Piero P. Bonissone

Selecting uncertainty calculi and granularity: an experiment in trading-off precision and complexity

The management of uncertainty in expert systems has usually been left to ad hoc representations and rules of combinations lacking either a sound theory or clear semantics. The objective of this paper is to establish a theoretical basis for defining the syntax and semantics of a small subset of calculi of uncertainty operating on a given term set of linguistic statements of likelihood. Each calculus will be defined by specifying a negation, a conjunction and a disjunction operator. Families of Triangular norms and conorms will provide the most general representations of conjunction and disjunction operators. These families provide us with a formalism for defining an infinite number of different calculi of uncertainty. The term set will define the uncertainty granularity, i.e. the finest level of distinction among different quantifications of uncertainty. This granularity will limit the ability to differentiate between two similar operators. Therefore, only a small finite subset of the infinite number of calculi will produce notably different results. This result is illustrated by an experiment where nine different calculi of uncertainty are used with three term sets containing five, nine, and thirteen elements, respectively.

Soft computing: the convergence of emerging reasoning technologies

Abstract The term Soft Computing (SC) represents the combination of emerging problem-solving technologies such as Fuzzy Logic (FL), Probabilistic Reasoning (PR), Neural Networks (NNs), and Genetic Algorithms (GAs). Each of these technologies provide us with complementary reasoning and searching methods to solve complex, real-world problems. After a brief description of each of these technologies, we will analyze some of their most useful combinations, such as the use of FL to control GAs and NNs parameters; the application of GAs to evolve NNs (topologies or weights) or to tune FL controllers; and the implementation of FL controllers as NNs tuned by backpropagation-type algorithms.

A Linguistic Approach to Decisionmaking with Fuzzy Sets

A technique for making linguistic decsions is presented. Fuzzy sets are assued to be an appropriate way of dealng with uncertainty, and it b therefore cncluded that decisions taken on the basis of such infomation must themselves be fuzzy. It b inappriate then to present the decision in numencal form; a statement in natural angug is much better. For brevity only a single-stage multlabute decsion problem is considered. Solutions to such problems are shown using ideas in linguisc approximation and truth qualiction. An extensive example illuminates the basic ideas and techniques.

Handbook of Fuzzy Computation

Foreword by Lotfi Zadeh Preface INTRODUCTION Background. Why fuzzy logic? FUNDAMENTAL CONCEPTS OF FUZZY COMPUTATION Vagueness and uncertainty: Theories of vagueness. Theories of uncertainty. Fuzzy sets: concepts and characterizations: Introduction. Operations on fuzzy sets. Interpretations of fuzzy sets. Fuzzy relations. Characterization of fuzzy sets. Fuzzy measure and integral. Fuzzy mathematical objects. Extension principle. Fuzzy set calculus: Introduction. Membership function elicitation. Fuzzy relational calculus. Fuzzy arithmetic. Possibility theory. Fuzzy reasoning: Introduction. Fuzzy inference. Defuzzification. FUZZY MODELS Fuzzy models. Modeling and simulation: Granule-based models. Logical aspects of fuzzy models. Statistical models. Fuzzy Petri Net model. Model acquisition. Approximation aspects of fuzzy models. HYBRID APPROACHES Introduction: motivation for hybrid approaches. Neuro-fuzzy systems. Fuzzy-evolutionary systems. FUZZY COMPUTATION ENVIRONMENTS Software approaches: Programming languages. Knowledge-based systems. Database management, information retrieval, and decision support systems. Hardware approaches: Desirable features. Adapting existing hardware to fuzzy computation. Analog approaches. Digital approaches. Hybrid (digital-analog) approaches. APPLICATIONS OF FUZZY COMPUTATION Knowledge based systems: Knowledge representation. Inference methods. Control methods. Design methods. Control. Principles of fuzzy controllers. Fuzzy control approaches: General design schemes. Cell maps. Sliding mode control. Predictive control. Hierarchical control. Model-based control. Optimal fuzzy control. Machine learning: Introduction: learning fuzzy concepts. Supervised learning. Reinforcement learning. Data and information management: Fuzzy databases. Information retrieval. Case-based reasoning. Decision making and optimization: Decision-making models. Optimization. Pattern analysis. Computer vision. FUZZY COMPUTATION IN PRACTICE Aerospace: Proximity operations spacecraft controller: a case study in fuzzy logic control. Systems control: DC/DC converters fuzzy control. Fuzzy control in telecommunications. Fuzzy-neural traffic control and forecasting. Systems control. Backlash compensation using fuzzy logic. Neurofuzzy modeling for nonlinear system identification. Nuclear engineering: Application of fuzzy logic control system for nuclear reactor control. Manufacturing: Applications of fuzzy set methodologies in manufacturing. Compensation of friction in mechanical positioning systems. Diagnostics: Possibilistic handling of uncertainty in fault diagnosis. Robotics: Autonomous mobile robot control. Chemical engineering: Chemical engineering application. Water treatment: Water treatment application. Automotive: Improvement of the relationship between driver and vehicle using fuzzy logic. Traffic engineering: Traffic engineering application. Civil engineering: Civil engineering application. Engineering design: A fuzzy sets application to preliminary passenger vehicle structure design. Oil refining: Neuro-fuzzy hybrid control system in petroleum plant. Medicine: CADIAG2: hospital-based computer-assisted differential diagnosis in internal medicine. Neural networks for ECG diagnostic classification. Information science: Case-based reasoning. Information retrieval: a case study of the CASHE: PVS systems. Economics, finance and business. Decision support system for foreign exchange trade (FOREX). Operations research: Scheduling. Fuzzy sets in operation research: forecasting, a case study. Quality design using possibilistic regression and optimization. Inventory control. Time series prediction. FUZZY COMPUTATION RESEARCH Directions for future research. APPENDICES

