Reconstruction problem and information granularity

The paper elaborates on the representation and reconstruction of numerical and nonnumerical data in fuzzy modeling. Proposed are general criteria leading to the distortion-free interfacing mechanisms that help transform information between the systems (or modeling environments) operating at different levels of information granularity. Distinguished are three basic categories of information: numerical, interval-valued, and linguistic (fuzzy). Since all of them are dealt with here, the paper subsumes the current studies concentrated exclusively on representing fuzzy sets through their numerical representatives (prototypes). The algorithmic framework in which the distortion-free interfacing is completed is realized through neural networks. Each category of information is treated separately and gives rise to its own specialized architecture of the neural network. Similarly, these networks require carefully designed training sets that fully capture the specificity of the reconstruction problem. Several carefully selected numerical examples are aimed at the illustration of the key ideas     

A novel fuzzy logic system based on N-version programming

For the consideration of different application systems, modeling the fuzzy logic rule, and deciding the shape of membership functions are very critical issues due to they play key roles in the design of fuzzy logic control system. This paper proposes a novel design methodology of fuzzy logic control system using the neural network and fault-tolerant approaches. The connectionist architecture with the learning capability of neural network and N-version programming development of a fault-tolerant technique are implemented in the proposed fuzzy logic control system. In other words, this research involves the modeling of parameterized membership functions and the partition of fuzzy linguistic variables using neural networks trained by the unsupervised learning algorithms. Based on the self-organizing algorithm, the membership function and partition of fuzzy class are not only derived automatically, but also the preconditions of fuzzy IF-THEN rules are organized. We also provide two examples, pattern recognition and tendency prediction, to demonstrate that the proposed system has a higher computational performance and its parallel architecture supports noise-tolerant capability. This generalized scheme is very satisfactory for pattern recognition and tendency prediction problems     

A novel semi-quantitative Fuzzy Cognitive Map model for complex systems for addressing challenging participatory real life problems

Fuzzy Cognitive Maps (FCM) are a promising approach for socio-ecological systems modelling. FCMs represent problem knowledge extracted from different stakeholders in the form of connected factors/variables with imprecise cause-effect relationships and many feedback loops. These typically large maps are condensed and aggregated to obtain a summary view of the system. However, representation, condensation and aggregation of previous FCM models are qualitative due to lack of appropriate quantitative methods. This study tackles these drawbacks by developing a semi-quantitative FCM model consisting of robust methods for adequately and accurately representing and manipulating imprecise data describing a complex problem involving stakeholders for pragmatic decision making. The model starts with collecting qualitative imprecise data from relevant stakeholders. These data are then transformed into stakeholder perceptions/FCMs with different causal relationship formats (linguistic or numeric) which the proposed model then represents in a unified format using a 2-tuple fuzzy linguistic representation model which allows combining imprecise linguistic and numeric values with different granularity and/or semantic without loss of information. The proposed model then condenses large FCMs using a semi-quantitative method that allows multi-level condensation. In each level of condensation, groups of similar variables are subjectively condensed and the corresponding imprecise connections are computationally condensed using robust calculations involving credibility weights assigned to variables (variables’ importance). The model then uses a quantitative fuzzy method to aggregate perceptions/FCMs into a stakeholder group or social perception/FCM based on the 2-tuple model and credibility weights assigned to FCMs (stakeholders’ importance). Thereafter, the structure of produced FCMs is analysed using graph theory indices to examine differences in perceptions between stakeholders or groups. Finally, the model applies various what-if policy scenario simulations on group FCMs using a dynamical systems approach with neural networks and analyses scenario outcomes to provide appropriate recommendations to decision makers. An example application illustrates method’s effectiveness and usefulness.     

A genetic-based neuro-fuzzy approach for modeling and control ofdynamical systems

Linguistic modeling of complex irregular systems constitutes the heart of many control and decision making systems, and fuzzy logic represents one of the most effective algorithms to build such linguistic models. In this paper, a linguistic (qualitative) modeling approach is proposed. The approach combines the merits of the fuzzy logic theory, neural networks, and genetic algorithms (GAs). The proposed model is presented in a fuzzy-neural network (FNN) form which can handle both quantitative (numerical) and qualitative (linguistic) knowledge. The learning algorithm of a FNN is composed of three phases. The first phase is used to find the initial membership functions of the fuzzy model. In the second phase, a new algorithm is developed and used to extract the linguistic-fuzzy rules. In the third phase, a multiresolutional dynamic genetic algorithm (MRD-GA) is proposed and used for optimized tuning of membership functions of the proposed model. Two well-known benchmarks are used to evaluate the performance of the proposed modeling approach, and compare it with other modeling approaches.     

