Fuzzy Integral

People recognize familiar faces in a similar way by using interior facial features (facial regions) such as eyes, nose, mouth, etc. However, the importance of these regions in the realization of face identification and a quantification of the impact of such regions on the recognition process could vary from one region to another. An intuitively appealing observation is that of monotonicity: the more regions are taken into account in the recognition process, the better. From a formal point of view, the relevance of the facial regions and an aggregation of these pieces of experimental evidence can be described in the formal setting of fuzzy measures. Fuzzy measures are of particular interest with this regard given their monotonicity property (which stands in a clear contrast with the more restrictive additivity property inherent to probability-like measures). In this study, we concentrate on the construction of fuzzy measures (more specifically, k-fuzzy measure) and characterize their performance in the problem of face recognition using a collection of experimental data.

Using parametric form of fuzzy numbers we convert a linear fuzzy Fredholm integral equation of the second kind to a linear system of integral equations of the second kind in crisp case. We use Adomian method and find the approximate solution of this system and hence obtain an approximation for fuzzy solution of the linear fuzzy Fredholm integral equation of the second kind. We apply the method to some examples. Ó 2004 Elsevier Inc. All rights reserved.

In this paper, a novel direct torque algorithm for IPMSM was analysed and simulated. The algorithm uses the output of two hysteresis controllers to determine two adjacent active vectors. It also uses the magnitude of the torque error to approximate the required average voltage level and then, together with the reflected stator flux position to select the switching time required for the selected vectors. The selection of the switching time utilizes the new table structure, which simplifies the calculation. The simulation of the algorithm shows adequate dynamic torque and considerable torque ripples reduction as well as lower harmonic current. APPENDIX See .

A problem of decision making under uncertainty in which the choice must be made between two sets of alternatives instead of two single ones is considered. A number of choice rules are proposed and their main properties are investigated, focusing particularly on the generalizations of stochastic dominance and statistical preference. The particular cases where imprecision is present in the utilities or in the beliefs associated to two alternatives are considered.

This paper describes a fuzzy hierarchical analytic approach to determine the weighting of subjective judgments. In addition, it presents a nonadditive fuzzy integral technique to evaluate a green engineering industry case as a fuzzy multicriteria decision-making (FMCDM) problem. When the invest-ment strategies are evaluated from various aspects, such as economic effectiveness, technical feasibility, and environmental regulation, it can be regarded as an FMCDM problem. Since stakeholders cannot clearly estimate each considered criterion in terms of numerical values for the anticipated alternatives/strategies, fuzziness is considered to be applicable. Consequently, this paper uses triangular fuzzy numbers to establish weights and anticipated achievement values. By ranking fuzzy weights and fuzzy synthetic utility values, we can determine the relative importance of criteria and decide the best strategies. This paper applies what is called a fuzzy measure and nonadditive fuzzy integral technique to evaluate the synthetic performance of green engineering strategies for aquatic products processors in Taiwan. In addition, we demonstrate that the nonadditive fuzzy integral is an effective evaluation and appears to be appropriate, especially when the criteria are not independent.

We discuss the equivalence between aggregation of fuzzy sets and integration with respect to a special class of nonadditive set functions. Both fuzzy integral and Choquet integral are considered. First, we study aggregation of a finite family of fuzzy sets and then we extend our results to aggregation of an infinite family. The concepts of comonotonic maxitivity and additivity play a central role. We argue that, for the purpose of aggregating fuzzy sets, comonotonic maxitivity is a more desirable requirement than comonotonic additivity. In the absence of any such requirement we explore a wider class of aggregation procedures.

Starting from the concept of 'equiordered functions' we characterize two types of fuzzy integrals that can be defined on any kind of fuzzy measure: Sugeno and Choquet integrals. The characterization theorems that we obtain allow us to carry out a comparative study of these two fuzzy integrals, pointing out their formal similarities and their conceptual differences.

