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Stochastic, as well as fuzzy uncertainty, can be found in most real-world systems. Considering both types of uncertainties simultaneously makes optimization problems incredibly challenging. In this paper we propose a fuzzy simheuristic to solve the Time Capacitated Arc Routing Problem (TCARP) when the nature of the travel time can either be deterministic, stochastic or fuzzy. The main goal is to find a solution (vehicle routes) that minimizes the total time spent in servicing the required arcs. However, due to uncertainty, other characteristics of the solution are also considered. In particular, we illustrate how reliability concepts can enrich the probabilistic information given to decision-makers. In order to solve the aforementioned optimization problem, we extend the concept of simheuristic framework so it can also include fuzzy elements. Hence, both stochastic and fuzzy uncertainty are simultaneously incorporated into the CARP. In order to test our approach, classical CARP instances have been adapted and extended so that customers' demands become either stochastic or fuzzy. The experimental results show the effectiveness of the proposed approach when compared with more traditional ones. In particular, our fuzzy simheuristic is capable of generating new best-known solutions for the stochastic versions of some instances belonging to the tegl, tcarp, val, and rural benchmarks. This work has been partially supported by the Spanish Ministry of Science (PID2019-111100RB-C21/AEI/10.13039/01100011033), as well as by the Barcelona Council and the “laCaixa” Foundation under the framework of the Barcelona Science Plan 2020-2023 (grant21S09355-01) and Generalitat Valenciana (PROMETEO/2021/065).

Corporate and organizational performance assessment is an important activity for both the managers and other stakeholders, as it provides them with an asset to evaluate their own strengths and weaknesses in relation to the competition, as well as guidelines for selecting appropriate measures to address the existing problems. The issue of criteria selection has been overcome through the literature review and the issue of criteria weights is handled by applying group decision making procedure. The procedure itself consists of using predefined linguistic expressions that are modelled by triangular fuzzy numbers and the aggregation of decision makers’ opinion based on the rules of rough sets algebra. The values of the decision matrix are determined by prognosis method and they are described by crisp values. The proposed algorithm is tested on the insurance companies that operate in the Republic of Serbia

Treballs Finals del Màster de Ciències Actuarials i Financeres, Facultat d'Economia i Empresa, Universitat de Barcelona, Curs: 2021-2022, Tutor: Ana María Gil Lafuente, The aim of this project is to continue adjusting the price of life insurance linked to credits according to the profiles of the different characteristics of the insured. We will focus on the mathematical development of the Pichat Algorithm method in the field of fuzzy logic study, with the help of the Hamming distance method to find the subrelations of maximum similarity between different life insurance products. It allows us to take a new approach to measuring the similarity of various life insurance products, incorporating uncertainty management to more accurately match policies with policyholders' profiles. Therefore, we minimize the impact of the lack of information when making the decision.

This manuscript explores fuzzy rule learning for sound synthesizer programming within the performative practice known as live coding. In this practice, sound synthesis algorithms are programmed in real time by means of source code. To facilitate this, one possibility is to automatically create variations out of a few synthesizer presets. However, the need for real-time feedback makes existent synthesizer programmers unfeasible to use. In addition, sometimes presets are created mid-performance and as such no benchmarks exist. Inductive rule learning has shown to be effective for creating real-time variations in such a scenario. However, logical IF-THEN rules do not cover the whole feature space. Here, we present an algorithm that extends IF-THEN rules to hyperrectangles, which are used as the cores of membership functions to create a map of the input space. To generalize the rules, the contradictions are solved by a maximum volume heuristics. The user controls the novelty-consistency balance with respect to the input data using the algorithm parameters. The algorithm was evaluated in live performances and by cross-validation using extrinsic-benchmarks and a dataset collected during user tests. The model&rsquo, s accuracy achieves state-of-the-art results. This, together with the positive criticism received from live coders that tested our methodology, suggests that this is a promising approach.

