehicle, driver and environment to assess driving competencies. After information acquisition, the current research focuses on automated segmentation of the selected manoeuvres from the driving scenario. This leads to the creation of a model that determines a “competency” criterion through the driving performance protocol used by driver trainers (i.e. expert knowledge) to assess drivers. This is achieved by comprehensively evaluating and assessing the data stream acquired from multiple in-vehicle sensors using fuzzy rules and classifying the driving manoeuvres (i.e. overtake, lane change, T-crossing and turn) between low and high competency. The fuzzy rules use parameters such as following distance, gaze depth and scan area, distance with respect to lanes and excessive acceleration or braking during the manoeuvres to assess competency. These rules that identify driving competency were initially designed with the help of expert’s knowledge (i.e. driver trainers). In-order to fine tune these rules and the parameters that define these rules, a driving experiment was conducted to identify the empirical differences between novice and experienced drivers. The results from the driving experiment indicated that significant differences existed between novice and experienced driver, in terms of their gaze pattern and duration, speed, stop time at the T-crossing, lane keeping and the time spent in lanes while performing the selected manoeuvres. These differences were used to refine the fuzzy membership functions and rules that govern the assessments of the driving tasks. Next, this research focused on providing an integrated visual assessment interface to both driver trainers and their trainees. By providing a rich set of interactive graphical interfaces, displaying information about the driving tasks, Intelligent Driver Training System (IDTS) visualisation module has the potential to give empirical feedback to its users. Lastly, the validation of the IDTS system’s assessment was conducted by comparing IDTS objective assessments, for the driving experiment, with the subjective assessments of the driver trainers for particular manoeuvres. Results show that not only IDTS was able to match the subjective assessments made by driver trainers during the driving experiment but also identified some additional driving manoeuvres performed in low competency that were not identified by the driver trainers due to increased mental workload of trainers when assessing multiple variables that constitute driving. The validation of IDTS emphasized the need for an automated assessment tool that can segment the manoeuvres from the driving scenario, further investigate the variables within that manoeuvre to determine the manoeuvre’s competency and provide integrated visualisation regarding the manoeuvre to its users (i.e. trainers and trainees). Through analysis and validation it was shown that IDTS is a useful assistance tool for driver trainers to empirically assess and potentially provide feedback regarding the manoeuvres undertaken by the drivers.

Exploring the challenges to industrialized residential building in China

Industrialised building (IB) is considered by many to have an important role to play in China's residential construction industry due to its potential for improved quality, productivity, efficiency, safety and sustainability. It is surprising, therefore, that although a large number of construction programmes have been completed in the country in recent years, very few have been built in this manner. Quite why this situation exists is unknown. The well-known problems with IB, such as the constraints placed on designer freedom, may be the cause. It is equally possible that, as is typical with developing countries such as China, cost or government issues dominate. On the other hand, in comparison with other countries, the construction industry in China has been widely criticised for its lack of modernity. Either way, there is an urgent need to assess and understand the hindrances to the adoption of IB in residential construction in order to identify what corrective measures, if any, need to be taken. Towards this end, we first identify a set of critical factors (CFs) for assessing the hindrances to IB adoption in China. This involves the analysis of research data collected by a questionnaire survey of experienced housing developers and professionals working in China's construction industry sector. Fuzzy set theory is used in the selection of the CFs. These CFs comprise, in rank order: higher initial cost; lack of skilled labour in IB; manufacturing capability and involvement issues and product quality problems; lack of supply chain; lack of codes and standards; and lack of government incentives, directives and promotion. The establishment of the CFs provides a basis for local construction sectors to better equip themselves for future implementation of IB. The findings also indicate a current need for formulating improved policies and strategies to encourage the further development of IB in China at present.

Measuring corruption in public construction projects in China

Corruption has been identified as the greatest obstacle to economic and social development. Public construction projects, in particular, face high corruption risk as public construction sector has been consecutively deemed as the most corrupt one. Despite considerable efforts have been undertaken to measure corruption at a nation level, few focus on the measurement of corruption in construction projects. This paper develops a fuzzy measurement model for the potential corruption in public construction projects in China. Through semi-structured interviews with 14 experts, followed by a questionnaire survey with 188 respondents, 24 measurement items of corruption were identified and further categorized into five constructs. The fuzzy set theory was then adopted to quantify each measurement item, construct and the overall corruption level. This model can facilitate in evaluating, revealing and monitoring corruption in public construction projects. Although this study focuses on measuring corruption in public construction projects in China, similar research methods can be applied in other countries around the world and thus contribute to the global body of knowledge of corruption.