In this paper, we have proposed an approach for face recognition by composing Symlet decomposition, Fisherface algorithm, and Sugeno and Choquet Fuzzy Integral. This approach consists of four main sections: the first section uses Symlet, one of the Wavelet families, to transform an image into four sub-images which are called approximate, horizontal, vertical and diagonal partial images respectively. The aim of this work is to extract intrinsic facial features. The second section of this approach uses Fisherface method which is composed of PCA and LDA. The reason for using this was that it is not sensitive to intensive light variations and facial expression and gesture. The third and forth section of this approach, are related to the aggregation of the individual classifiers by means of the fuzzy integral. Both Sugeno and Choquet fuzzy integral are considered as methods for classifier aggregation. In this paper, Olivetti Research Labs face database is used for acquiring experimental results. The approach presented in this paper, will lead to better classification performance compared to other classification methods.

There has recently been considerable focus on finding reliable and more effective numerical methods for solving different mathematical problems with integral equations. The Runge–Kutta methods in numerical analysis are a family of iterative methods, both implicit and explicit, with different orders of accuracy, used in temporal and modification for the numerical solutions of integral equations. Fuzzy Integral equations (known as FIEs) make extensive use of many scientific analysis and engineering applications. They appear because of the incomplete information from their mathematical models and their parameters under fuzzy domain. In this paper, the sixth order Runge-Kutta is used to solve second-kind fuzzy Volterra integral equations numerically. The proposed method is reformulated and updated for solving fuzzy second-kind Volterra integral equations in general form by using properties and descriptions of fuzzy set theory. Furthermore a Volterra fuzzy integral equation, based on the parametric form of a fuzzy numbers, transforms into two integral equations of the second kind in the crisp case under fuzzy properties. We apply our modified method using the specific example with a linear fuzzy integral Volterra equation to illustrate the strengths and accurateness of this process. A comparison of evaluated numerical results with the exact solution for each fuzzy level set is displayed in the form of table and figures. Such results indicate that the proposed approach is remarkably feasible and easy to use.

A mechatronic system needs an integrated, concurrent, and system-based design approach due to the existence of interactions among its subsystems, and also the existence of interactions between the criteria involved in a realistic evaluation of a mechatronic product. This paper presents a systematic methodology for a detailed mechatronic design based on a mechatronic design quotient (MDQ). MDQ is a multicriteria index, reflecting a system-based evaluation of a mechatronic design, which is calculated using soft computing techniques, thereby accommodating interactions between criteria and human experience. A niching genetic algorithm is utilized to explore the huge search space raised due to concurrent and integrated design approach, with the aim to find the elite representatives of different possible configurations. To demonstrate the method, it is applied to an industrial fish cutting machine called the Iron Butcher-an electromechanical system that falls into the class of mixed or multidomain systems.

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Recently, the two most general and well-known fuzzy integrals (Sugeno's integral and Choquet's integral) were characterized. It was also shown how both integrals fitted the same formal model, and they only differed in the operators used. In this paper we try to analyze whether it is possible to improve those characterization theorems, and we also study the possibility of defining other fuzzy integrals following the same model but using other operators.

In this paper the integration formulas of Newton CotÕs methods with positive coefficient for fuzzy integrations in [T. Allahviranloo, Newton CotÕs methods for integration of fuzzy functions, in press] are considered and then are followed by Romberg integration to obtain improvements of the approximations of fuzzy integrations. The proposed algorithm is illustrated by solving some numerical examples.

There has recently been considerable focus on finding reliable and more effective numerical methods for solving different mathematical problems with integral equations. The Runge–Kutta methods in numerical analysis are a family of iterative methods, both implicit and explicit, with different orders of accuracy, used in temporal and modification for the numerical solutions of integral equations. Fuzzy Integral equations (known as FIEs) make extensive use of many scientific analysis and engineering applications. They appear because of the incomplete information from their mathematical models and their parameters under fuzzy domain. In this paper, the sixth order Runge-Kutta is used to solve second-kind fuzzy Volterra integral equations numerically. The proposed method is reformulated and updated for solving fuzzy second-kind Volterra integral equations in general form by using properties and descriptions of fuzzy set theory. Furthermore a Volterra fuzzy integral equation, based on the...

In this paper we study the effectiveness of using multiple classifier combination for EEG signals classification aiming to obtain more accurate results than it possible from single classifier system. The developed system employs different features vectors fused at the abstract and measurement levels for integrating information to reach a collective decision. For making decision, the majority voting scheme has been used. While at the measurement level, fuzzy integral, majority vote, decision template and some other types of combination methods have been investigated. The ensemble classification task is completed by feeding the Support Vectors Machines with Redial Basis Kernel functions classifiers with different features extracted from the EEG signal for imagination of right and left hands movements (i.e., at EEG channels C3 and C4). The parameters of SVM classifiers were optimized by genetic algorithm. The results show that using classifier fusion methods improved the overall classification performance.

