Construction of Capacities from Overlap Indexes

In many problems, it is crucial to find a relation between groups of data. Such relation can be expressed, for instance, in terms of an appropriate fuzzy measure or capacity([10, 21]) which reflects the way the different data are connected to each other [20]. In this chapter, taking into account this fact and following the developments in [8],we introduce a method to build capacities ([20, 21]) directly from the data (inputs) of a given problem. In order to do so, we make use of the notions of overlap function and overlap index ([5, 12, 13, 7, 4, 14, 16]) for constructing capacities which reflect how different data are related to each other. This paper is organized as follows: after providing some preliminaries, we analyse, in Section 3, some properties of overlap functions and indexes. In Sections 4 we discuss a method for constructing capacities from overlap functions and overlap indexes. Finally, we present some conclusions and references

Designing Fuzzy Expert System to select managers based upon competency Case Study: Middle Managers of Automobile manufacturing company (Iran Khodro)

An essential and inevitable component of the efficiency of an organization is efficient managers. This study aims to design a fuzzy expert system in order to select Automobile manufacturing company middle managers based upon their competency. In contrast to conventional methods, which restrict assessment and measurement to specific criteria and supervisor's opinion, this research provides a comprehensive study to measure and compare managers' abilities. Thus, it has an applicable aspect. In terms of data collections and variables construct, this study is a descriptive research aims to modeling. The method of collecting data is field work and documentary research uses databases and experts' opinions. In order to construct a model, it used a mathematical framework (fuzzy Inference system). After designing a conceptual framework and verifying its validity, a MATLAB fuzzy toolbox has been used to design a fuzzy Inference system. In order to measure competency of a manager, a fuzzy deductive system has been designed at three levels. Sensivity analysis and limit analysis were used to measure the validity of the model. Finally, the designed model has been implemented in the area of research

On the development of decision-making systems based on fuzzy models to assess water quality in rivers

There are many situations where a linguistic description of complex phenomena allows better assessments. It is well known that the assessment of water quality continues depending heavily upon subjective judgments and interpretation, despite the huge datasets available nowadays. In that sense, the aim of this study has been to introduce intelligent linguistic operations to analyze databases, and produce self interpretable water quality indicators, which tolerate both imprecision and linguistic uncertainty. Such imprecision typically reflects the ambiguity of human thinking when perceptions need to be expressed. Environmental management concepts such as: "water quality", "level of risk", or "ecological status" are ideally dealt with linguistic variables. In the present Thesis, the flexibility of computing with words offered by fuzzy logic has been considered in these management issues. Firstly, a multipurpose hierarchical water quality index has been designed with fuzzy reasoning. It integrates a wide set of indicators including: organic pollution, nutrients, pathogens, physicochemical macro-variables, and priority micro-contaminants. Likewise, the relative importance of the water quality indicators has been dealt with the analytic hierarchy process, a decision-aiding method. Secondly, a methodology based on a hybrid approach that combines fuzzy inference systems and artificial neural networks has been used to classify ecological status in surface waters according to the Water Framework Directive. This methodology has allowed dealing efficiently with the non-linearity and subjective nature of variables involved in this classification problem. The complexity of inference systems, the appropriate choice of linguistic rules, and the influence of the functions that transform numerical variables into linguistic variables have been studied. Thirdly, a concurrent neuro-fuzzy model based on screening ecological risk assessment has been developed. It has considered the presence of hazardous substances in rivers, and incorporates an innovative ranking and scoring system, based on a self-organizing map, to account for the likely ecological hazards posed by the presence of chemical substances in freshwater ecosystems. Hazard factors are combined with environmental concentrations within fuzzy inference systems to compute ecological risk potentials under linguistic uncertainty. The estimation of ecological risk potentials allows identifying those substances requiring stricter controls and further rigorous risk assessment. Likewise, the aggregation of ecological risk potentials, by means of empirical cumulative distribution functions, has allowed estimating changes in water quality over time. The neuro-fuzzy approach has been validated by comparison with biological monitoring. Finally, a hierarchical fuzzy inference system to deal with sediment based ecological risk assessment has been designed. The study was centered in sediments, since they produce complementary findings to water quality analysis, especially when temporal trends are required. Results from chemical and eco-toxicological analyses have been used as inputs to two parallel inference systems which assess levels of contamination and toxicity, respectively. Results from both inference engines are then treated in a third inference engine which provides a final risk characterization, where the risk is provided in linguistic terms, with their respective degrees of certitude. Inputs to the risk system have been the levels of potentially toxic substances, mainly metals and chlorinated organic compounds, and the toxicity measured with a screening test which uses the photo-luminescent bacteria Vibrio fischeri. The Ebro river basin has been selected as case study, although the methodologies here explained can easily be applied to other rivers. In conclusion, this study has broadly demonstrated that the design of water quality indexes, based on fuzzy logic, emerges as suitable and alternative tool to support decision makers involved in effective sustainable river basin management plans.Existen diversas situaciones en las cuales la descripción en términos lingüísticos de fenómenos complejos permite mejores resultados. A pesar de los volúmenes de información cuantitativa que se manejan actualmente, es bien sabido que la gestión de la calidad del agua todavía obedece a juicios subjetivos y de interpretación de los expertos. Por tanto, el reto en este trabajo ha sido la introducción de operaciones lógicas que computen con palabras durante el análisis de los datos, para la elaboración de indicadores auto-interpretables de calidad del agua, que toleren la imprecisión e incertidumbre lingüística. Esta imprecisión típicamente refleja la ambigüedad del pensamiento humano para expresar percepciones. De allí que las variables lingüísticas se presenten como muy atractivas para el manejo de conceptos de la gestión medioambiental, como es el caso de la "calidad del agua", el "nivel de riesgo" o el "estado ecológico". Por tanto, en la presente Tesis, la flexibilidad de la lógica difusa para computar con palabras se ha adaptado a diversos tópicos en la gestión de la calidad del agua. Primero, se desarrolló un índice jerárquico multipropósito de calidad del agua que se obtuvo mediante razonamiento difuso. El índice integra un extenso grupo de indicadores que incluyen: contaminación orgánica, nutrientes, patógenos, variables macroscópicas, así como sustancias prioritarias micro-contaminantes. La importancia relativa de los indicadores al interior del sistema de inferencia se estimó con un método de análisis de decisiones, llamado proceso jerárquico analítico. En una segunda fase, se utilizó una metodología híbrida que combina los sistemas de inferencia difusos y las redes neuronales artificiales, conocida como neuro-fuzzy, para el estudio de la clasificación del estado ecológico de los ríos, de acuerdo con los lineamientos de la Directiva Marco de Aguas. Esta metodología permitió un manejo adecuado de la no-linealidad y naturaleza subjetiva de las variables involucradas en este problema clasificatorio. Con ella, se estudió la complejidad de los sistemas de inferencia, la selección apropiada de reglas lingüísticas y la influencia de las funciones que transforman las variables numéricas en lingüísticas. En una tercera fase, se desarrolló un modelo conceptual neuro-fuzzy concurrente basado en la metodología de evaluación de riesgo ecológico preliminar. Este modelo consideró la presencia de sustancias peligrosas en los ríos, e incorporó un mapa auto-organizativo para clasificar las sustancias químicas, en términos de su peligrosidad hacia los ecosistemas acuáticos. Con este modelo se estimaron potenciales de riesgo ecológico por combinación de factores de peligrosidad y de concentraciones de las sustancias químicas en el agua. Debido a la alta imprecisión e incertidumbre lingüística, estos potenciales se obtuvieron mediante sistemas de inferencia difusos, y se integraron por medio de distribuciones empíricas acumuladas, con las cuales se pueden analizar cambios espacio-temporales en la calidad del agua. Finalmente, se diseñó un sistema jerárquico de inferencia difuso para la evaluación del riesgo ecológico en sedimentos de ribera. Este sistema estima los grados de contaminación, toxicidad y riesgo en los sedimentos en términos lingüísticos, con sus respectivos niveles de certeza. El sistema se alimenta con información proveniente de análisis químicos, que detectan la presencia de sustancias micro-contaminantes, y de ensayos eco-toxicológicos tipo "screening" que usan la bacteria Vibrio fischeri. Como caso de estudio se seleccionó la cuenca del río Ebro, aunque las metodologías aquí desarrolladas pueden aplicarse fácilmente a otros ríos. En conclusión, este trabajo demuestra ampliamente que el diseño y aplicación de indicadores de calidad de las aguas, basados en la metodología de la lógica difusa, constituyen una herramienta sencilla y útil para los tomadores de decisiones encargados de la gestión sostenible de las cuencas hidrográficas