Improved Kalman filter initialisation using neurofuzzy estimation

It is traditional to initialise Kalman filters and extended Kalman filters with estimates of the states calculated directly from the observed (raw) noisy inputs, but unfortunately their performance is extremely sensitive to state initialisation accuracy: good initial state estimates ensure fast convergence whereas poor estimates may give rise to slow convergence or even filter divergence. Divergence is generally due to excessive observation noise and leads to error magnitudes that quickly become unbounded (R.J. Fitzgerald, 1971). When a filter diverges, it must be re initialised but because the observations are extremely poor, re initialised states will have poor estimates. The paper proposes that if neurofuzzy estimators produce more accurate state estimates than those calculated from the observed noisy inputs (using the known state model), then neurofuzzy estimates can be used to initialise the states of Kalman and extended Kalman filters. Filters whose states have been initialised with neurofuzzy estimates should give improved performance by way of faster convergence when the filter is initialised, and when a filter is re started after divergence

Devolution of forest-related rights: Comparative analyses of six developing countries

The study focused on the different ways that forest-related rights can be devolved to the local level according to the current legal frameworks in Laos, Nepal, Vietnam, Kenya, Mozambique and Tanzania. The eleven case studies represented the main ways in which forest-related rights can be devolved to communities or households in these countries. The objectives of this study were to 1) analyse the contents and extent of forest-related rights that can be devolved to the local level, 2) develop an empirical typology that represents the main types of devolution, and 3) compare the cases against a theoretical ideal type to assess in what way and to what extent the cases are similar to or differ from the theoretical construct. Fuzzy set theory, Qualitative Comparative Analysis and ideal type analysis were used in analysing the case studies and in developing an empirical typology. The theoretical framework, which guided data collection and analyses, was based on institutional economics and theories on property rights, common pool resources and collective action. On the basis of the theoretical and empirical knowledge, the most important attributes of rights were defined as use rights, management rights, exclusion rights, transfer rights and the duration and security of the rights. The ideal type was defined as one where local actors have been devolved comprehensive use rights, extensive management rights, rights to exclude others from the resource and rights to transfer these rights. In addition, the rights are to be secure and held perpetually. The ideal type was used to structure the analysis and as a tool against which the cases were analysed. The contents, extent and duration of the devolved rights varied greatly. In general, the results show that devolution has mainly meant the transfer of use rights to the local level, and has not really changed the overall state control over forest resources. In most cases the right holders participate, or have a limited role in the decision making regarding the harvesting and management of the resource. There was a clear tendency to devolve the rights to enforce rules and to monitor resource use and condition more extensively than the powers to decide on the management and development of the resource. The empirical typology of the cases differentiated between five different types of devolution. The types can be characterised by the devolution of 1) restricted use and control rights, 2) extensive use rights but restricted control rights, 3) extensive rights, 4) insecure, short term use and restricted control rights, and 5) insecure extensive rights. Overall, the case studies conformity to the ideal type was very low: only two cases were similar to the ideal type, all other cases differed considerably from the ideal type. The restricted management rights were the most common reason for the low conformity to the ideal type (eight cases). In three cases, the short term of the rights, restricted transfer rights, restricted use rights or restricted exclusion rights were the reason or one of the reasons for the low conformity to the ideal type. In two cases the rights were not secure.

Modeling reservoir irrigation in uncertain hydrologic environment

In a detailed model for reservoir irrigation taking into account the soil moisture dynamics in the root zone of the crops, the data set for reservoir inflow and rainfall in the command will usually be of sufficient length to enable their variations to be described by probability distributions. However, the potential evapotranspiration of the crop itself depends on the characteristics of the crop and the reference evaporation, the quantification of both being associated with a high degree of uncertainty. The main purpose of this paper is to propose a mathematical programming model to determine the annual relative yield of crops and to determine its reliability, for a single reservoir meant for irrigation of multiple crops, incorporating variations in inflow, rainfall in the command area, and crop consumptive use. The inflow to the reservoir and rainfall in the reservoir command area are treated as random variables, whereas potential evapotranspiration is modeled as a fuzzy set. The model's application is illustrated with reference to an existing single-reservoir system in Southern India.

Methods for Automatic Evaluation of Sentence Extract Summaries

This paper describes three novel techniques to automatically evaluate sentence extract summaries. Two of these techniques called FuSE and DeFuSE evaluate the quality of the generated extract summary based on the degree of similarity to the model summary. They use a fuzzy set theoretic basis to generate a match score. DeFuSE is an enhancement to FuSE and uses WordNet based hypernymy structures to detect similarity between sentences at abstracted levels. The third technique focuses on quantifying the quality of an extract summary based on the difficulty in generating such a summary. Advantages of these techniques are described with examples.

Identification and optimization of ammonia reactors through hybrid simulation

A hybrid simulation technique for identification and steady state optimization of a tubular reactor used in ammonia synthesis is presented. The parameter identification program finds the catalyst activity factor and certain heat transfer coefficients that minimize the sum of squares of deviation from simulated and actual temperature measurements obtained from an operating plant. The optimization program finds the values of three flows to the reactor to maximize the ammonia yield using the estimated parameter values. Powell's direct method of optimization is used in both cases. The results obtained here are compared with the plant data.