Acoustic events produced in meeting environments may contain useful information for perceptually aware interfaces and multimodal behavior analysis. In this paper, a system to detect and recognize these events from a multimodal perspective is presented combining information from multiple cameras and microphones. First, spectral and temporal features are extracted from a single audio channel and spatial localization is achieved by exploiting crosscorrelation among microphone arrays. Second, several video cues obtained from multi-person tracking, motion analysis, face recognition, and object detection provide the visual counterpart of the acoustic events to be detected. A multimodal data fusion at score level is carried out using two approaches: weighted mean average and fuzzy integral. Finally, a multimodal database containing a rich variety of acoustic events has been recorded including manual annotations of the data. A set of metrics allow assessing the performance of the presented algorithms. This dataset is made publicly available for research purposes.

Computational intelligence techniques are very useful tools for solving problems that involve understanding, modeling, and analysis of large data sets. One of the numerous fields where computational intelligence has found an extremely important role is finance. More precisely, optimization issues of one's financial investments, to guarantee a given return, at a minimal risk, have been solved using intelligent techniques such as genetic algorithm, rule-based expert system, neural network, and support-vector machine. Even though these methods provide good and usually fast approximation of the best investment strategy, they suffer some common drawbacks including the neglect of the dependence among among criteria characterizing investment assets (i.e. return, risk, etc.), and the assumption that all available data are precise and certain. To face these weaknesses, we propose a novel approach involving utility-based multi-criteria decision making setting and fuzzy integration over intervals.

Generalization of the Chebyshev inequality for semi(co)normed fuzzy integrals on an abstract fuzzy measure space based on a binary operation is given. Also, Minkowski's and Hölder's inequalities for semi(co)normed fuzzy integrals are studied in a rather general form. The main results of this paper generalize some previous results. Finally, a conclusion is drawn and an open problem for further investigations is given. Keywords Fuzzy measure Á Sugeno integral Á Seminormed fuzzy integrals Á Semiconormed fuzzy integrals Á Comonotone functions Á Chebyshev's inequality Á Hölder's inequality Á Minkowski's inequality Franulič and Román-Flores (2007), Román-Flores and Chalco-Cano (2006), Román-Flores and Chalco-Cano (2007), Román-Flores et al. (2007a, b, Román-Flores et al. 2008), and then followed by many authors (Agahi and Eslami

Uncertainty abounds in pattern recognition problems. Therefore, management of uncertainty is an important problem in the development of automated systems for the detection, recognition, and interpretation of objects from their feature measurements. Fuzzy set theory offers numerous methodologies for the modeling and management of uncertainty. One such fuzzy set theoretic technology which has proven quite useful in pattern recognition is the fuzzy integral. The purpose of this paper is to examine new utilizations of the fuzzy integral as a decision making model in the area of object recognition. In particular, we develop generalizations of the fuzzy integral and show that these generalizations can achieve higher recognition rates in an automatic target recognition problem. Also, we demonstrate significant increases in recognition rates using the fuzzy integral to fuse the results of different neural network classifiers in a complex handwritten character recognition domain.

It is well known that fuzzy measures and fuzzy integrals are suitable tools for dealing with events affected by nonstatistical uncertainty. Indeed, the main assumption in these situations is the release of additivity conditions, while continuity and monotonicity are preserved. The validity of a number of results in classical measure theory have been confirmed in fuzzy measure theory. In this paper, a B. Levi theorem is restated in the new context. Some properties of the fuzzy integral function are considered, together with closure properties, similar to the classical measures and Choquet's capacity measures. The concept of decreasing rearrangement of a (fuzzy) measurable function expressed in terms of distribution functions, gives rise to a representation of the integral; such a representation is analogous to the classical form. This approach allows comparison of the forms of uncertainty arising from fuzziness and randomness and extends the definitions and properties of some parameters and functions, such as expectation and distributions.

