A new modularity measure for Fuzzy Community detection problems based on overlap and grouping functions

One of the main challenges of fuzzy community detection problems is to be able to measure the quality of a fuzzy partition. In this paper, we present an alternative way of measuring the quality of a fuzzy community detection output based on n-dimensional grouping and overlap functions. Moreover, the proposed modularity measure generalizes the classical Girvan–Newman (GN) modularity for crisp community detection problems and also for crisp overlapping community detection problems. Therefore, it can be used to compare partitions of different nature (i.e. those composed of classical, overlapping and fuzzy communities). Particularly, as is usually done with the GN modularity, the proposed measure may be used to identify the optimal number of communities to be obtained by any network clustering algorithm in a given network. We illustrate this usage by adapting in this way a well-known algorithm for fuzzy community detection problems, extending it to also deal with overlapping community detection problems and produce a ranking of the overlapping nodes. Some computational experiments show the feasibility of the proposed approach to modularity measures through n-dimensional overlap and grouping functions.

A calibration approach based on Takagi-Sugeno fuzzy inference system for digital electronic compasses

Recently, the development of industrial processes brought on the outbreak of technologically complex systems. This development generated the necessity of research relative to the mathematical techniques that have the capacity to deal with project complexities and validation. Fuzzy models have been receiving particular attention in the area of nonlinear systems identification and analysis due to it is capacity to approximate nonlinear behavior and deal with uncertainty. A fuzzy rule-based model suitable for the approximation of many systems and functions is the Takagi-Sugeno (TS) fuzzy model. IS fuzzy models are nonlinear systems described by a set of if then rules which gives local linear representations of an underlying system. Such models can approximate a wide class of nonlinear systems. In this paper a performance analysis of a system based on IS fuzzy inference system for the calibration of electronic compass devices is considered. The contribution of the evaluated IS fuzzy inference system is to reduce the error obtained in data acquisition from a digital electronic compass. For the reliable operation of the TS fuzzy inference system, adequate error measurements must be taken. The error noise must be filtered before the application of the IS fuzzy inference system. The proposed method demonstrated an effectiveness of 57% at reducing the total error based on considered tests. (C) 2011 Elsevier Ltd. All rights reserved.

A two-dimensional fuzzy random model of soil pore structure

A new conceptual model for soil pore-solid structure is formalized. Soil pore-solid structure is proposed to comprise spatially abutting elements each with a value which is its membership to the fuzzy set ''pore,'' termed porosity. These values have a range between zero (all solid) and unity (all pore). Images are used to represent structures in which the elements are pixels and the value of each is a porosity. Two-dimensional random fields are generated by allocating each pixel a porosity by independently sampling a statistical distribution. These random fields are reorganized into other pore-solid structural types by selecting parent points which have a specified local region of influence. Pixels of larger or smaller porosity are aggregated about the parent points and within the region of interest by controlled swapping of pixels in the image. This creates local regions of homogeneity within the random field. This is similar to the process known as simulated annealing. The resulting structures are characterized using one-and two-dimensional variograms and functions describing their connectivity. A variety of examples of structures created by the model is presented and compared. Extension to three dimensions presents no theoretical difficulties and is currently under development.

A Bayesian approach to fuzzy hypotheses testing for the estimation of optimal age for vaccination against measles

Fuzzy Bayesian tests were performed to evaluate whether the mother`s seroprevalence and children`s seroconversion to measles vaccine could be considered as ""high"" or ""low"". The results of the tests were aggregated into a fuzzy rule-based model structure, which would allow an expert to influence the model results. The linguistic model was developed considering four input variables. As the model output, we obtain the recommended age-specific vaccine coverage. The inputs of the fuzzy rules are fuzzy sets and the outputs are constant functions, performing the simplest Takagi-Sugeno-Kang model. This fuzzy approach is compared to a classical one, where the classical Bayes test was performed. Although the fuzzy and classical performances were similar, the fuzzy approach was more detailed and revealed important differences. In addition to taking into account subjective information in the form of fuzzy hypotheses it can be intuitively grasped by the decision maker. Finally, we show that the Bayesian test of fuzzy hypotheses is an interesting approach from the theoretical point of view, in the sense that it combines two complementary areas of investigation, normally seen as competitive. (C) 2007 IMACS. Published by Elsevier B.V. All rights reserved.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Optimal fuzzy PID control tuned with genetic algorithms