A Hybrid Learning Method for the Data-Driven Design of Linguistic Dynamic Systems

In lots of data based prediction or modeling applications, uncertainties and/or noises in the observed data cannot be avoided. In such cases, it is more preferable and reasonable to provide linguistic (fuzzy) predicted results described by fuzzy memberships or fuzzy sets instead of the crisp estimates depicted by numbers. Linguistic dynamic system (LDS) provides a powerful tool for yielding linguistic (fuzzy) results. However, it is still difficult to construct LDS models from observed data. To solve this issue, this paper first presents a simplified LDS whose inputoutput mapping can be determined by closed-form formulas. Then, a hybrid learning method is proposed to construct the data-driven LDS model. The proposed hybrid learning method firstly generates fuzzy rules by the subtractive clustering method, then carries out further optimization of centers of the consequent triangular fuzzy sets in the fuzzy rules, and finally adopts multiobjective optimization algorithm to determine the left and right end-points of the consequent triangular fuzzy sets. The proposed approach is successfully applied to three real-world prediction applications which are: prediction of energy consumption of a building, forecasting of the traffic flow, and prediction of the wind speed. Simulation results show that the uncertainties in the data can be effectively captured by the linguistic (fuzzy) estimates. It can also be extended to some other prediction or modeling problems, in which observed data have high levels of uncertainties.      

Genetic tuning of fuzzy rule deep structures preserving interpretability and its interaction with fuzzy rule set reduction

Tuning fuzzy rule-based systems for linguistic fuzzy modeling is an interesting and widely developed task. It involves adjusting some of the components of the knowledge base without completely redefining it. This contribution introduces a genetic tuning process for jointly fitting the fuzzy rule symbolic representations and the meaning of the involved membership functions. To adjust the former component, we propose the use of linguistic hedges to perform slight modifications keeping a good interpretability. To alter the latter component, two different approaches changing their basic parameters and using nonlinear scaling factors are proposed. As the accomplished experimental study shows, the good performance of our proposal mainly lies in the consideration of this tuning approach performed at two different levels of significance. The paper also analyzes the interaction of the proposed tuning method with a fuzzy rule set reduction process. A good interpretability-accuracy tradeoff is obtained combining both processes with a sequential scheme: first reducing the rule set and subsequently tuning the model.     

Towards true linguistic modelling through optimal numerical solutions

This paper is concerned with both the problems of quantitative and qualitative modelling of complex systems by using fuzzy techniques. A unified approach for the identification and subsequent extraction of linguistic knowledge of systems using fuzzy relational models is addressed. This approach deals with the identification problem by means of optimal numerical solutions based on weighted least squares and quadratic programming formulations. The linguistic knowledge is extracted in the form of consistent fuzzy rules that describe linguistically the behaviour of the identified system. A new methodology for the simplification of the extracted rules is derived by using a pruning criterion based on the representability matrix concept introduced in previous work. Several numerical aspects concerning the proposed optimization schemes and a covering discussion about the linguistic interpretation of the resulting models are also included together with illustrative examples in the contexts of pattern classification and dynamic systems identification. The paper also provides an overview of fuzzy modelling techniques that intends to situate the relational models among other fuzzy model architectures typically adopted in the literature, highlighting their main advantages and drawbacks.     

A Proposal for the Genetic Lateral Tuning of Linguistic Fuzzy Systems and Its Interaction With Rule Selection

Linguistic fuzzy modeling allows us to deal with the modeling of systems by building a linguistic model which is clearly interpretable by human beings. However, since the accuracy and the interpretability of the obtained model are contradictory properties, the necessity of improving the accuracy of the linguistic model arises when complex systems are modeled. To solve this problem, one of the research lines in recent years has led to the objective of giving more accuracy to linguistic fuzzy modeling without losing the interpretability to a high level. In this paper, a new postprocessing approach is proposed to perform an evolutionary lateral tuning of membership functions, with the main aim of obtaining linguistic models with higher levels of accuracy while maintaining good interpretability. To do so, we consider a new rule representation scheme base on the linguistic 2-tuples representation model which allows the lateral variation of the involved labels. Furthermore, the cooperation of the lateral tuning together with fuzzy rule reduction mechanisms is studied in this paper, presenting results on different real applications. The obtained results show the good performance of the proposed approach in high-dimensional problems and its ability to cooperate with methods to remove unnecessary rules.     