Fuzzy measures and fuzzy integrals have been successfully used in many real applications. How to determine fuzzy measures is the most difficult problem in these applications. Though there have existed some methodologies for solving this problem, such as genetic algorithms, gradient descent algorithms and neural networks, it is hard to say which one is more appropriate and more feasible. Each method has its advantages and limitations. Therefore it is necessary to develop new methods or techniques to learn distinct fuzzy measures. In this paper, we make the first attempt to design a special particle swarm algorithm to determine a type of general fuzzy measures from data, and demonstrate that the algorithm is effective and efficient. Furthermore we extend this algorithm to identify and revise other types of fuzzy measures. To test our algorithms, we compare them with the basic particle swarm algorithms, gradient descent algorithms and genetic algorithms in literatures. In addition, for verifying whether our algorithms are robust in noisy-situations, a number of numerical experiments are conducted. Theoretical analysis and experimental results show that, for determining fuzzy measures, the particle swarm optimization is feasible and has a better performance than the existing genetic algorithms and gradient descent algorithms.

This paper presents four schemes for soft fusion of the outputs of multiple classi®ers. In the ®rst three approaches, the weights assigned to the classi®ers or groups of them are data dependent. The ®rst approach involves the calculation of fuzzy integrals. The second scheme performs weighted averaging with data-dependent weights. The third approach performs linear combination of the outputs of classi®ers via the BADD defuzzi®cation strategy. In the last scheme, the outputs of multiple classi®ers are combined using Zimmermann's compensatory operator. An empirical evaluation using widely accessible data sets substantiates the validity of the approaches with data-dependent weights, compared to various existing combination schemes of multiple classi®ers. Ó 0167-8655/99/$ ± see front matter Ó 1999 Elsevier Science B.V. All rights reserved. PII: S 0 1 6 7 -8 6 5 5 ( 9 9 ) 0 0 0 1 2 -4

This paper, based on the fuzzy measures and fuzzy integrals given by Sugeno, first defines interval number fuzzy measures (INF-measures) and fuzzy number fuzzy measures (FNF-measures), and the fuzzy integral of function with respect to INF-measures are given. Then it defines the fuzzy integral of functions with respect to FNF-measures, and the properties and convergence theorems are obtained. All these

Adequate assessment of risk is essential to assist the stakeholders in planning for efficient risk allocation and mitigation and to ensure success in business and projects. However, it is problematic due to the difficulty in quantification of certain risks, existence of interactions , and multiattribute structure of the project risk assessment task. This paper reports research in which relevant risks were identified for power and transport infrastructure public-private partnership (PPP) projects, which are globally the most active infrastructure sectors for private investment. It further proposes, demonstrates, and validates a novel multiattribute risk assessment model that supports both sectoral and project risk analysis to assist stakeholders in risk management decision making. A 45-factor risk register, established based on literature review and PPP experts' interviews, was administered to solicit industry-wide perceptions for risk assessment. Application of fuzzy set theory to risk analysis revealed 22 critical risk factors (CRFs) that were categorized into seven critical risk groups (CRGs) of correlated factors using factor analysis. Risk factors that achieved a linguistic assessment of high impact reflect issues related to institutional capacity and the local economy. Further analysis based on fuzzy measure and nonadditive fuzzy integral combined with arithmetic mean helped to obtain an overall risk index (ORI) which indicated a moderate risk outlook for both power and transport infrastructure sectors. Whereas public sector maturity was assessed as a high impact CRG in the power sector, project planning and implementation, project finance, and project revenue were additionally rated as high impact CRGs in the transport infrastructure sector. Demonstration of the developed methodology for a build-operate-transfer (BOT) motorway case study project showed that the private sector stakeholders viewed the project at high risk with all the CRGs evaluated as high impact except the political stability CRG, which was assessed as moderately risky. Test results show that the methodology performed satisfactorily in approximating experts holistic project risk assessments. The developed framework can be used to assess a country's condition or overall project risk at the initial project stage with little input of time and resources, thus facilitating an efficient and robust risk assessment. Application of fuzzy measure based nonadditive fuzzy integral combined with arithmetic mean for sectoral and project risk assessment, and comparison of sectoral risk analysis from a developing country perspective are some of the key features of this study.

