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Introduction to Fuzzy Set Theory

An introduction to fuzzy set theory is described. Topics covered include: neural networks and fuzzy systems; the dynamical systems approach to machine intelligence; intelligent behavior as adaptive model-free estimation; fuzziness versus probability; fuzzy sets; the entropy-subsethood theorem; adaptive fuzzy systems for backing up a truck-and-trailer; product-space clustering with differential competitive learning; and adaptive fuzzy system for target tracking.

Kosko, Bart↗

Automated cloud classification with a fuzzy logic expert system

An unresolved problem in current cloud retrieval algorithms concerns the analysis of scenes containing overlapping cloud layers. Cloud parameterizations are very important both in global climate models and in studies of the Earth's radiation budget. Most cloud retrieval schemes, such as the bispectral method used by the International Satellite Cloud Climatology Project (ISCCP), have no way of determining whether overlapping cloud layers exist in any group of satellite pixels. One promising method uses fuzzy logic to determine whether mixed cloud and/or surface types exist within a group of pixels, such as cirrus, land, and water, or cirrus and stratus. When two or more class types are present, fuzzy logic uses membership values to assign the group of pixels partially to the different class types. The strength of fuzzy logic lies in its ability to work with patterns that may include more than one class, facilitating greater information extraction from satellite radiometric data. The development of the fuzzy logic rule-based expert system involves training the fuzzy classifier with spectral and textural features calculated from accurately labeled 32x32 regions of Advanced Very High Resolution Radiometer (AVHRR) 1.1-km data. The spectral data consists of AVHRR channels 1 (0.55-0.68 mu m), 2 (0.725-1.1 mu m), 3 (3.55-3.93 mu m), 4 (10.5-11.5 mu m), and 5 (11.5-12.5 mu m), which include visible, near-infrared, and infrared window regions. The textural features are based on the gray level difference vector (GLDV) method. A sophisticated new interactive visual image Classification System (IVICS) is used to label samples chosen from scenes collected during the FIRE IFO II. The training samples are chosen from predefined classes, chosen to be ocean, land, unbroken stratiform, broken stratiform, and cirrus. The November 28, 1991 NOAA overpasses contain complex multilevel cloud situations ideal for training and validating the fuzzy logic expert system.

Tovinkere, Vasanth↗

Fuzzy-neural control of an aircraft tracking camera platform

A fuzzy-neural control system simulation was developed for the control of a camera platform used to observe aircraft on final approach to an aircraft carrier. The fuzzy-neural approach to control combines the structure of a fuzzy knowledge base with a supervised neural network's ability to adapt and improve. The performance characteristics of this hybrid system were compared to those of a fuzzy system and a neural network system developed independently to determine if the fusion of these two technologies offers any advantage over the use of one or the other. The results of this study indicate that the fuzzy-neural approach to control offers some advantages over either fuzzy or neural control alone.

Mcgrath, Dennis↗

Fuzzy Logic Approaches to Multi-Objective Decision-Making in Aerospace Applications

Fuzzy logic allows for the quantitative representation of multi-objective decision-making problems which have vague or fuzzy objectives and parameters. As such, fuzzy logic approaches are well-suited to situations where alternatives must be assessed by using criteria that are subjective and of unequal importance. This paper presents an overview of fuzzy logic and provides sample applications from the aerospace industry. Applications include an evaluation of vendor proposals, an analysis of future space vehicle options, and the selection of a future space propulsion system. On the basis of the results provided in this study, fuzzy logic provides a unique perspective on the decision-making process, allowing the evaluator to assess the degree to which each option meets the evaluation criteria. Future decision-making should take full advantage of fuzzy logic methods to complement existing approaches in the selection of alternatives.

Hardy, Terry L.↗

Fuzzy logic techniques for rendezvous and docking of two geostationary satellites

Large assemblings in space require the ability to manage rendezvous and docking operations. In future these techniques will be required for the gradual build up of big telecommunication platforms in the geostationary orbit. The paper discusses the use of fuzzy logic to model and implement a control system for the docking/berthing of two satellites in geostationary orbit. The system mounted in a chaser vehicle determines the actual state of both satellites and generates torques to execute maneuvers to establish the structural latching. The paper describes the proximity operations to collocate the two satellites in the same orbital window, the fuzzy guidance and navigation of the chaser approaching the target and the final Fuzzy berthing. The fuzzy logic system represents a knowledge based controller that realizes the close loop operations autonomously replacing the conventional control algorithms. The goal is to produce smooth control actions in the proximity of the target and during the docking to avoid disturbance torques in the final assembly orbit. The knowledge of the fuzzy controller consists of a data base of rules and the definitions of the fuzzy sets. The knowledge of an experienced spacecraft controller is captured into a set of rules forming the Rules Data Base.