RSPOP: rough set-based pseudo outer-product fuzzy rule identification algorithm

System modeling with neuro-fuzzy systems involves two contradictory requirements: interpretability verses accuracy. The pseudo outer-product (POP) rule identification algorithm used in the family of pseudo outer-product-based fuzzy neural networks (POPFNN) suffered from an exponential increase in the number of identified fuzzy rules and computational complexity arising from high-dimensional data. This decreases the interpretability of the POPFNN in linguistic fuzzy modeling. This article proposes a novel rough set-based pseudo outer-product (RSPOP) algorithm that integrates the sound concept of knowledge reduction from rough set theory with the POP algorithm. The proposed algorithm not only performs feature selection through the reduction of attributes but also extends the reduction to rules without redundant attributes. As many possible reducts exist in a given rule set, an objective measure is developed for POPFNN to correctly identify the reducts that improve the inferred consequence. Experimental results are presented using published data sets and real-world application involving highway traffic flow prediction to evaluate the effectiveness of using the proposed algorithm to identify fuzzy rules in the POPFNN using compositional rule of inference and singleton fuzzifier (POPFNN-CRI(S)) architecture. Results showed that the proposed rough set-based pseudo outer-product algorithm reduces computational complexity, improves the interpretability of neuro-fuzzy systems by identifying significantly fewer fuzzy rules, and improves the accuracy of the POPFNN.     

A proposal for improving the accuracy of linguistic modeling

We propose accurate linguistic modeling, a methodology to design linguistic models that are accurate to a high degree and may be suitably interpreted. This approach is based on two main assumptions related to the interpolative reasoning developed by fuzzy rule-based systems: a small change in the structure of the linguistic model based on allowing the linguistic rule to have two consequents associated; and a different way to obtain the knowledge base based on generating a preliminary fuzzy rule set composed of a large number of rules and then selecting the subset of them best cooperating. Moreover, we introduce two variants of an automatic design method for these kinds of linguistic models based on two well-known inductive fuzzy rule generation processes and a genetic process for selecting rules. The accuracy of the proposed methods is compared with other linguistic modeling techniques with different characteristics when solving of three different applications     

On some idea of a neuro-fuzzy controller

The paper presents a neuro-fuzzy technique for the design of controllers. This technique can effectively deal with two main types of knowledge which usually describe the control strategy for complex systems, that is, a qualitative, linguistic, fuzzy knowledge usually expressed in the form of linguistic rules, and a quantitative, nonfuzzy information in the form of measurements and other numerical data. The proposed technique combines artificial neural networks with fuzzy logic yielding a structure that can be called a neuro-fuzzy controller or, broadly speaking, a fuzzy neural network. The paper presents a general structure of a neuro-fuzzy controller and two essential phases of its design, that is, a learning phase and a functioning phase. In turn, a numerical example which illustrates how the proposed controller works is presented. Finally, the paper describes an application of a neuro-fuzzy control to inverter drive systems for electric vehicles. The results of simulation and experimental investigations carried out on the laboratory model of an inverter drive system are also provided.     

Learning of fuzzy cognitive maps using density estimate

Fuzzy cognitive maps (FCMs) are convenient and widely used architectures for modeling dynamic systems, which are characterized by a great deal of flexibility and adaptability. Several recent works in this area concern strategies for the development of FCMs. Although a few fully automated algorithms to learn these models from data have been introduced, the resulting FCMs are structurally considerably different than those developed by human experts. In particular, maps that were learned from data are much denser (with the density over 90% versus about 40% density of maps developed by humans). The sparseness of the maps is associated with their interpretability: the smaller the number of connections is, the higher is the transparency of the map. To this end, a novel learning approach, sparse real-coded genetic algorithms (SRCGAs), to learn FCMs is proposed. The method utilizes a density parameter to guide the learning toward a formation of maps of a certain predefined density. Comparative tests carried out for both synthetic and real-world data demonstrate that, given a suitable density estimate, the SRCGA method significantly outperforms other state-of-the-art learning methods. When the density estimate is unknown, the new method can be used in an automated fashion using a default value, and it is still able to produce models whose performance exceeds or is equal to the performance of the models generated by other methods.     

Multilayer Cognitive Maps in the Resolution of Problems using the FCM Designer Tool

Cognitive maps are a tool to represent knowledge from a qualitative perspective, allowing to create models of complex systems where an exact mathematical model cannot be used because of the complexity of the system. In the literature, several tools have been proposed to develop cognitive maps and fuzzy cognitive maps (FCMs); one of them is FCM Designer. This paper designs and implements an extension to the FCM Designer tool that allows creating multilayer FCM. With this extension, it is possible to have several FCMs for the same problem, where each one expresses a different level of knowledge of the system under study, but interlinked. Thus, one can have a first level of detailed abstraction of the system with specific information and then more general levels. In addition, we can have different levels where the variables of one level depend on those of another level. That is, the multilayer approach enriches the modeled systems with flow of information between layers, to derive information about the concepts involved in layers from the concepts in other layers. In our multilayer approach, the relationship between the cognitive maps in different layers can be carried out in various ways: with fuzzy rules, connections with weights and with mathematical equations. This work presents the design and the implementation of the extension of the FCM Designer tool, and several test cases in different domains: a FCM to analyze emergent properties of Wikipedia a FCM for medical analysis for diagnosis, and another like recommender system.     