The huge number of voxels in fMRI over time poses a major challenge to for effective analysis. Fast, accurate, and reliable classifiers are required for estimating the decoding accuracy of brain activities. Although machine-learning classifiers seem promising, individual classifiers have their own limitations. To address this limitation, the present paper proposes a method based on the ensemble of neural networks to analyze fMRI data for cognitive state classification for application across multiple subjects. Similarly, the fuzzy integral (FI) approach has been employed as an efficient tool for combining different classifiers. The FI approach led to

With the growth of digital television TV program classification has become a major research topic. Recent classification techniques have reported acceptable results for specific genre detection. Cartoons is one of these genres which has deceived some attention because of its importance in push scenarios where parents want to control their children's access to television. In this paper a flexible scheme based on a non-linear classifier called Fuzzy Integral is presented. This operator is supposed not only to classify but also to give a relevance measure to all the features involved in the classification. Preliminary results using this operator for cartoon detection are presented and compared with other well known statistical clasification methods like PCA, LDA or K-NN.

Internet evolution has affected all industrial and commercial activity and accelerated e-learning growth. Due to cost, time, or flexibility for designer courses and learners, e-learning has been adopted by corporations as an alternative training method. E-learning effectiveness evaluation is vital, and evaluation criteria are diverse. A large effort has been made regarding e-learning effectiveness evaluation; however, a generalized quantitative evaluation model, which considers both the interaffected relation between criteria and the fuzziness of subjective perception concurrently, is lacking. In this paper, the proposed new novel hybrid MCDM model addresses the independent relations of evaluation criteria with the aid of factor analysis and the dependent relations of evaluation criteria with the aid of DEM-ATEL. The AHP and the fuzzy integral methods are used for synthetic utility in accordance with subjective perception environment. Empirical experimental results show the proposed model is capable of producing effective evaluation of e-learning programs with adequate criteria that fit with respondent's perception patterns, especially when the evaluation criteria are numerous and intertwined.

Multiple classi"er fusion may generate more accurate classi"cation than each of the constituent classi"ers. Fusion is often based on "xed combination rules like the product and average. Only under strict probabilistic conditions can these rules be justi"ed. We present here a simple rule for adapting the class combiner to the application. c decision templates (one per class) are estimated with the same training set that is used for the set of classi"ers. These templates are then matched to the decision pro"le of new incoming objects by some similarity measure. We compare 11 versions of our model with 14 other techniques for classi"er fusion on the Satimage and Phoneme datasets from the database ELENA. Our results show that decision templates based on integral type measures of similarity are superior to the other schemes on both data sets.

This paper describes a fuzzy hierarchical analytic approach to determine the weighting of subjective judgments. In addition, it presents a nonadditive fuzzy integral technique to evaluate a green engineering industry case as a fuzzy multicriteria decision-making (FMCDM) problem. When the investment strategies are evaluated from various aspects, such as economic effectiveness, technical feasibility, and environmental regulation, it can be regarded as an FMCDM problem. Since stakeholders cannot clearly estimate each considered criterion in terms of numerical values for the anticipated alternatives/strategies, fuzziness is considered to be applicable. Consequently, this paper uses triangular fuzzy numbers to establish weights and anticipated achievement values. By ranking fuzzy weights and fuzzy synthetic utility values, we can determine the relative importance of criteria and decide the best strategies. This paper applies what is called a fuzzy measure and nonadditive fuzzy integral technique to evaluate the synthetic performance of green engineering strategies for aquatic products processors in Taiwan. In addition, we demonstrate that the nonadditive fuzzy integral is an effective evaluation and appears to be appropriate, especially when the criteria are not independent.

The paper discusses about the Choquet Fuzzy Integral (CFI) based identification and control of a Real Time Dynamical System. The plant is modeled using Choquet fuzzy Integral based Neural Network with Gradient Descent as learning algorithm. This model is used for designing and simulating CFI based controller. Then this designed controller is implemented on real time system through MATLAB. Finally the performance of CFI based controller is compared with Feed Forward Neural Network taking Square of Error as the parameter of comparison.

In this paper the integration formulas of Gaussian methods with positive coefficient for fuzzy integrations are discussed and then are followed by convergence theorem. The proposed algorithms are illustrated and compared with Newton CotÕs methods [T. Allahviranloo, Newton CotÕs methods for integration of fuzzy functions, Appl. Math. Comp., in press] by solving some numerical examples.