Fuzzy logic controllers (FLC) are intelligent systems, based on heuristic knowledge, that have been largely applied in numerous areas of everyday life. They can be used to describe a linear or nonlinear system and are suitable when a real system is not known or too difficult to find their model. FLC provide a formal methodology for representing, manipulating and implementing a human heuristic knowledge on how to control a system. These controllers can be seen as artificial decision makers that operate in a closed-loop system, in real time. The main aim of this work was to develop a single optimal fuzzy controller, easily adaptable to a wide range of systems – simple to complex, linear to nonlinear – and able to control all these systems. Due to their efficiency in searching and finding optimal solution for high complexity problems, GAs were used to perform the FLC tuning by finding the best parameters to obtain the best responses. The work was performed using the MATLAB/SIMULINK software. This is a very useful tool that provides an easy way to test and analyse the FLC, the PID and the GAs in the same environment. Therefore, it was proposed a Fuzzy PID controller (FL-PID) type namely, the Fuzzy PD+I. For that, the controller was compared with the classical PID controller tuned with, the heuristic Ziegler-Nichols tuning method, the optimal Zhuang-Atherton tuning method and the GA method itself. The IAE, ISE, ITAE and ITSE criteria, used as the GA fitness functions, were applied to compare the controllers performance used in this work. Overall, and for most systems, the FL-PID results tuned with GAs were very satisfactory. Moreover, in some cases the results were substantially better than for the other PID controllers. The best system responses were obtained with the IAE and ITAE criteria used to tune the FL-PID and PID controllers.

Reducing the number of membership functions in linguistic variables

Dissertation presented at Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia in fulfilment of the requirements for the Masters degree in Mathematics and Applications, specialization in Actuarial Sciences, Statistics and Operations Research

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.

Data fusion with computational intelligence techniques: a case study of fuzzy inference for terrain assessment

Dissertação apresentada para obtenção do Grau de Mestre em Engenharia Electrotécnica e de Computadores, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Application of Fuzzy Variables for Systems of Management Decision Support

The following article describes an approach covering the variety of opinions and uncertainties of estimates within the chosen technique of decision support. Mathematical operations used for assessment of options are traced to operations of working with functions that are used for assessment of possible options of decision-making. Approach proposed could be used within any technique of decision support based on elementary mathematical operations. In this article the above-mentioned approach is described under analytical hierarchy process.

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Measures of fit in multiple correspondence analysis of crisp and fuzzy coded data

When continuous data are coded to categorical variables, two types of coding are possible: crisp coding in the form of indicator, or dummy, variables with values either 0 or 1; or fuzzy coding where each observation is transformed to a set of "degrees of membership" between 0 and 1, using co-called membership functions. It is well known that the correspondence analysis of crisp coded data, namely multiple correspondence analysis, yields principal inertias (eigenvalues) that considerably underestimate the quality of the solution in a low-dimensional space. Since the crisp data only code the categories to which each individual case belongs, an alternative measure of fit is simply to count how well these categories are predicted by the solution. Another approach is to consider multiple correspondence analysis equivalently as the analysis of the Burt matrix (i.e., the matrix of all two-way cross-tabulations of the categorical variables), and then perform a joint correspondence analysis to fit just the off-diagonal tables of the Burt matrix - the measure of fit is then computed as the quality of explaining these tables only. The correspondence analysis of fuzzy coded data, called "fuzzy multiple correspondence analysis", suffers from the same problem, albeit attenuated. Again, one can count how many correct predictions are made of the categories which have highest degree of membership. But here one can also defuzzify the results of the analysis to obtain estimated values of the original data, and then calculate a measure of fit in the familiar percentage form, thanks to the resultant orthogonal decomposition of variance. Furthermore, if one thinks of fuzzy multiple correspondence analysis as explaining the two-way associations between variables, a fuzzy Burt matrix can be computed and the same strategy as in the crisp case can be applied to analyse the off-diagonal part of this matrix. In this paper these alternative measures of fit are defined and applied to a data set of continuous meteorological variables, which are coded crisply and fuzzily into three categories. Measuring the fit is further discussed when the data set consists of a mixture of discrete and continuous variables.

