Sparse distributed fuzzy inference systems

The sparse distributed architecture described would be shown to function effectively as a fuzzy inference system giving essentially the same results as conventional techniques. However, whereas the conventional model reaches a glass ceiling as the order of target systems increases due to computer architectural limitations, this design is able to surpass this limit. It uses the same principles of max–min composition to solve inference problems, and comprises fuzzy sets that can encode a level of linguistic expression typical of such systems. It however expresses fuzzy sets differently, and performs the required computation in a manner suitable to the alternative representation. It may seem a rather complicated solution for low order problems (which it is) with the situation reversing itself for high order problems, the conventional solution being complicated if not impossible and the new architecture simple. The limitation, errors and performance of the new method when compared to the conventional method is documented and quantified by software written to model the two representations considered.     

Interpreting and extracting fuzzy decision rules from fuzzy information systems and their inference

Information systems, which contain only crisp data, precise and unique attribute values for all objects, have been widely investigated. Due to the fact that in realworld applications imprecise data are abundant, uncertainty is inherent in real information systems. In this paper, information systems are called fuzzy information systems, and formalized by (objects; attributes; f), in which f is a fuzzy set and expresses some uncertainty between an object and its attribute values. To interpret and extract fuzzy decision rules from fuzzy information systems, the meta-theory based on modal logic proposed by Resconi et al. is modified. The modified meta-theory not only expresses uncertainty between objects and their attributes, but also uncertainty in the process of recognizing fuzzy information systems. In addition, according to perception computing (proposed by Zadeh), granules of fuzzy information systems can be represented by fuzzy decision rules, so that, fuzzy inference methods can be used to obtain the decision attribute of a new object. Finally, a novel way of combining evidences based on the modified meta-theory is introduced, which extends the concept of combining evidences based on Dempster-Shafer theory.     

Learning interpretable fuzzy inference systems with FisPro

Fuzzy inference systems (FIS) are likely to play a significant part in system modeling, provided that they remain interpretable following learning from data. The aim of this paper is to set up some guidelines for interpretable FIS learning, based on practical experience with fuzzy modeling in various fields. An open source software system called FisPro has been specifically designed to provide generic tools for interpretable FIS design and learning. It can then be extended with the addition of new contributions. This work presents a global approach to design data-driven FIS that satisfy certain interpretability and accuracy criteria. It includes fuzzy partition generation, rule learning, input space reduction and rule base simplification. The FisPro implementation is discussed and illustrated through several detailed case studies.     

Online tuning of fuzzy inference systems using dynamic fuzzy Q-learning

This paper presents a dynamic fuzzy Q-learning (DFQL) method that is capable of tuning fuzzy inference systems (FIS) online. A novel online self-organizing learning algorithm is developed so that structure and parameters identification are accomplished automatically and simultaneously based only on Q-learning. Self-organizing fuzzy inference is introduced to calculate actions and Q-functions so as to enable us to deal with continuous-valued states and actions. Fuzzy rules provide a natural mean of incorporating the bias components for rapid reinforcement learning. Experimental results and comparative studies with the fuzzy Q-learning (FQL) and continuous-action Q-learning in the wall-following task of mobile robots demonstrate that the proposed DFQL method is superior.     

Petrophysical data prediction from seismic attributes using committee fuzzy inference system

This study presents an intelligent model based on fuzzy systems for making a quantitative formulation between seismic attributes and petrophysical data. The proposed methodology comprises two major steps. Firstly, the petrophysical data, including water saturation (S_w) and porosity, are predicted from seismic attributes using various fuzzy inference systems (FISs), including Sugeno (SFIS), Mamdani (MFIS) and Larsen (LFIS). Secondly, a committee fuzzy inference system (CFIS) is constructed using a hybrid genetic algorithms-pattern search (GA-PS) technique. The inputs of the CFIS model are the outputs and averages of the FIS petrophysical data. The methodology is illustrated using 3D seismic and petrophysical data of 11 wells of an Iranian offshore oil field in the Persian Gulf. The performance of the CFIS model is compared with a probabilistic neural network (PNN). The results show that the CFIS method performed better than neural network, the best individual fuzzy model and a simple averaging method.     