Neuro-fuzzy approach versus rough-set inspired methodology for intelligent decision support

One of the two goals of this paper is to briefly present two different methodologies that can be used to the design of intelligent decision support systems, in particular, from the field of medicine. The first approach, combining artificial neural networks and fuzzy sets, yields a neuro-fuzzy classifier that can be trained with both purely numerical data as well as qualitative, linguistic, fuzzy data that describe the decision-making process. The second approach – resulting in a rough classifier – combines all positive aspects of rule induction systems with the flexibility of statistical techniques for classification. The second goal of this paper is to perform a broad comparative analysis of both proposed methodologies (and two others) applied to: (a) the problem of selecting surgical and non-surgical cases in the veterinary domain of equine colic, (b) the problem of diagnosing benign and malign types of breast cancer, and (c) the problem of corporate bankruptcy prediction (corporate ‘financial health'). Several aspects of comparison have been considered including the accuracy of the systems, diversity of the data processed, transparency and the form of decisions made.     

A probabilistic fuzzy approach to modeling nonlinear systems

Recently, the study of incorporating probability theory and fuzzy logic has received much interest. To endow the traditional fuzzy rule-based systems (FRBs) with probabilistic features to handle randomness, this paper presents a probabilistic fuzzy neural network (ProFNN) by introducing the probability of input linguistic terms and providing linguistic meaning into the connectionist architecture. ProFNN integrates the probabilistic information of fuzzy rules into the antecedent parts and quantifies the impacts of the rules on the consequent parts using mutual subsethood, which work in conjunction with volume defuzzification in a gradient descent learning frame work. Despite the increase in the number of parameters, ProFNN provides a promising solution to deal with randomness and fuzziness in a single frame. To evaluate the performance and applicability of the proposed approach, ProFNN is carried out on various benchmarking problems and compared with other existing models with a performance better than most of them.     

Fuzzy cognitive map software tool for treatment management of uncomplicated urinary tract infection

Uncomplicated urinary tract infection (uUTI) is a bacterial infection that affects individuals with normal urinary tracts from both structural and functional perspective. The appropriate antibiotics and treatment suggestions to individuals suffer of uUTI is an important and complex task that demands a special attention. How to decrease the unsafely use of antibiotics and their consumption is an important issue in medical treatment. Aiming to model medical decision making for uUTI treatment, an innovative and flexible approach called fuzzy cognitive maps (FCMs) is proposed to handle with uncertainty and missing information. The FCM is a promising technique for modeling knowledge and/or medical guidelines/treatment suggestions and reasoning with it. A software tool, namely FCM-uUTI DSS, is investigated in this work to produce a decision support module for uUTI treatment management. The software tool was tested (evaluated) in a number of 38 patient cases, showing its functionality and demonstrating that the use of the FCMs as dynamic models is reliable and good. The results have shown that the suggested FCM-uUTI tool gives a front-end decision on antibiotics’ suggestion for uUTI treatment and are considered as helpful references for physicians and patients. Due to its easy graphical representation and simulation process the proposed FCM formalization could be used to make the medical knowledge widely available through computer consultation systems.     

Fuzzy bounded least-squares method for the identification of linearsystems

This paper presents the fuzzy bounded least-squares method which uses both linguistic information and numerical data to identify linear systems. This method introduces a new type of fuzzy system, i.e., a fuzzy interval system. The steps in the method are as follows: 1) to utilize all the available linguistic information to obtain a fuzzy interval system and then to use the fuzzy interval system to give the admissible model set (i.e., the set of all models which are acceptable and reasonable from the point of view of linguistic information); 2) to find a model in the admissible model set which best fits the available numerical data. It is shown that such a model can be obtained by a quadratic programming approach. By comparing this method with the least-squares method, it is proved that the model obtained by this method fits a real system better than the model obtained by the least-squares method. In addition, this method also checks the adequacy of linear models for modeling a given system during the identification process and can help one to decide whether it is necessary to use nonlinear models     

Fuzzy cognitive map architectures for medical decision support systems

Medical decision support systems can provide assistance in crucial clinical judgments, particularly for inexperienced medical professionals. Fuzzy cognitive maps (FCMs) is a soft computing technique for modeling complex systems, which follows an approach similar to human reasoning and the human decision-making process. FCMs can successfully represent knowledge and human experience, introducing concepts to represent the essential elements and the cause and effect relationships among the concepts to model the behavior of any system. Medical decision systems are complex systems that can be decomposed to non-related and related subsystems and elements, where many factors have to be taken into consideration that may be complementary, contradictory, and competitive; these factors influence each other and determine the overall clinical decision with a different degree. Thus, FCMs are suitable for medical decision support systems and appropriate FCM architectures are proposed and developed as well as the corresponding examples from two medical disciplines, i.e. speech and language pathology and obstetrics, are described.