The energy consumption used for domestic purposes in Europe is, to a considerable extent, due to heating and cooling. This energy is produced mostly by burning fossil fuels, which has a high negative environmental impact. The characteristics of a building are an important factor to determine the necessities of heating and cooling loads. Therefore, the study of the relevant characteristics of the buildings, regarding the heating and cooling needed to maintain comfortable indoor air conditions, could be very useful in order to design and construct energy-efficient buildings. In previous studies, different machine-learning approaches have been used to predict heating and cooling loads from the set of variables: relative compactness, surface area, wall area, roof area, overall height, orientation, glazing area and glazing area distribution. However, none of these methods are based on fuzzy logic. In this research, we study two fuzzy logic approaches, i.e., fuzzy inductive reasoning (FIR) and adaptive neuro fuzzy inference system (ANFIS), to deal with the same problem. Fuzzy approaches obtain very good results, outperforming all the methods described in previous studies except one. In this work, we also study the feature selection process of FIR methodology as a pre-processing tool to select the more relevant variables before the use of any predictive modelling methodology. It is proven that FIR feature selection provides interesting insights into the main building variables causally related to heating and cooling loads. This allows better decision making and design strategies, since accurate cooling and heating load estimations and correct identification of parameters that affect building energy demands are of high importance to optimize building designs and equipment specifications.

In this chapter, the problem of fault-tolerant control of a service robot is addressed. The proposed approach is based on using a fault estimation scheme based on an Robust Unknown-Input Observer (RUIO) that allows to estimate the fault as well as the robot state. This fault estimation scheme is integrated with the control algorithm that is based on a observer-based state feedback control. After the fault occurrence, from the fault estimation, a feedforward control action is added to the feedback control action to compensate the fault effect. To cope with the robot non-linearity, its non-linear model is transformed into a Takagi-Sugeno model. Then, the statefeedback and RUIO are designed using an LMI-based approach considering a gainscheduling scheme. To illustrate the proposed fault-tolerant scheme a mobile service robot TIAGo, developed by PAL robotics, is used., This work is supported by the Spanish State Research Agency through the María de Maeztu Seal of Excellence to IRI MDM-2016-0656

The usage of indicators as constituent parts of composite indices is an extended practice in many fields of knowledge. Even if rigorous statistical analyses are implemented, many of the methodologies follow simple arithmetic assumptions to aggregate indicators to build an index. One of the consequences of such assumptions can be the concealment of the influence of some of the composite index&rsquo, s components. We developed a fuzzy method that aggregates indicators using non-linear methods and, in this paper, compare it to a well-known example in the field of risk assessment, called Moncho&rsquo, s equation, which combines physical and social components and uses a linear aggregation method to estimate a level of seismic risk. By comparing the spatial pattern of the risk level obtained from these two methodologies, we were able to evaluate to what extent a fuzzy approach allows a more realistic representation of how social vulnerability levels might shape the seismic risk panorama in an urban environment. We found that, in some cases, this approach can lead to risk level values that are up to 80% greater than those obtained using a linear aggregation method for the same areas.