Summarizing and propagating uncertain information with triangular norms

Abstract A wide variety of numerical or symbolic approaches to reasoning with uncertainty have been proposed in the artificial intelligence (AI) literature. This article postulates a list of desiderata that any such formalism should try to satisfy. The author then proposes a new approach to reasoning with uncertainty, which is organized in three layers: representation, inference, and control. In the representation layer the structure required to capture information used in the inference layer and meta-information used in the control layer are described. In this structure, numerical slots take values on linguistic term sets with fuzzy-valued semantics. These term sets capture the input granularity usually provided by users or experts. In the inference layer a large number of uncertainty calculi based on triangular norms (T-norms), intersection operators whose truth functionality entails low computational complexity, are described. It is shown that for a common negation operator, the selection of a T-norm uniquely and completely describes an uncertainty calculus. Previous experiments have determined the existence of a small number of equivalence classes among the uncertainty calculi (as a function of the input granularity). This property drastically reduces the number of different combining rules to be considered. In the control layer the policy selection for the different calculi used in the inference layer, based on their meanings, properties, and contextual information, is specified. Conflicts and ignorance measurements are also defined. The proposed formalism is compared against the requirements of the desiderata and contrasted with existing schemes for reasoning with uncertainty.

Evolutionary algorithms + domain knowledge = real-world evolutionary computation

We discuss implicit and explicit knowledge representation mechanisms for evolutionary algorithms (EAs). We also describe offline and online metaheuristics as examples of explicit methods to leverage this knowledge. We illustrate the benefits of this approach with four real-world applications. The first application is automated insurance underwriting-a discrete classification problem, which requires a careful tradeoff between the percentage of insurance applications handled by the classifier and its classification accuracy. The second application is flexible design and manufacturing-a combinatorial assignment problem, where we optimize design and manufacturing assignments with respect to time and cost of design and manufacturing for a given product. Both problems use metaheuristics as a way to encode domain knowledge. In the first application, the EA is used at the metalevel, while in the second application, the EA is the object-level problem solver. In both cases, the EAs use a single-valued fitness function that represents the required tradeoffs. The third application is a lamp spectrum optimization that is formulated as a multiobjective optimization problem. Using domain customized mutation operators, we obtain a well-sampled Pareto front showing all the nondominated solutions. The fourth application describes a scheduling problem for the maintenance tasks of a constellation of 25 low earth orbit satellites. The domain knowledge in this application is embedded in the design of a structured chromosome, a collection of time-value transformations to reflect static constraints, and a time-dependent penalty function to prevent schedule collisions.

Industrial applications of fuzzy logic at General Electric

Fuzzy logic control (FLC) technology has drastically reduced the development time and deployment cost for the synthesis of nonlinear controllers for dynamic systems. As a result we have experienced an increased number of FLC applications. We illustrate some of our efforts in FLC technology transfer, covering projects in turboshaft aircraft engine control, steam turbine startup, steam turbine cycling optimization, resonant converter power supply control, and data-induced modeling of the nonlinear relationship between process variables in a rolling mill stand. We compare these applications in a cost/complexity framework, and examine the driving factors that led to the use of FLCs in each application. We emphasize the role of fuzzy logic in developing supervisory controllers and in maintaining explicit tradeoff criteria used to manage multiple control strategies. Finally, we describe some of our FLC technology research efforts in automatic rule base tuning and generation, leading to a suite of programs for reinforcement learning, supervised learning, genetic algorithms, steepest descent algorithms, and rule clustering. >

Hybrid soft computing systems: industrial and commercial applications

Soft computing (SC) is an association of computing methodologies that includes as its principal members fuzzy logic, neurocomputing, evolutionary computing and probabilistic computing. We present a collection of methods and tools that can be used to perform diagnostics, estimation, and control. These tools are a great match for real-world applications that are characterized by imprecise, uncertain data and incomplete domain knowledge. We outline the advantages of applying SC techniques and in particular the synergy derived from the use of hybrid SC systems. We illustrate some combinations of hybrid SC systems, such as fuzzy logic controllers (FLCs) tuned by neural networks (NNs) and evolutionary computing (EC), NNs tuned by EC or FLCs, and EC controlled by FLCs. We discuss three successful real-world examples of SC applications to industrial equipment diagnostics, freight train control, and residential property valuation.

Genetic algorithms for automated tuning of fuzzy controllers: a transportation application

We describe the design and tuning of a controller for enforcing compliance with a prescribed velocity profile for a rail-based transportation system. This requires following a trajectory, rather than fixed set-points (as in automobiles). We synthesize a fuzzy controller for tracking the velocity profile, while providing a smooth ride and staying within the prescribed speed limits. We use a genetic algorithm to tune the fuzzy controllers performance by adjusting its parameters (the scaling factors and the membership functions) in a sequential order of significance. We show that this approach results in a controller that is superior to the manually designed one, and with only modest computational effort. This makes it possible to customize automated tuning to a variety of different configurations of the route, the terrain, the power configuration, and the cargo.

On heuristics as a fundamental constituent of soft computing

Although as such one dates back the idea of setting the area of soft computing to 1990, it was in 1994 that L.A. Zadeh established his worldwide accepted definition of soft computing. As it is well known since the seminal definition of a fuzzy set, different equivalent definitions of the concept have been proposed, analyzed and used. But, in spite of the former main constituents could be currently others and hence they should be revised, and the same cannot be said of soft computing. From this point of view, in order to narrow this gap, in this paper the role played until now by these main soft computing ingredients is analyzed, and then an original proposal of the new constituents, mainly focused on the introduction of the broader topic of metaheuristics instead of evolutionary algorithms, is justified, presented and described.