Multimodal fuzzy fusion for enhancing the motor-imagery-based brain computer interface

© 2005-2012 IEEE. Brain-computer interface technologies, such as steady-state visually evoked potential, P300, and motor imagery are methods of communication between the human brain and the external devices. Motor imagery-based brain-computer interfaces are popular because they avoid unnecessary external stimuli. Although feature extraction methods have been illustrated in several machine intelligent systems in motor imagery-based brain-computer interface studies, the performance remains unsatisfactory. There is increasing interest in the use of the fuzzy integrals, the Choquet and Sugeno integrals, that are appropriate for use in applications in which fusion of data must consider possible data interactions. To enhance the classification accuracy of brain-computer interfaces, we adopted fuzzy integrals, after employing the classification method of traditional brain-computer interfaces, to consider possible links between the data. Subsequently, we proposed a novel classification framework called the multimodal fuzzy fusion-based brain-computer interface system. Ten volunteers performed a motor imagery-based brain-computer interface experiment, and we acquired electroencephalography signals simultaneously. The multimodal fuzzy fusion-based brain-computer interface system enhanced performance compared with traditional brain-computer interface systems. Furthermore, when using the motor imagery-relevant electroencephalography frequency alpha and beta bands for the input features, the system achieved the highest accuracy, up to 78.81% and 78.45% with the Choquet and Sugeno integrals, respectively. Herein, we present a novel concept for enhancing brain-computer interface systems that adopts fuzzy integrals, especially in the fusion for classifying brain-computer interface commands

Fuzzy-TLX: using fuzzy integrals for evaluating human mental workload with NASA-Task Load indeX in laboratory and field studies

International audienceThe aim of this study was to assess mental workload in which various load sources must be integrated to derive reliable workload estimates. We report a new algorithm for computing weights from qualitative fuzzy integrals and apply it to the National Aeronautics and Space Administration -Task Load indeX (NASA-TLX) subscales in order to replace the standard pair-wise weighting technique (PWT). In this paper, two empirical studies were reported: (1) In a laboratory experiment, age- and task-related variables were investigated in 53 male volunteers and (2) In a field study, task- and job-related variables were studied on aircrews during 48 commercial flights. The results found in this study were as follows: (i) in the experimental setting, fuzzy estimates were highly correlated with classical (using PWT) estimates; (ii) in real work conditions, replacing PWT by automated fuzzy treatments simplified the NASA-TLX completion; (iii) the algorithm for computing fuzzy estimates provides a new classification procedure sensitive to various variables of work environments and (iv) subjective and objective measures can be used for the fuzzy aggregation of NASA-TLX subscales