Inductive inference of monotonic formal systems from positive data

A formal system is a finite set of expressions, such as a grammar or a Prolog program. A semantic mapping from formal systems to concepts is said to be monotonic if it maps larger formal systems to larger concepts. A formal system Γ is said to be reduced with respect to a finite setX if the concept defined by Γ containsX but the concepts defined by any proper subset Γ′ of Γ cannot contain some part ofX. Assume a semantic mapping is monotonic and formal systems consisting of at mostn expressions that are reduced with respect toX can define only finitely many concepts for any finite setX and anyn. Then, the class of concepts defined by formal systems consisting of at mostn expressions is shown to be inferable from positive data. As corollaries, the class of languages defined by length-bounded elementary formal systems consisting of at most,n axioms, the class of languages generated by context-sensitive grammars consisting of at mostn productions, and the class of minimal models of linear Prolog programs consisting of at mostn definite clauses are all shown to be inferable from positive data.     

Fuzzy relation equations and fuzzy inference systems: an insideapproach

This paper investigates and extends the use of fuzzy relation equations for the representation and study of fuzzy inference systems. Using the generalized sup-t (t is a triangular norm) composition of fuzzy relations and the study of sup-t fuzzy relation equations, interesting results are provided concerning the completeness and the theoretical soundness of the representation, as well as the ability to mathematically formulate and satisfy application-oriented design demands. Furthermore, giving a formal study of fuzzy partitions and some useful aspects of fuzzy associations and fuzzy systems, the paper can be used as a theoretical background for designing consistent fuzzy inference systems.     

Adaptive fuzzy spiking neural P systems for fuzzy inference and learning

Fuzzy spiking neural P systems (in short, FSN P systems) are a novel class of distributed parallel computing models, which can model fuzzy production rules and apply their dynamic firing mechanism to achieve fuzzy reasoning. However, these systems lack adaptive/learning ability. Addressing this problem, a class of FSN P systems are proposed by introducing some new features, called adaptive fuzzy spiking neural P systems (in short, AFSN P systems). AFSN P systems not only can model weighted fuzzy production rules in fuzzy knowledge base but also can perform dynamically fuzzy reasoning. It is important to note that AFSN P systems have learning ability like neural networks. Based on neuron's firing mechanisms, a fuzzy reasoning algorithm and a learning algorithm are developed. Moreover, an example is included to illustrate the learning ability of AFSN P systems.     

Fast inference in SAM fuzzy systems using transition matrices

Fast inference using transition matrices (FITM) is a new fast algorithm for performing inferences in fuzzy systems. It is based on the assumption that fuzzy inputs can be expressed as a linear composition of the fuzzy sets used in the rule base. This representation let us interpret a fuzzy set as a vector, so we can just work with the coordinates of it instead of working with the whole set. The inference is made using transition matrices. The key of the method is the fact that a lot of operations can be precomputed offline to obtain the transition matrices, so actual inferences are reduced to a few online matrix additions and multiplications. The algorithm is designed for the standard additive model using the sum-product inference composition.     

Gaussian kernel-based fuzzy inference systems for high dimensional regression

We propose a novel architecture for a higher order fuzzy inference system (FIS) and develop a learning algorithm to build the FIS. The consequent part of the proposed FIS is expressed as a nonlinear combination of the input variables, which can be obtained by introducing an implicit mapping from the input space to a high dimensional feature space. The proposed learning algorithm consists of two phases. In the first phase, the antecedent fuzzy sets are estimated by the kernel-based fuzzy c-means clustering. In the second phase, the consequent parameters are identified by support vector machine whose kernel function is constructed by fuzzy membership functions and the Gaussian kernel. The performance of the proposed model is verified through several numerical examples generally used in fuzzy modeling. Comparative analysis shows that, compared with the zero-order fuzzy model, first-order fuzzy model, and polynomial fuzzy model, the proposed model exhibits higher accuracy, better generalization performance, and satisfactory robustness.     

