Inference Operations Research Articles

Adaptive Dynamic RBF Fuzzy Neural Controller Design with a Constructive Learning

Radial basis function (RBF) network can be viewed as a fuzzy rule base with specified membership functions and fuzzy inference operations. However, there is a trade-off between the approximation performance of RBF network and the number of hidden neurons. To tackle this problem, this paper proposes a dynamic RBF (DRBF) network with a constructive learning. This DRBF network not only can create the new hidden neurons, but also can prune the insignificant hidden neurons. Then, an adaptive dynamic RBF fuzzy neural control (ADRFNC) system, including a neural controller and a saturation compensator, is developed. The neural controller uses a DRBF network to on-line mimic an ideal controller and the saturation compensator is designed to dispel the approximation error introduced by the neural controller. Finally, the proposed ADRFNC system is applied to a chaotic circuit and a DC motor control system. Simulation and experimental results show the proposed ADRFNC system can achieve a favorable tracking performance when the controller’s parameters have been learned and the network structure has been constructed by the proposed learning algorithm.

CHOQUET INTEGRAL–OWA BASED ADAPTIVE NEURAL FUZZY INFERENCE SYSTEM WITH APPLICATION

In order to solve the defects of consequent part expression in ANFIS model and several shortcomings in FIS, this paper presents a Choquet Integral–OWA based Fuzzy Inference System, known as AggFIS. This model has advantages in consequent part of fuzzy rule, universal expression of fuzzy inference operator and importance factor of each criteria and each rule, which is trying to establish fuzzy inference system that can fully reflect the essence of fuzzy logic and human thinking pattern. If we combine AggFIS with a feed forward-type neural network according to the basic principles of fuzzy neural network, we can obtain Choquet Integral–OWA based Adaptive Neural Fuzzy Inference System, which is named Agg-ANFIS. We apply this Agg-ANFIS model into the evaluation of traffic level of service. The experimental results show that Choquet Integral–OWA based Adaptive Neural Fuzzy Inference System (Agg-ANFIS) is a universal approximator because of its infinite approximating capability by training and can be used in complex systems modeling, analysis and prediction.

A fuzzy-logic-based model to predict biogas and methane production rates in a pilot-scale mesophilic UASB reactor treating molasses wastewater

A MIMO (multiple inputs and multiple outputs) fuzzy-logic-based model was developed to predict biogas and methane production rates in a pilot-scale 90-L mesophilic up-flow anaerobic sludge blanket (UASB) reactor treating molasses wastewater. Five input variables such as volumetric organic loading rate (OLR), volumetric total chemical oxygen demand (TCOD) removal rate ( R V), influent alkalinity, influent pH and effluent pH were fuzzified by the use of an artificial intelligence-based approach. Trapezoidal membership functions with eight levels were conducted for the fuzzy subsets, and a Mamdani-type fuzzy inference system was used to implement a total of 134 rules in the IF-THEN format. The product (prod) and the centre of gravity (COG, centroid) methods were employed as the inference operator and defuzzification methods, respectively. Fuzzy-logic predicted results were compared with the outputs of two exponential non-linear regression models derived in this study. The UASB reactor showed a remarkable performance on the treatment of molasses wastewater, with an average TCOD removal efficiency of 93 (±3)% and an average volumetric TCOD removal rate of 6.87 (±3.93) kg TCOD removed/m 3-day, respectively. Findings of this study clearly indicated that, compared to non-linear regression models, the proposed MIMO fuzzy-logic-based model produced smaller deviations and exhibited a superior predictive performance on forecasting of both biogas and methane production rates with satisfactory determination coefficients over 0.98.

A decision-theoretic saliency, its biological plausibility and implications for pre-attentive vision

A decision-theoretic formulation of visual saliency, first proposed for top-down processing (object recognition) in (Gao & Vasconcelos, 2005) is extended to the problem of bottom-up saliency. Under this formulation, optimality is defined in the minimum probability of error sense, under a constraint of computational parsimony. The saliency of the visual features at a given location of the visual field is defined as the power of those features to discriminate between the stimulus at the location and a null hypotheses. For bottom-up saliency, this is the set of visual features that surround the location under consideration. Discrimination is defined in an information-theoretic sense and the optimal saliency detector derived for a class of stimuli that complies with known statistical properties of natural images. It is shown that the optimal detector consists of what is usually referred to as the standard architecture of V1 (Carandini, Demb, Mante, Tolhurst, Dan, Olshausen, et al., 2005): a cascade of linear filtering, divisive normalization, rectification and spatial pooling. The optimal detector is also shown to replicate the fundamental properties of the psychophysics of saliency (Treisman & Gelade, 1980): stimulus pop-out, saliency asymmetries for stimulus presence vs. absence, disregard of feature conjunctions, and Weber’s law. Finally, it is shown that the optimal saliency architecture can be applied to the solution of generic inference problems. In particular, for the class stimuli studied, it performs the three fundamental operations of statistical inference: assessment of probabilities, implementation of Bayes decision rule, and feature selection.