Protein function is related to its chemical reaction to the surrounding environment including other proteins. On the other hand, this depends on the spatial shape and tertiary structure of protein and folding of its constituent components in space. The correct identification of protein domain fold solely using extracted information from protein sequence is a complicated and controversial task in the current computational biology. In this article a combined classifier based on the information content of extracted features from the primary structure of protein has been introduced to face this challenging problem. In the first stage of our proposed two-tier architecture, there are several classifiers each of which is trained with a different sequence based feature vector. Apart from the application of the predicted secondary structure, hydrophobicity, van der Waals volume, polarity, polarizability, and different dimensions of pseudo-amino acid composition vectors in similar studies, the position specific scoring matrix (PSSM) has also been used to improve the correct classification rate (CCR) in this study. Using K-fold cross validation on training dataset related to 27 famous folds of SCOP, the 28 dimensional probability output vector from each evidence theoretic K-NN classifier is used to determine the information content or expertness of corresponding feature for discrimination in each fold class. In the second stage, the outputs of classifiers for test dataset are fused using Sugeno fuzzy integral operator to make better decision for target fold class. The expertness factor of each classifier in each fold class has been used to calculate the fuzzy integral operator weights. Results make it possible to provide deeper interpretation about the effectiveness of each feature for discrimination in target classes for query proteins..▶ In this study we use combined classifier for identification of protein domain fold. ▶ Information content of extracted features of protein has been introduced to face this problem. ▶ We show that position specific scoring matrix improves the correct classification rate. ▶ Results provide deeper interpretation about the effectiveness of each feature for discrimination.

In actual environmental investment for industry, the stakeholders are often required to evaluate the investment strategies according to their own subjective preferences in terms of numerical values from various criteria, such as economic e ectiveness, technique feasibility and environmental regulation. Thus, this situation can be regarded as a fuzzy multiple criteria decision-making (MCDM) problem, so the fuzziness and uncertainty of subjective perception should be considered. This paper proposes an alternative approach, the non-additive fuzzy integral, to cope with evaluation of fuzzy MCDM problems particularly while there is dependence among considered criteria. To illustrate the proposed procedure, the sustainable development strategy for aquatic product processors in Taiwan is investigated. In this paper we employ triangular fuzzy numbers to represent the decision makers' subjective preferences on the considered criteria, as well as for the criteria measurements to evaluate a sustainable development planning case for industry. Firstly, in this study we employ factor analysis to extract four independent common factors from those criteria. Secondly, we construct the evaluation frame using AHP composed of the above four common factors with twelve evaluated criteria, and then derive the relative weights with respect to considered criteria. Thirdly, the synthetic utility value corresponding to each sustainable development strategy is aggregated by the fuzzy weights with fuzzy performance values, and the best investment strategies can then be decided. Through this study, we successfully demonstrate that the non-additive fuzzy integral is an e ective evaluation and appears to be more appropriate than the traditional simple additive weighted method, especially when the criteria are dependent. ?

Organizational transformations have been widely adopted by firms who wish to improve their competitive advantage to be better prepared to face external challenges. This research has chosen Communities of Practice (CoPs) as the subject of discussion for an assessment model to reform organizations that undertake CoPs for collective knowledge to enhance their core competencies. Given the interrelationships between criteria, this research uses the nonadditive fuzzy integral to develop a framework for the CoPs performance assessment. The purposes of this paper are to identify the key dimensions/criteria in the CoPs, to use fuzzy logic method to analyze the relative importance of each criterion, and to rank the criteria so that proper resources can be allocated while managing the CoPs. Through interviews with experts, four strategy alternatives and 16 criteria along four dimensions are generated. A survey of the CoPs practitioners is then conducted to compare the results of each criterion. The results will not only help organizations that intend to initiate changes via the CoPs activities to decide the ranking of their appraisal criteria, but it can also assist them in guiding the behavior of their staff while effectively monitoring and improving the performances of the CoPs.