Subsystem inference representation for fuzzy systems based uponproduct-sum-gravity rule

A new representation which expresses a product-sum-gravity (PSG) inference in terms of additive and multiplicative subsystem inferences of single variable is proposed. The representation yields additional insight into the structure of a fuzzy system and produces an approximate functional characterization of its inferred output. The form of the approximating function is dictated by the choice or polynomial, sinusoidal, or other designs of subsystem inferences. With polynomial inferences, the inferred output approximates a polynomial function the order of which is dependent on the numbers of input membership functions. Explicit expressions for the function and corresponding error of approximation are readily obtained for analysis. Subsystem inferences emulating sinusoidal functions are also discussed. With proper scaling, they produce a set of orthonormal subsystem inferences. The orthonormal set points to a possible “modal” analysis of fuzzy inference and yields solution to an additive decomposable approximation problem. This work also shows that, as the numbers of input membership functions become large, a fuzzy system with PSG inference would converge toward polynomial or Fourier series expansions. The result suggests a new framework to consider fuzzy systems as universal approximators     

Fuzzy inference and fuzzy inference processor

Fuzzy inference, a data processing method based on the fuzzy theory that has found wide use in the control field, is reviewed. Consumer electronics, which accounts for most current applications of this concept, does not require very high speeds. Although software running on a conventional microprocessor can perform these inferences, high-speed control applications require much greater speeds. A fuzzy inference date processor that operates at 200000 fuzzy logic inferences per second and features 12-b input and 16-b output resolution is described     

A knowledge-based cooperative differential evolution for neural fuzzy inference systems

This study presents a knowledge-based cooperative differential evolution (KCoDE) for neural fuzzy inference systems to solve nonlinear control system problems. KCoDE decomposes the fuzzy system into subpopulations, and each individual within each subpopulation evolves separately. The KCoDE method uses five mutation strategies of differential evolution as the knowledge sources to generate a new population space to influence the population space. The exemplary individuals are selected from the population space to the belief space. The belief space in KCoDE is the information repository in which individuals can store their experiences to guide others. Finally, the experimental results show that the proposed KCoDE method better approximates the global optimal solution and has a faster convergence rate than the other methods.     

Protecting location privacy in mobile geoservices using fuzzy inference systems

Mobile geoservices, especially location-based services (LBSs), are becoming more popular each day. The most important goal of these services is to use a user’s location to provide location-aware services. Because the user’s spatial information can be abused by organizations or advertisers, and sometimes for criminal purposes, the protection of this information is a necessary part of such services. There has been substantial research on privacy protection in LBSs and mobile geoservices; most studies have attempted to anonymize the user and hide his/her identity or to engage the user in the protection process. The major defects of these previous approaches include an increased complexity of system architecture, a decrease in service capabilities, undesirable processing times, and a failure to satisfy users. Additionally, anonymization is not a suitable solution for context-aware services. Therefore, in this paper, a new approach is proposed to locate users with different levels of spatial precision, based on his/her spatio-temporal context and a user’s group, through fuzzy inference systems. The user’s location and the time of the request determine the spatio-temporal context of the user. A fuzzy rule base is formed separately for each group of users and services. An interview is a simple method to extract the rules. The spatial precision of a user’s location, which is obtained from a fuzzy system, goes to a spatial function called the conceptualization function, to determine the user’s location based on one of the following five levels of qualitative precision: geometrical coordinates, streets, parish, region, and qualitative location, such as the eastern part of the city. Thus, there is no need to anonymize users in mobile geoservices or to turn the service off. The applicability and efficiency of the proposed method are shown for a group of taxi drivers.     

A new GRASS GIS fuzzy inference system for massive data analysis

GIS systems are frequently coupled with fuzzy logic systems implemented in statistical packages. For large GIS data sets including millions or tens of millions of cells, such an approach is relatively time-consuming. For very large data sets there is also an input/output bottleneck between the GIS and external software. The aim of this paper is to present low-level implementation of Mamdani’s fuzzy inference system designed to work with massive GIS data sets, using the GRASS GIS raster data processing engine.     