Aim Fuzzy wavelet neural network (FWNN) has proven to be a promising strategy in the identification of nonlinear systems. The network considers both global and local properties, deals with imprecision present in sensory data, leading to desired precisions. In this paper, we proposed a new FWNN model nominated “Fuzzy Jump Wavelet Neural Network” (FJWNN) for identifying dynamic nonlinear-linear systems, especially in practical applications. Methods The proposed FJWNN is a fuzzy neural network model of the Takagi-Sugeno-Kang type whose consequent part of fuzzy rules is a linear combination of input regressors and dominant wavelet neurons as a sub-jump wavelet neural network. Each fuzzy rule can locally model both linear and nonlinear properties of a system. The linear relationship between the inputs and the output is learned by neurons with linear activation functions, whereas the nonlinear relationship is locally modeled by wavelet neurons. Orthogonal least square (OLS) method and genetic algorithm (GA) are respectively used to purify the wavelets for each sub-JWNN. In this paper, fuzzy rule induction improves the structure of the proposed model leading to less fuzzy rules, inputs of each fuzzy rule and model parameters. The real-world gas furnace and the real electromyographic (EMG) signal modeling problem are employed in our study. In the same vein, piecewise single variable function approximation, nonlinear dynamic system modeling, and Mackey–Glass time series prediction, ratify this method superiority. The proposed FJWNN model is compared with the state-of-the-art models based on some performance indices such as RMSE, RRSE, Rel ERR%, and VAF%. Results The proposed FJWNN model yielded the following results: RRSE (mean±std) of 10e-5±6e-5 for piecewise single-variable function approximation, RMSE (mean±std) of 2.6–4±2.6e-4 for the first nonlinear dynamic system modelling, RRSE (mean±std) of 1.59e-3±0.42e-3 for Mackey–Glass time series prediction, RMSE of 0.3421 for gas furnace modelling and VAF% (mean±std) of 98.24±0.71 for the EMG modelling of all trial signals, indicating a significant enhancement over previous methods. Conclusions The FJWNN demonstrated promising accuracy and generalization while moderating network complexity. This improvement is due to applying main useful wavelets in combination with linear regressors and using fuzzy rule induction. Compared to the state-of-the-art models, the proposed FJWNN yielded better performance and, therefore, can be considered a novel tool for nonlinear system identification

In this study, we explored hybrid fuzzy logic modelling techniques to predict the burned area of forest fires. Fast detection is crucial for successful firefighting, and a model with an accurate prediction ability is extremely useful for optimizing fire management. Fuzzy Inductive Reasoning (FIR) and the Adaptive Neuro-Fuzzy Inference System (ANFIS) are two powerful fuzzy techniques for modelling burned areas of forests in Portugal. The results obtained from them were compared with those of other artificial intelligence techniques applied to the same datasets found in the literature.

Composite indices are used in many of the traditional approaches to measure risk to natural hazards. However, such indices are often built assuming linear interdependencies between the aggregated components, comprising in this way any realistic representation of the intricate and unseen processes that are behind each component along with their mutual influences when it comes to encapsulate a complex reality in a single construct. In this paper we used a Fuzzy Inference Systems type Mamdami to aggregate physical seismic risk and social vulnerability indicators without assuming linearity. The aggregation is made by establishing rules (if-then type) over the indicators in order to get a fuzzy composite index. We generated solution surfaces representing the outcome of a widely known linear aggregation method and the fuzzy system. Finally we performed a qualitative comparison between both to highlight their differences and possible consequences in terms of risk management.

Energy recasting has been an area of great interest in the last years. It unlocks, not only the Smart Grid's potential with load balancing but also new business models and added value services. To achieve an accurate, robust and fast prediction, model's parametrization is key and becomes a bottleneck in the value-chain. In this article, we present an improved version of Flexible Fuzzy Inductive Reasoning (Flexible FIR) that selects the most optimal number of nearest neighbours during FIR prediction phase, called K nearest neighbour Optimal Selection (KOS). To this end, a real smart grid forecasting application, i.e. electricity load forecasting, has been chosen in this study. The results show that the best forecasting accuracy, on average, is when the KOS is used on Flexible FIR. While with KOS the optimal parameter k is found online, without it is not, which increases the computational time.

Purpose: Just-In-Time (JIT) production has continuously been considered by industrial practitioners and researchers as a leading strategy for the yet popular Lean production. Pull Production Control Policies (PPCPs) are the major enablers of JIT that locally control the level of inventory by authorizing the production in each station. Aiming to improve the PPCPs, three authorization mechanisms: Kanban, constant-work-in-process (ConWIP), and a hybrid system, are evaluated by considering uncertainty. Design/methodology/approach: Multi-Criteria Decision Making (MCDM) methods are successful in evaluating alternatives with respect to several objectives. The proposed approach of this study applies the fuzzy set theory together with an integrated Analytical Hierarchy Process (AHP) and a Technique for Order Performance by Similarity to Ideal Solution (TOPSIS) method. Findings: The study finds that hybrid Kanban-ConWIP pull production control policies have a better performance in controlling the studied multi-layer multi-stage manufacturing and assembly system. Practical implications: To examine the approach a real case from automobile electro-mechanical part production industry is studied. The production system consists of multiple levels of manufacturing, feeding a multi-stage assembly line with stochastic processing times to satisfy the changing demand. Originality/value: This study proposes the integrated Kanban-ConWIP hybrid pull control policies and implements several alternatives on a multi-stage and multi-layer manufacturing and assembly production system. An integrated Fuzzy AHP TOPSIS method is developed to evaluate the alternatives with respect to several JIT criteria