Electrically driven fertilizer applicator controlled by fuzzy logic

The present study shows the development, simulation and actual implementation of a closed-loop controller based on fuzzy logic that is able to regulate and standardize the mass flow of a helical fertilizer applicator. The control algorithm was developed using MATLAB's Fuzzy Logic Toolbox. Both open and closed-loop simulations of the controller were performed in MATLAB's Simulink environment. The instantaneous deviation of the mass flow from the set point (SP), its derivative, the equipment´s translation velocity and acceleration were all used as input signals for the controller, whereas the voltage of the applicator's DC electric motor (DCEM) was driven by the controller as output signal. Calibration and validation of the rules and membership functions of the fuzzy logic were accomplished in the computer simulation phase, taking into account the system's response to SP changes. The mass flow variation coefficient, measured in experimental tests, ranged from 6.32 to 13.18%. The steady state error fell between -0.72 and 0.13g s-1 and the recorded average rise time of the system was 0.38 s. The implemented controller was able to both damp the oscillations in mass flow that are characteristic of helical fertilizer applicators, and to effectively respond to SP variations.

Creating possibilities for collective creativity : Brokerage Functions in Practice-Based Innovation

In the network era, creative achievements like innovations are more and more often created in interaction among different actors. The complexity of today‘s problems transcends the individual human mind, requiring not only individual but also collective creativity. In collective creativity, it is impossible to trace the source of new ideas to an individual. Instead, creative activity emerges from the collaboration and contribution of many individuals, thereby blurring the contribution of specific individuals in creating ideas. Collective creativity is often associated with diversity of knowledge, skills, experiences and perspectives. Collaboration between diverse actors thus triggers creativity and gives possibilities for collective creativity. This dissertation investigates collective creativity in the context of practice-based innovation. Practice-based innovation processes are triggered by problem setting in a practical context and conducted in non-linear processes utilising scientific and practical knowledge production and creation in cross-disciplinary innovation networks. In these networks diversity or distances between innovation actors are essential. Innovation potential may be found in exploiting different kinds of distances. This dissertation presents different kinds of distances, such as cognitive, functional and organisational which could be considered as sources of creativity and thus innovation. However, formation and functioning of these kinds of innovation networks can be problematic. Distances between innovating actors may be so great that a special interpretation function is needed – that is, brokerage. This dissertation defines factors that enhance collective creativity in practice-based innovation and especially in the fuzzy front end phase of innovation processes. The first objective of this dissertation is to study individual and collective creativity at the employee level and identify those factors that support individual and collective creativity in the organisation. The second objective is to study how organisations use external knowledge to support collective creativity in their innovation processes in open multi-actor innovation. The third objective is to define how brokerage functions create possibilities for collective creativity especially in the context of practice-based innovation. The research objectives have been studied through five substudies using a case-study strategy. Each substudy highlights various aspects of creativity and collective creativity. The empirical data consist of materials from innovation projects arranged in the Lahti region, Finland, or materials from the development of innovation methods in the Lahti region. The Lahti region has been chosen as the research context because the innovation policy of the region emphasises especially the promotion of practice-based innovations. The results of this dissertation indicate that all possibilities of collective creativity are not utilised in internal operations of organisations. The dissertation introduces several factors that could support collective creativity in organisations. However, creativity as a social construct is understood and experienced differently in different organisations, and these differences should be taken into account when supporting creativity in organisations. The increasing complexity of most potential innovations requires collaborative creative efforts that often exceed the boundaries of the organisation and call for the involvement of external expertise. In practice-based innovation different distances are considered as sources of creativity. This dissertation gives practical implications on how it is possible to exploit different kinds of distances knowingly. It underlines especially the importance of brokerage functions in open, practice-based innovation in order to create possibilities for collective creativity. As a contribution of this dissertation, a model of brokerage functions in practice-based innovation is formulated. According to the model, the results and success of brokerage functions are based on the context of brokerage as well as the roles, tasks, skills and capabilities of brokers. The brokerage functions in practice-based innovation are also possible to divide into social and cognitive brokerage.

Simulation of Active Control Using Fuzzy Logic Applied to a Pulse Combustor

This work analyzes an active fuzzy logic control system in a Rijke type pulse combustor. During the system development, a study of the existing types of control for pulse combustion was carried out and a simulation model was implemented to be used with the package Matlab and Simulink. Blocks which were not available in the simulator library were developed. A fuzzy controller was developed and its membership functions and inference rules were established. The obtained simulation showed that fuzzy logic is viable in the control of combustion instabilities. The obtained results indicated that the control system responded to pulses in an efficient and desirable way. It was verified that the system needed approximately 0.2 s to increase the tube internal pressure from 30 to 90 mbar, with an assumed total delay of 2 ms. The effects of delay variation were studied. Convergence was always obtained and general performance was not affected by the delay. The controller sends a pressure signal in phase with the Rijke tube internal pressure signal, through the speakers, when an increase the oscillations pressure amplitude is desired. On the other hand, when a decrease of the tube internal pressure amplitude is desired, the controller sends a signal 180º out of phase.