Sampling based inference with linear probabilistic population codes

Event Abstract Back to Event Sampling based inference with linear probabilistic population codes Jeff Beck1*, Alexandre Pouget2 and Peter Latham1 1 University College London, United Kingdom 2 University of Rochester , United States An ever increasing corpus of behavioural data from animals as simple as insects and those as complex as humans indicates that probabilistic reasoning is the rule when it comes to tasks that range from low level sensory-motor transformation to high level cognition and decision making. This remarkable set of behaviours require a neural code which (1) represents probability distributions over task relevant latent variables (stimuli), (2) is consistent with observed neural statistics, and (3) can be used to implement the operations of probabilistic inference using biologically plausible neural operations. Over the past few years we have worked to develop such a probabilistic population code or PPC and have utilized such a code to model tasks which involve probabilistic operations such as cue combination, evidence accumulation, prior implementation, and maximum a posteriori estimation. However, to some extent, these are the easy problems probabilistic inference, or at least, these are the problems of probabilistic inference for which the specific type of PPC which we have proposed, the linear PPC, is ideally suited. Unfortunately, as is often the case, a representation which makes a particular problem easy can make another problem difficult. In this case, the probabilistic operation made difficult by this choice of code is the marginalization operation. Here, marginalization involves taking a complex generative model for neural activity, r, which is conditioned upon many latent variables (i.e. some p(r|s1,s2,...,sn)) and then inverting that model to obtain a posterior distribution over only a few task relevant latent variables. This involves a potentially high dimensional integral over say s2..sn to obtain a marginal posterior distribution p(s1|r). Previously, we had some success in generating biologically plausible networks which perform the relatively low dimensional marginalization operations needed to implement computations such as non-linear coordinate transforms for sensory-motor information integration, Kalman filters for motor control and object tracking, explaining away in infants (a.k.a backward masking), and auditory localization. This was accomplished using networks which implement a quadratic non-linearity and divisive normalization, operations which are observed throughout cortex. This was intriguing as, previously, divisive normalization had been implicated in gain control, attention and redundancy reduction, and these results suggest a more generic and possibly unifying computational role. Unfortunately, it was not clear from this previous work that these results would generalize to higher dimensional marginalization operations which can only be made tractable by utilizing sampling methods. Indeed, it was not initially clear that sampling methods were compatible with the probabilistic population coding approach at all. In this work, we address this issue by first demonstrating that samples can be generated naturally within the PPC framework in a variety of ways, some of which require nothing more than stochastic synapses and dynamic attractor networks comparable to those used to generate maximum a posteriori estimates. Moreover, we show that the samples generated in this way can be easily adapted to the purpose of implementing the marginalization operation in a way that, once again, indicates that divisive normalization performs a critical computation role. Conference: Computational and Systems Neuroscience 2010, Salt Lake City, UT, United States, 25 Feb - 2 Mar, 2010. Presentation Type: Poster Presentation Topic: Poster session III Citation: Beck J, Pouget A and Latham P (2010). Sampling based inference with linear probabilistic population codes. Front. Neurosci. Conference Abstract: Computational and Systems Neuroscience 2010. doi: 10.3389/conf.fnins.2010.03.00258 Copyright: The abstracts in this collection have not been subject to any Frontiers peer review or checks, and are not endorsed by Frontiers. They are made available through the Frontiers publishing platform as a service to conference organizers and presenters. The copyright in the individual abstracts is owned by the author of each abstract or his/her employer unless otherwise stated. Each abstract, as well as the collection of abstracts, are published under a Creative Commons CC-BY 4.0 (attribution) licence (https://creativecommons.org/licenses/by/4.0/) and may thus be reproduced, translated, adapted and be the subject of derivative works provided the authors and Frontiers are attributed. For Frontiers’ terms and conditions please see https://www.frontiersin.org/legal/terms-and-conditions. Received: 05 Mar 2010; Published Online: 05 Mar 2010. * Correspondence: Jeff Beck, University College London, London, United Kingdom, bayesian.empirimancer@googlemail.com Login Required This action requires you to be registered with Frontiers and logged in. To register or login click here. Abstract Info Abstract The Authors in Frontiers Jeff Beck Alexandre Pouget Peter Latham Google Jeff Beck Alexandre Pouget Peter Latham Google Scholar Jeff Beck Alexandre Pouget Peter Latham PubMed Jeff Beck Alexandre Pouget Peter Latham Related Article in Frontiers Google Scholar PubMed Abstract Close Back to top Javascript is disabled. Please enable Javascript in your browser settings in order to see all the content on this page.