In power conversion applications grid synchronization systems should face very different network operating conditions such as: generic grid connection, faulty or distorted scenarios or islanded conditions among others. However, all the existing synchronization systems have issues operating in all these scenarios if the control tuning parameters cannot be adapted to the grid conditions. This paper proposes a Fuzzy Gain Scheduling PLL (FGS-PLL) to be used for grid synchronization, which has a robust performance in case of severe voltage sag, where there is even a null value of voltage, and phase jump conditions. Moreover, the proposed method employs a fuzzy gain scheduling technique to adjust the proportional and integral gains of the proposed PLL during amplitude, phase and frequency variations in the grid voltage waveform to build a flexible PLL in case of severe grid conditions. This PLL structure permits to adjust the performance in different conditions as well as to provide a voltage reference, even in case of 100% voltage sag.

In this paper, we bring together two concepts related to uncertainty and vagueness: fuzzy numbers and intervals. With them, we build a new structure whose elements we call interval fuzzy segments. We have undertaken this based on the conviction that the fuzzy numbers are a correct representation of the real numbers under situations of indeterminacy. We also believe that if it makes sense to consider the set of real numbers between two real bounds, then it also makes sense to consider the set of all the fuzzy numbers between two fuzzy number bounds. In this way, we extend the concept of real interval to the concept of interval fuzzy segment defined by two fuzzy bounds and a transition mapping that leads from the lower fuzzy bound to the upper fuzzy bound and this transition mapping generates the set of all the fuzzy numbers comprised between those fuzzy bounds. At the same time, this transition mapping brings the concept of interval fuzzy segment closer to the concept of line segment.

This paper considers zonotopic fault detection observer design in the finite-frequency domain for discrete-time Takagi–Sugeno fuzzy systems with unknown but bounded disturbances and measurement noise. We present a novel fault detection observer structure, which is more general than the commonly used Luenberger form. To make the generated residual sensitive to faults and robust against disturbances, we develop a finite-frequency fault detection observer based on generalised Kalman–Yakubovich–Popov lemma and P-radius criterion. The design conditions are expressed in terms of linear matrix inequalities. The major merit of the proposed method is that residual evaluation can be easily implemented via zonotopic approach. Numerical examples are conducted to demonstrate the proposed method., This work was supported by National Natural Science Foundation of China [grant number 61773145, 61403104 ] and the Key Laboratory Opening Funds of Harbin Institute of Technology [grant HIT.KLOF.2018.073]

We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name 'modal interval trapezoidal fuzzy numbers'. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to maintain the traditional graphic representation of trapezoidal fuzzy numbers and we must use the interval plane in order to represent our modal interval trapezoidal fuzzy numbers graphically. Using this representation, we can correctly reflect the modality of the alpha cuts. We define some concepts from modal interval analysis and we study some of the related properties and structures, proving, among other things, that the inclusion relation provides a lattice structure on this set. We will also provide a semantic interpretation deduced from the modal interval extensions of real continuous functions and the semantic modal interval theorem. The application of modal intervals in the field of fuzzy numbers also provides a new perspective on and new applications of fuzzy numbers.

