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.     

面向后件集的模糊推理机制: 用于区间型type-2模糊逻辑系统

目前,大多数模糊推理都是利用t-范数和t-余范数或其改进形式对连接词进行建模,这些模型不能将模糊规则中前件集与后件集之间的相关性信息引入到模糊推理过程,这会丢失蕴含在规则中的一些信息甚至导致推理结果与实际经验严重不符.为解决此问题,本文首先引入模糊集合面向对象变换的概念,并将其推广,建立了合成type-2模糊集合模型.基于此模型,针对区间型type-2模糊逻辑系统,提出一种面向后件集的模糊推理机制,该机制能将前件集与后件集的相关性信息(包括清晰数和模糊数两种情形)引入到模糊推理过程.仿真结果表明,该方法能捕获到模糊规则中更多的不确定性信息,并为模糊逻辑系统的设计提供更大的自由度.     

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.     

Genetic tuning of fuzzy inference within fuzzy classifier systems

Abstract: In generating a suitable fuzzy classifier system, significant effort is often placed on the determination and the fine tuning of the fuzzy sets. However, in such systems little thought is given to the way in which membership functions are combined within the fuzzy rules. Often traditional fuzzy inference strategies are used which consequently provide no control over how strongly or weakly the inference is applied within these rules. Furthermore such strategies will allow no interaction between grades of membership. A number of theoretical fuzzy inference operators have been proposed for both regression and classification problems but they have not been investigated in the context of real-world applications. In this paper we propose a novel genetic algorithm framework for optimizing the strength of fuzzy inference operators concurrently with the tuning of membership functions for a given fuzzy classifier system. Each fuzzy system is generated using two well-established decision tree algorithms: C4.5 and CHAID. This will enable both classification and regression problems to be addressed within the framework. Each solution generated by the genetic algorithm will produce a set of fuzzy membership functions and also determine how strongly the inference will be applied within each fuzzy rule. We investigate several theoretical proven fuzzy inference techniques (T-norms) in the context of both classification and regression problems. The methodology proposed is applied to a number of real-world data sets in order to determine the effects of the simultaneous tuning of membership functions and inference parameters on the accuracy and robustness of fuzzy classifiers.     

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.     

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.     

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.     

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.     

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.     

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.     

Learning fuzzy inference systems using an adaptive membershipfunction scheme

An adaptive membership function scheme for general additive fuzzy systems is proposed in this paper. The proposed scheme can adapt a proper membership function for any nonlinear input-output mapping, based upon a minimum number of rules and an initial approximate membership function. This parameter adjustment procedure is performed by computing the error between the actual and the desired decision surface. Using the proposed adaptive scheme for fuzzy system, the number of rules can be minimized. Nonlinear function approximation and truck backer-upper control system are employed to demonstrate the viability of the proposed method.     

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     

直觉F推理与普通F推理的比较研究

直觉F推理克服了普通F推理在不确定性信息的描述、推理结果可信性等方面存在的局限性。在介绍普通F推理直觉化扩展的基础上,首先分析了两类推理算法的相互转化问题,指出普通F推理是直觉F推理的一种特例,当直觉指数为0时二者可相互转化。其次,比较了两类算法的还原性,分析表明Zadeh型、Mamdani型、Larsen型直觉F推理算法与其对应的普通F推理算法具有相同的还原性。最后,通过实例研究了直觉F推理算法在推理结果精度、可信性上的优势,从而较普通F推理更适用于智能控制与决策。     

Increasing fuzzy rules cooperation based on evolutionary adaptive inference systems

This article presents a study on the use of parametrized operators in the Inference System of linguistic fuzzy systems adapted by evolutionary algorithms, for achieving better cooperation among fuzzy rules. This approach produces a kind of rule cooperation by means of the inference system, increasing the accuracy of the fuzzy system without losing its interpretability. We study the different alternatives for introducing parameters in the Inference System and analyze their interpretation and how they affect the rest of the components of the fuzzy system. We take into account three applications in order to analyze their accuracy in practice. © 2007 Wiley Periodicals, Inc. Int J Int Syst 22: 1035–1064, 2007.     

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 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.     

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.