Geometry Tutoring Supported by an Intelligent Drawing Interface and Automatic Problem Solving

In a scientific domain, learning comprises studying a finite set of principles of the domain and applying them to solve a wide variety of problems. Therefore an intelligent tutoring system in a scientific domain is required to possess an adequate methodology to deal with this principle. We suggest a tutoring architecture for geometry where the domain principles are automatically converted to inference operators for use by the domain-independent, inferential portion of the tutoring system. An important part of this architecture is an intelligent drawing interface that facilitates automatic conversion of the figures in geometry into an internal form that is suitable for problemsolving tutoring. During student problem solving, the system monitors the student’s steps, tracks a step that has multiple inferences, and gives hints and explanations. We discuss the advantages of our approach in enhancing the performance and interactivity of the tutoring system.

Decision-Theoretic Saliency: Computational Principles, Biological Plausibility, and Implications for Neurophysiology and Psychophysics

A decision-theoretic formulation of visual saliency, first proposed for top-down processing (object recognition) (Gao & Vasconcelos, 2005a), is extended to the problem of bottom-up saliency. Under this formulation, optimality is defined in the minimum probability of error sense, under a constraint of computational parsimony. The saliency of the visual features at a given location of the visual field is defined as the power of those features to discriminate between the stimulus at the location and a null hypothesis. For bottom-up saliency, this is the set of visual features that surround the location under consideration. Discrimination is defined in an information-theoretic sense and the optimal saliency detector derived for a class of stimuli that complies with known statistical properties of natural images. It is shown that under the assumption that saliency is driven by linear filtering, the optimal detector consists of what is usually referred to as the standard architecture of V1: a cascade of linear filtering, divisive normalization, rectification, and spatial pooling. The optimal detector is also shown to replicate the fundamental properties of the psychophysics of saliency: stimulus pop-out, saliency asymmetries for stimulus presence versus absence, disregard of feature conjunctions, and Weber's law. Finally, it is shown that the optimal saliency architecture can be applied to the solution of generic inference problems. In particular, for the class of stimuli studied, it performs the three fundamental operations of statistical inference: assessment of probabilities, implementation of Bayes decision rule, and feature selection.

New geometric inference techniques for type-2 fuzzy sets

This paper presents new techniques for performing logical operations on type-2 fuzzy sets. These techniques make significant use of geometric methods to give, for the first time, logic operators that can be implemented over continuous domains, thereby eliminating the need for discretisation. We give a full exposition of the geometric inference operations and consider computational speed and accuracy. We show this novel approach to be more accurate, although slightly slower than existing techniques.

Adaptive fuzzy logic controller for DC–DC converters

This paper introduces a complete design method to construct an adaptive fuzzy logic controller (AFLC) for DC–DC converter. In a conventional fuzzy logic controller (FLC), knowledge on the system supplied by an expert is required for developing membership functions (parameters) and control rules. The proposed AFLC, on the other hand, do not required expert for making parameters and control rules. Instead, parameters and rules are generated using a model data file, which contains summary of input–output pairs. The FLC use Mamdani type fuzzy logic controllers for the defuzzification strategy and inference operators. The proposed controller is designed and verified by digital computer simulation and then implemented for buck, boost and buck–boost converters by using an 8-bit microcontroller.

The Impact of Transitive Inference Operations on Mathematics Problem Solving Abilities of Pre-Primary School Children

This study examined the extent to which operations of transitive inference tasks have affected the mathematics problem solving abilities of pre-primary school children. Four research hypotheses were tested at 0.05 level of significance using 400 nursery school children whose ages ranged between 4.5 and 5.5 years respectively. Two instruments namely; Generalized tasks on Transitivity and Mathematics test were validated and used to collect data. Significant relationship was found between transitive inference operations and mathematics problem solving abilities of pre- school children. Also, there was a significant difference between the mathematics problem solving abilities of children who could perform transitive inference tasks and those who could not. No significant gender difference was however observed in mathematics problem solving abilities of children who could perform transitive inference. Thus, transitive inference acquisition has opened up educational possibilities for preschoolers to solve problems in mathematics. Therefore, children need a lot of practice on the logical concept to improve their reasoning skills in mathematics. The Nigerian Journal of Guidance Counselling Vol. 10 (1) 2005: pp. 85-94