Dealing with missing data is of great practical and theoretical interest in forecasting applications. In this study, we deal with the problem of forecasting with missing data in smart grid and BEMS applications, where the information from home area sensors and/or smart meters is sometimes missing, which may hinder or even prevent the forecasting of the next hours and days. In concrete, we focus in a Soft Computing technique called Fuzzy Inductive Reasoning (FIR) and its improved version that can cope with missing information in the forecasting process: flexible FIR. In this article eight different strategies for flexible FIR forecasting are defined and studied taking into account: causal relevance of input variables, consistency of predictions, inertia criterion and K-Nearest Neighbours. Furthermore, we evaluate the implications of prediction accuracy and number of predictions, when the number of Missing Values (MVs) in the training dataset is increased progressively. To this end, a real smart grid forecasting application, i.e. electricity load forecasting, has been chosen in this study. The results show that all eight strategies proposed are able to cope with MVs and take advantage of the inherent information in the data, with better results in those strategies making use of causal relevance. In addition, the robustness of flexible FIR and its eight strategies are proved taking into account that the percentage of electricity load predictions from the test dataset is on average 96.15% when the %MVs in training dataset was around 73%.

Purpose Innovation has been recognized as one of the main sources of competitive advantage for organizations and nations. The purpose of this study is to present an innovation management measurement approach by applying fuzzy techniques to small- and medium-sized manufacturing enterprises. Design/methodology/approach This study presents a survey focusing on seven innovation measurement areas: innovation strategy, knowledge management, project management, portfolio management, internal enablers, organization and structure and external enablers. A total of 91 small- and medium-sized enterprises (SMEs) located in the city of Morelia, Mexico, participated in the study. Furthermore, the data collected were analyzed under a multi-criteria decision-making approach using the theory of expertons and the induced generalized ordered weighted averaging operator. Findings The results show that the most valued areas are innovation strategy, organization and structure, knowledge management and project management. Furthermore, portfolio management, external drivers and internal drivers are the areas with the lowest valuations. Originality/value This paper presents an original methodological structure based on an expertise process designed to achieve well-founded results from uncertain and subjective opinions directly from the managers of the surveyed SMEs.

© 2017 IOS Press and the authors. All rights reserved. Fuzzy decision-making consists in making decisions under complex and uncertain environments where the information can be assessed with fuzzy sets and systems. The aim of this study is to review the main contributions in this field by using a bibliometric approach. For doing so, the article uses a wide range of bibliometric indicators including the citations and the h-index. Moreover, it also uses the VOS viewer software in order to map the main trends in this area. The work considers the leading journals, articles, authors and institutions. The results indicate that the USA was the traditional leader in this field with the most significant researcher. However, during the last years, this field is receiving more attention by Asian authors that are starting to lead the field. This discipline has a strong potential and the expectations for the future is that it will continue to grow.

P2P systems are very important for future distributed systems and applications. In such systems, the computational burden of the system can be distributed to peer nodes of the system. Therefore, in decentralized systems users become themselves actors by sharing, contributing and controlling the resources of the system. This characteristic makes P2P systems very interesting for the development of decentralized applications. Data replication techniques are commonplace in P2P systems. Data replication means storing copies of the same data at multiple peers thus improving availability and scalability. The trustworthiness of peers also is very important for safe communication in P2P system. The trustworthiness of a peer can be evaluated based on the reputation and actual behaviour of peers to provide services to other peers. In this paper, we propose two fuzzy-based systems for data replication and peer trustworthiness for JXTA-Overlay P2P platform. The simulation results have shown that in the first system, replication factor increases proportionally with increase of number of documents per peer, replication percentage and scale of replication per peer parameters and the second system can be used successfully to select the most reliable peer candidate to execute the tasks.

This is a copy of the author's final draft version of an article published in the journal Soft computing. The reliability of peers is very important for safe communication in peer-to-peer (P2P) systems. The reliability of a peer can be evaluated based on the reputation and interactions with other peers to provide different services. However, for deciding the peer reliability there are needed many parameters, which make the problem NP-hard. In this paper, we present two fuzzy-based systems (called FBRS1 and FBRS2) to improve the reliability of JXTA-overlay P2P platform. In FBRS1, we considered three input parameters: number of interactions (NI), security (S), packet loss (PL) to decide the peer reliability (PR). In FBRS2, we considered four input parameters: NI, S, PL and local score to decide the PR. We compare the proposed systems by computer simulations. Comparing the complexity of FBRS1 and FBRS2, the FBRS2 is more complex than FBRS1. However, it also considers the local score, which makes it more reliable than FBRS1.