This paper describes a fuzzy hierarchical analytic approach to determine the weighting of subjective judgments. In addition, it presents a nonadditive fuzzy integral technique to evaluate a mutual fund case as a fuzzy multi-criteria decision-making (FMCDM) problem. When the investment strategies are evaluated from various aspects, such as market timing, stock selection ability, fund size and team work, it can be regarded as an FMCDM problem. Since investors can not clearly estimate each considered criterion in terms of numerical values for the anticipated alternatives/strategies, fuzziness is considered to be applicable. Consequently, this paper uses triangular fuzzy numbers to establish weights and anticipated achievement values. By ranking fuzzy weights and fuzzy synthetic performance values, we can determine the relative importance of criteria and decide the best strategies.

In this paper, we present the theoretical framework for the generalization of classical hidden Markov models using fuzzy measures and fuzzy integrals. The main characteristic of the generalization is the relaxation of the usual additivity constraint of probability measures. Fuzzy integrals are defined with respect to fuzzy measures, whose key property is monotonicity with respect to set inclusion. This property is far weaker than the usual additivity property of probability measures. As a result of the new formulation, the statistical independence assumption of the classical hidden Markov models is relaxed. Two attractive properties of this generalization are: the generalized hidden Markov model reduces to the classical hidden Markov model if we used the Choquet fuzzy integral and probability measures; and the establishment of a relation between the generalized hidden Markov model and the classical nonstationary hidden Markov model in which the transitional parameters vary with time

In this study, the different phases of pressure sore generation and healing are investigated through a combined analysis of high-frequency ultrasound (20 MHz) images and digital color photographs. Pressure sores were artificially induced in guinea pigs, and the injured regions were monitored for 21 days (data were obtained on days 3, 7, 14, and 21). Several statistical features of the images were extracted, relating to both the altering pattern of tissue and its superficial appearance. The features were grouped into five independent categories, and each category was used to train a neural network whose outputs were the four days. The outputs of the five classifiers were then fused using a fuzzy integral to provide the final decision. We demonstrate that the suggested method provides a better decision regarding tissue status than using either imaging technique separately. This new approach may be a viable tool for detecting the phases of pressure sore generation and healing in clinic...

The main objective of this contribution is to present a design methodology for application specific fuzzy integrated circuits. This methodology is based on an specific architecture and a user-friendly design environment which enables the specification, verification and synthesis of fuzzy systems taking into account conceptual as well as microelectronics considerations.

Kernel  methods  for  classification  is  a  well-studied area  in  which  data  are  implicitly  mapped  from  a  lower-
dimensional  space  to  a  higher-dimensional  space  to improve classification  accuracy.  However,  for  most  kernel  methods,  one must  still  choose  a  kernel  to  use  for  the  problem.  Since  there is,  in  general,  no  way  of  knowing  which  kernel  is  the  best, multiple kernel learning
(MKL)  is  a  technique  used  to  learn  the aggregation of a set of valid kernels into a single (ideally) superior
kernel. The aggregation can be done using weighted sums of the pre-computed  kernels,  but  determining  the  summation  weights is  not  a  trivial  task.  A  popular  and  successful  approach  to  this problem  is MKL-group lasso (MKLGL),  where  the  weights  and classification surface are simultaneously solved by iteratively optimizing a min-max optimization until convergence. In this work, we  propose  an
lp-normed genetic algorithm MKL (GAMKLp), which  uses  a  genetic  algorithm  to  learn  the  weights  of  a  set  of pre-computed  kernel  matrices  for  use  with  MKL  classification. We  prove  that  this  approach  is  equivalent  to  a  previously proposed  fuzzy  integral  aggregation  of  multiple  kernels  called fuzzy integral: genetic algorithm (FIGA).  A  second  algorithm, which  we  call
decision-level fuzzy integral MKL (DeFIMKL),
is  also  proposed,  where  a  fuzzy  measure  with  respect  to  the fuzzy  Choquet  integral  is  learned  via  quadratic  programming, and  the  decision  value—viz.,  the  class  label—is  computed  using the  fuzzy Choquet  integral aggregation.  Experiments on  several benchmark  data  sets  show  that  our  proposed  algorithms  can outperform  MKLGL  when  applied  to support vector machine (SVM)-based classification.

In this paper we study the effectiveness of using multiple classifier combination for EEG signal classification aiming to obtain more accurate results than it possible from each of the constituent classifiers. The developed system employs two linear classifiers (SVM,LDA) fused at the abstract and measurement levels for integrating information to reach a collective decision. For making decision, the majority voting