Recording and Minimizing Nogoods from Restarts

In this paper, nogood recording is investigated for CSP within the randomization and restart framework. Our goal is to avoid the same situations to occur from one run to the next ones. More precisely, nogoods are recorded when the current cutoff value is reached, i.e. before restarting the search algorithm. Such a set of nogoods is extracted from the last branch of the current search tree and exploited using the structure of watched literals originally proposed for SAT. We prove that the worst-case time complexity of extracting such nogoods at the end of each run is only O(n^2 d) where n is the number of variables of the constraint network and d the size of the greatest domain, whereas for any node of the search tree, the worst-case time complexity of exploiting these nogoods to enforce Generalized Arc Consistency (GAC) is O(n|B|) where |B| denotes the number of recorded nogoods. As the number of nogoods recorded before each new run is bounded by the length of the last branch, the total number of recorded nogoods is polynomial in the number of restarts. Interestingly, we show that when the minimization of the nogoods is envisioned with respect to an inference operator φ, it is possible to directly identify some nogoods that cannot be minimized. For φ = AC (i.e. for MAC), the worst-case time complexity of extracting minimal nogoods is slightly increased to O(en2 d3 ) where e is the number of constraints of the network. Experimentation over a wide range of CSP instances using a generic state-of-the-art CSP solver demonstrates the effectiveness of this approach. Recording nogoods (and in particular, minimal nogoods) from restarts significantly improves the robustness of the solver.

Modelling Inference in Argumentation through Labelled Deduction: Formalization and Logical Properties

Artificial Intelligence (AI) has long dealt with the issue of finding a suitable formalization for commonsense reasoning. Defeasible argumentation has proven to be a successful approach in many respects, proving to be a con- fluence point for many alternative logical frameworks. Dierent formalisms have been developed, most of them sharing the common notions of argument and warrant. In defeasible argumentation, an argument is a tentative (de- feasible) proof for reaching a conclusion. An argument is warranted when it ultimately prevails over other conflicting arguments. In this context, defeasi- ble consequence relationships for modelling argument and warrant as well as their logical properties have gained particular attention. This article analyzes two non-monotonic inference operators Carg and Cwar intended for modelling argument construction and dialectical analysis (warrant), respectively. As a basis for such analysis we will use the LDSar framework, a unifying approach to computational models of argument using Labelled Deductive Systems (LDS). In the context of this logical framework, we show how labels can be used to represent arguments as well as argument trees, facilitating the definition and study of non-monotonic inference op- erators, whose associated logical properties are studied and contrasted. We contend that this analysis provides useful comparison criteria that can be extended and applied to other argumentation frameworks. Mathematics Subject Classification (2000). Primary 03B22; Secondary 03B42.

Inferential language models for information retrieval

Language modeling (LM) has been widely used in IR in recent years. An important operation in LM is smoothing of the document language model. However, the current smoothing techniques merely redistribute a portion of term probability according to their frequency of occurrences only in the whole document collection. No relationships between terms are considered and no inference is involved. In this article, we propose several inferential language models capable of inference using term relationships. The inference operation is carried out through a semantic smoothing either on the document model or query model, resulting in document or query expansion. The proposed models implement some of the logical inference capabilities proposed in the previous studies on logical models, but with necessary simplifications in order to make them tractable. They are a good compromise between inference power and efficiency. The models have been tested on several TREC collections, both in English and Chinese. It is shown that the integration of term relationships into the language modeling framework can consistently improve the retrieval effectiveness compared with the traditional language models. This study shows that language modeling is a suitable framework to implement basic inference operations in IR effectively.

Genetic tuning of fuzzy inference within fuzzy classifier systems

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.

Operations for inference in continuous Bayesian networks with linear deterministic variables

An important class of continuous Bayesian networks are those that have linear conditionally deterministic variables (a variable that is a linear deterministic function of its parents). In this case, the joint density function for the variables in the network does not exist. Conditional linear Gaussian (CLG) distributions can handle such cases when all variables are normally distributed. In this paper, we develop operations required for performing inference with linear conditionally deterministic variables in continuous Bayesian networks using relationships derived from joint cumulative distribution functions. These methods allow inference in networks with linear deterministic variables and non-Gaussian distributions.