In this paper we deal with propositional fuzzy formulae containing several propositional symbols linked with connectives defined in a lattice of truth degrees more complex than Bool. Instead of focusing on satisfiability (i.e., proving the existence of at least one model) as usually done in a SAT/SMT setting, our interest moves to the problem of finding the whole set of models (with a finite domain) for a given fuzzy formula. We reuse a previous method based on fuzzy logic programming where the formula is conceived as a goal whose derivation tree, provided by our FLOPER tool, contains on its leaves all the models of the original formula, together with other interpretations. Next, we use the ability of the FuzzyXPath tool (developed in our research group with FLOPER) for exploring these derivation trees once exported in XML format, in order to discover whether the formula is a tautology, satisfiable, or a contradiction, thus reinforcing the bi-lateral synergies between FuzzyXPath and FLOPER This work has been partially supported by the EU (FEDER), and the Spanish MINECO Ministry (Ministerio de Economía y Competitividad) under grants TIN2013-44742-C4-4-R, TIN2012-33042 and TIN2013-45732-C4-2-P

The final publication is available at IOS Press through http://dx.doi.org/10.3233/JHS-150506 In P2P systems, each peer has to obtain information of other peers and propagate the information to other peers through neighboring peers. Thus, it is important for each peer to have some number of neighbor peers. Moreover, it is more significant to discuss if each peer has reliable neighbor peers. In reality, each peer might be faulty or might send obsolete, even incorrect information to the other peers. We have implemented a P2P platform called JXTA-Overlay, which defines a set of protocols that standardize how different devices may communicate and collaborate among them. It abstracts a new layer on the top of JXTA through a set of primitive operations and services that are commonly used in JXTA-based applications and provides a set of primitives that can be used by other applications, which will be built on top of the overlay, with complete independence. JXTA-Overlay provides a set of basic functionalities, primitives, intended to be as complete as possible to satisfy the needs of most JXTA-based applications. In this paper, we present two fuzzy-based systems (called FRS1 and FRS2) to improve the reliability of JXTA-Overlay P2P platform. We make a comparison study between the fuzzy-based reliability systems. Comparing the complexity of FRS1 and FRS2, the FRS2 is more complex than FRS1. However, it considers also the security; therefore, it can be used in real application for secure systems.

Purpose: The aim of this study is applying a new method for Industrial robotic system selection.Design/methodology/approach: In this paper, the weights of each criterion are calculated using fuzzy Shannon’s Entropy. After that, fuzzy TOPSIS is utilized to rank the alternatives. Then we select the best Industrial Robotic System based on these results.Findings and Originality/value: The outcome of this research is ranking and selecting industrial robotic systems with the help of Fuzzy Shannon’s Entropy and Fuzzy TOPSIS techniques.Originality/value: This paper offers a new integrated method for industrial robotic system selection.

Purpose: The aim of this research is to develop a more realistic approach to solve project time-cost optimization problem under uncertain conditions, with fuzzy time periods. Design/methodology/approach: Deterministic models for time-cost optimization are never efficient considering various uncertainty factors. To make such problems realistic, triangular fuzzy numbers and the concept of a-cut method in fuzzy logic theory are employed to model the problem. Because of NP-hard nature of the project scheduling problem, Genetic Algorithm (GA) has been used as a searching tool. Finally, Dev-C++ 4.9.9.2 has been used to code this solver. Findings: The solution has been performed under different combinations of GA parameters and after result analysis optimum values of those parameters have been found for the best solution. Research limitations/implications: For demonstration of the application of the developed algorithm, a project on new product (Pre-paid electric meter, a project under government finance) launching has been chosen as a real case. The algorithm is developed under some assumptions. Practical implications: The proposed model leads decision makers to choose the desired solution under different risk levels. Originality/value: Reports reveal that project optimization problems have never been solved under multiple uncertainty conditions. Here, the function has been optimized using Genetic Algorithm search technique, with varied level of risks and fuzzy time periods.