Sliding mode neural network inference fuzzy logic control foractive suspension systems

In the automotive industry, suspension systems are designed to provide desirable vehicle ride and handling properties. This paper presents the development of a robust intelligent nonlinear controller for active suspension systems based on a comprehensive and realistic nonlinear model. The inherent complex nonlinear system model's structure, and the presence of parameter uncertainties, have increased the difficulties of applying conventional linear and nonlinear control techniques. Recently, the combination of sliding mode, fuzzy logic, and neural network methodologies has emerged as a promising technique for dealing with complex uncertain systems. In this paper, a sliding mode neural network inference fuzzy logic controller is designed for automotive suspension systems in order to enhance the ride and comfort. Extensive simulations are performed on a quarter-car model, and the results show that the proposed controller outperforms existing conventional controllers with regard to body acceleration, suspension deflection, and tire deflection     

Multicriterial classification of investment projects using fuzzy inference systems and multisets

The problem of decision taking in the task of investment project classification and selection in a multicriterial medium is considered. The project selection is performed according to a certain set of criteria. An approach to the classification of investment projects is proposed, which allows all expert opinions (including contradictory ones) to be taken into account in the classification of projects.     

Immediate water quality assessment in shrimp culture using fuzzy inference systems

The continuous monitoring of physical, chemical and biological parameters in shrimp culture is an important activity for detecting potential crisis that can be harmful for the organisms. Water quality can be assessed through toxicological tests evaluated directly from water quality parameters involved in the ecosystem; these tests provide an indicator about the water quality. The aim of this study is to develop a fuzzy inference system based on a reasoning process, which involves aquaculture criteria established by official organizations and researchers for assessing water quality by analyzing the main factors that affect a shrimp ecosystem. We propose to organize the water quality parameters in groups according to their importance; these groups are defined as daily, weekly and by request monitoring. Additionally, we introduce an analytic hierarchy process to define priorities for more critical water quality parameters and groups. The proposed system analyzes the most important parameters in shrimp culture, detects potential negative situations and provides a new water quality index (WQI), which describes the general status of the water quality as excellent, good, regular and poor. The Canadian water quality and other well-known hydrological indices are used to compare the water quality parameters of the shrimp water farm. Results show that WQI index has a better performance than other indices giving a more accurate assessment because the proposed fuzzy inference system integrates all environmental behaviors giving as result a complete score. This fuzzy inference system emerges as an appropriated tool for assessing site performance, providing assistance to improve production through contingency actions in polluted ponds.     

A GA-based method for constructing fuzzy systems directly from numerical data

A method based on the concepts of genetic algorithm (GA) and recursive least-squares method is proposed to construct a fuzzy system directly from some gathered input-output data of the discussed problem. The proposed method can find an appropriate fuzzy system with a low number of rules to approach an identified system under the condition that the constructed fuzzy system must satisfy a predetermined acceptable performance. In this method, each individual in the population is constructed to determine the number of fuzzy rules and the premise part of the fuzzy system, and the recursive least-squares method is used to determine the consequent part of the constructed fuzzy system described by this individual. Finally, three identification problems of nonlinear systems are utilized to illustrate the effectiveness of the proposed method.     

Adaptive-tree-structure-based fuzzy inference system

A new fuzzy inference system named adaptive-tree-structure-based fuzzy inference system (ATSFIS) is proposed, which is abbreviated as fuzzy tree (FT). The fuzzy partition of input data set and the membership function of every subset are obtained by means of the fuzzy binary tree structure based algorithm. Two structures of FT, FT-I, and FT-II, are presented. The characteristics of FT are: 1) The parameters of antecedent and consequent for a Takagi-Sugeno fuzzy model are learned simultaneously; and 2) The fuzzy partition of input data set is adaptive to the pattern of data distribution to optimize the number of the subsets automatically. The main advantage of FT is more suitable to solve the problems, for which the number of input dimension is large, since by using the fuzzy binary tree, every farther set will be partitioned into only two subsets no matter how large the input dimension is. Therefore, in some sense the "rule explosion" will be avoided possibly. In comparison with some existing fuzzy inference systems, it is shown that the FT is also of less computation and high accuracy. The advantages of FT are illustrated by simulation results.