Fuzzy logic model for the prediction of cement compressive strength

A fuzzy logic prediction model for the 28-day compressive strength of cement mortar under standard curing conditions was created. Data collected from a cement plant were used in the model construction and testing. The input variables of alkali, Blaine, SO 3, and C 3S and the output variable of 28-day cement strength were fuzzified by the use of artificial neural networks (ANNs), and triangular membership functions were employed for the fuzzy subsets. The Mamdani fuzzy rules relating the input variables to the output variable were created by the ANN model and were laid out in the If–Then format. Product (prod) inference operator and the centre of gravity (COG; centroid) defuzzification methods were employed. The prediction of 50 sets of the 28-day cement strength data by the developed fuzzy model was quite satisfactory. The average percentage error levels in the fuzzy model were successfully low (2.69%). The model was compared with the ANN model for its error levels and ease of application. The results indicated that through the application of fuzzy logic algorithm, a more user friendly and more explicit model than the ANNs could be produced within successfully low error margins.

Some Preliminary Results on the Stableness of Extended F-rule Systems

In this paper we shall investigate an extended version of F-rule systems, in which each F-rule can include an arbitrary combination of disjunctions and conjunctions of atoms in the premise. The first main result here is a way to determine values assigned to these extended facts, based on two basic operators ⊕ and x;, which are shown to be equivalent to external probabilistic reasoning by resolving linear programming problem. Based on this, a definition on mixed inference operator for extended F-rule systems is discussed. We have shown that an extended F-rule system with the defined reasoning operator is stable iff its corresponding F-rule system is stable. This proposition allows us to apply all our available research results on F-rule systems to extended F-rule systems.

Circuit implementation of linguistic-hedge fuzzy logic controller in current-mode approach

In this paper, a novel fuzzy logic controller called linguistic-hedge fuzzy logic controller in a mixed-signal circuit design is discussed. The linguistic-hedge fuzzy logic controller has the following advantages: 1) it needs only three simple-shape membership functions for characterizing each variable prior to the linguistic-hedge modifications; 2) it is sufficient to adopt nine rules for inference; 3) the rules are developed intuitively without heavy dependence on the endeavors of experts; 4) it performs better than conventional fuzzy logic controllers; and 5) it can be realized with a lower design complexity and a smaller hardware overhead as compared with the controllers that required more than nine rules. In this implementation, a current-mode approach is adopted in designing the signal processing portions to simplify the circuit complexity; digital circuits are adopted to implement the programmable units. This design was fabricated with a TSMC 0.35 /spl mu/m single-polysilicon-quadruple-metal CMOS process. In this chip, the LHFLC processes two input variables and one output variable. Each variable is specified using three membership functions. Nine inference rules, scheduled in a rule table with a dimension of 3 /spl times/ 3, define the relationship implications between these three variables. Under a supply voltage of 3.3 V, the measurement results show that the measured control surface and the control goal are consistent. The speed of inference operation goes up to 0.5M FLIPS that is fast enough for the control application of the cart-pole balance system. The cart-pole balance system experimental results show that this chip works with nine inference rules. Furthermore, by performing some off-chip modifications, such as shifting and scaling on the input signals and output signal of this design, according to the specifications defined by the controlled plants, this design is suitable for many control applications.

Fuzzy control of dc–dc converters based on user friendly design

The aim of this paper is to show how to build a fuzzy controller and its membership functions automatically. In a fuzzy logic controller (FLC), the proposed method allows one easily to construct a set of membership functions, called shrinking-span membership functions (SSMFs). The FLC uses Mamdani-type fuzzy controllers for the defuzzification strategy and inference operators. The FLC hardware implementation is performed on an 8-bit microcontroller. Simulation results and experimental results demonstrate that the converter can be regulated with good performance even when subjected to input disturbance and load variation. The presented approach is generally valid for the design of an FLC, and can be applied to any dc–dc converter topologies.

On implicative closure operators in approximate reasoning

This paper introduces a new class of fuzzy closure operators called implicative closure operators, which generalize some notions of fuzzy closure operators already introduced by different authors. We show that implicative closure operators capture some usual consequence relations used in Approximate Reasoning, like Chakraborty’s graded consequence relation, Castro et al.’s fuzzy consequence relation, similarity-based consequence operators introduced by Dubois et al. and Gerla’s canonical extension of classical closure operators. We also study the relation of the implicative closure operators to other existing fuzzy inference operators as the Natural Inference Operators defined by Boixader and Jacas and the fuzzy operators defined by Biacino, Gerla and Ying.