In P2P systems, evaluation of trustworthiness of the peers is very important for a safe communication. In order to decide the peer trustworthiness different parameters are needed. In this paper, we propose two fuzzy-based peer trustworthiness systems for JXTA-Overlay P2P platform. In the first system, we considered two parameters: Actual Behavior Criterion (ABC) and Reputation (R). In the second system, we took in consideration three parameters: Actual Behavior Criterion (ABC), Mutually Agreed Behavior (MAB) and Reputation(R). We compared the performance of the proposed systems by computer simulations. The simulation results have shown that in general the system with three parameters has better performance, but the complexity is higher.

Several definitions of an atom in a molecule (AIM) in three-dimensional (3D) space, including both fuzzy and disjoint domains, are used to calculate electron sharing indices (ESI) and related electronic aromaticity measures, namely, Iringand multicenter indices (MCI), for a wide set of cyclic planar aromatic and nonaromatic molecules of different ring size. The results obtained using the recent iterative Hirshfeld scheme are compared with those derived from the classical Hirshfeld method and from Bader's quantum theory of atoms in molecules. For bonded atoms, all methods yield ESI values in very good agreement, especially for C-C interactions. In the case of nonbonded interactions, there are relevant deviations, particularly between fuzzy and QTAIM schemes. These discrepancies directly translate into significant differences in the values and the trends of the aromaticity indices. In particular, the chemically expected trends are more consistently found when using disjoint domains. Careful examination of the underlying effects reveals the different reasons why the aromaticity indices investigated give the expected results for binary divisions of 3D space M.S. is grateful for the nancial help furnished by the Spanish MICINN Project No. CTQ2008-03077/BQU and by the Catalan DIUE through project No. 2009SGR637

Estudi i implementació d'un sistema multiagent intel·ligent i la seva aplicació a sistemes difusos. Utilització de les llibreries JADE i JFuzzyLogic. Study and implementation of an intelligent multi-agent system and its application to fuzzy systems. Using the JADE libraries and JFuzzyLogic. Estudio e implementación de un sistema multiagente inteligente y su aplicación a sistemas difusos. Utilización de las librerías JADE y JFuzzyLogic.

This paper deals with the assessment of how far into the future a time series can be safely predicted using inductive modelling and extrapolation techniques. Three different time series are used to demonstrate the viability of the approaches presented in the paper: one time series representing the water demand of the city of Barcelona, another characterizing the water demand of a section of the city of Rotterdam, and a third describing weather data for the city of Tucson. Fuzzy inductive reasoning (FIR) is used to predict future values of these time series on the basis of their own past. FIR predictions come with two different built-in measures of confidence that can be used to obtain a quantitative estimate of how far into the future a time series can be predicted.

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process.

In 2000 the European Statistical Office published the guidelines for developing the Harmonized European Time Use Surveys system. Under such a unified framework, the first Time Use Survey of national scope was conducted in Spain during 2002– 03. The aim of these surveys is to understand human behavior and the lifestyle of people. Time allocation data are of compositional nature in origin, that is, they are subject to non-negativity and constant-sum constraints. Thus, standard multivariate techniques cannot be directly applied to analyze them. The goal of this work is to identify homogeneous Spanish Autonomous Communities with regard to the typical activity pattern of their respective populations. To this end, fuzzy clustering approach is followed. Rather than the hard partitioning of classical clustering, where objects are allocated to only a single group, fuzzy method identify overlapping groups of objects by allowing them to belong to more than one group. Concretely, the probabilistic fuzzy c-means algorithm is conveniently adapted to deal with the Spanish Time Use Survey microdata. As a result, a map distinguishing Autonomous Communities with similar activity pattern is drawn. Key words: Time use data, Fuzzy clustering; FCM; simplex space; Aitchison distance Geologische Vereinigung; Institut d’Estadística de Catalunya; International Association for Mathematical Geology; Càtedra Lluís Santaló d’Aplicacions de la Matemàtica; Generalitat de Catalunya, Departament d’Innovació, Universitats i Recerca; Ministerio de Educación y Ciencia; Ingenio 2010.