Ortega, Guillermo↗

Robust Fault Detection Using Robust Z1 Estimation and Fuzzy Logic

This research considers the application of robust Z(sub 1), estimation in conjunction with fuzzy logic to robust fault detection for an aircraft fight control system. It begins with the development of robust Z(sub 1) estimators based on multiplier theory and then develops a fixed threshold approach to fault detection (FD). It then considers the use of fuzzy logic for robust residual evaluation and FD. Due to modeling errors and unmeasurable disturbances, it is difficult to distinguish between the effects of an actual fault and those caused by uncertainty and disturbance. Hence, it is the aim of a robust FD system to be sensitive to faults while remaining insensitive to uncertainty and disturbances. While fixed thresholds only allow a decision on whether a fault has or has not occurred, it is more valuable to have the residual evaluation lead to a conclusion related to the degree of, or probability of, a fault. Fuzzy logic is a viable means of determining the degree of a fault and allows the introduction of human observations that may not be incorporated in the rigorous threshold theory. Hence, fuzzy logic can provide a more reliable and informative fault detection process. Using an aircraft flight control system, the results of FD using robust Z(sub 1) estimation with a fixed threshold are demonstrated. FD that combines robust Z(sub 1) estimation and fuzzy logic is also demonstrated. It is seen that combining the robust estimator with fuzzy logic proves to be advantageous in increasing the sensitivity to smaller faults while remaining insensitive to uncertainty and disturbances.

Curry, Tramone↗

Fuzzy Q-Learning for Generalization of Reinforcement Learning

Fuzzy Q-Learning, introduced earlier by the author, is an extension of Q-Learning into fuzzy environments. GARIC is a methodology for fuzzy reinforcement learning. In this paper, we introduce GARIC-Q, a new method for doing incremental Dynamic Programming using a society of intelligent agents which are controlled at the top level by Fuzzy Q-Learning and at the local level, each agent learns and operates based on GARIC. GARIC-Q improves the speed and applicability of Fuzzy Q-Learning through generalization of input space by using fuzzy rules and bridges the gap between Q-Learning and rule based intelligent systems.

Berenji, Hamid R.↗

Navigating a Mobile Robot Across Terrain Using Fuzzy Logic

A strategy for autonomous navigation of a robotic vehicle across hazardous terrain involves the use of a measure of traversability of terrain within a fuzzy-logic conceptual framework. This navigation strategy requires no a priori information about the environment. Fuzzy logic was selected as a basic element of this strategy because it provides a formal methodology for representing and implementing a human driver s heuristic knowledge and operational experience. Within a fuzzy-logic framework, the attributes of human reasoning and decision- making can be formulated by simple IF (antecedent), THEN (consequent) rules coupled with easily understandable and natural linguistic representations. The linguistic values in the rule antecedents convey the imprecision associated with measurements taken by sensors onboard a mobile robot, while the linguistic values in the rule consequents represent the vagueness inherent in the reasoning processes to generate the control actions. The operational strategies of the human expert driver can be transferred, via fuzzy logic, to a robot-navigation strategy in the form of a set of simple conditional statements composed of linguistic variables. These linguistic variables are defined by fuzzy sets in accordance with user-defined membership functions. The main advantages of a fuzzy navigation strategy lie in the ability to extract heuristic rules from human experience and to obviate the need for an analytical model of the robot navigation process.

Seraji, Homayoun↗

Distance measures for higher order dual hesitant fuzzy sets

In this study, we propose new distance measures for dual hesitant fuzzy sets (DHFSs) in terms of the mean, standard deviation of dual hesitant fuzzy elements (DHFEs), respectively, which overcome some drawbacks of the existing distance measures. Meanwhile, we extend DHFS to its higher order type and refer to it as the higher order dual hesitant fuzzy set (HODHFS). HODHFS is the actual extension of DHFS that enables us to define the membership and non-membership of a given element in terms of several possible generalized type of fuzzy sets (G-Type FSs). The rationale behind HODHFS can be seen in the case that the decision makers are not satisfied by providing exact values for the membership degrees and the non-membership degrees. To indicate HODHFSs have a good performance in decision making, we introduce several distance measures for HODHFSs based on our proposed new distance for dual hesitant fuzzy sets. Finally, we practice our proposed measures for HODHFSs in multi-attribute decision making illustrating their applicability and availability.

97 MATHEMATICS AND COMPUTING↗

Applications of Fuzzy Set Theory to Satellite Soundings

The introduction of an appropriate fuzzy setting for satellite soundings and its application to clustering methods via unimodal fuzzy sets in the future is proposed. Methods of hard clustering analysis and fuzzy partitioned clustering were applied on simulated data with very encouraging results. The proposed clustering technique is discussed. The notion of a unimodal fuzzy set was chosen to represent the partition of a data set for two reasons: (1) it detects all the locations in the vector space where highly concentrated clusters of points exist; and (2) the notion is general enough to represent clusters that exhibit quite general distributions of points. The technique detects all of the existing unimodal fuzzy sets and realizes the maximum separation among them. It is economical in memory space and computational time requirements and also detects groups that are fairly generally distributed in the feature space.

Munteanu, M. J.↗

A formalization of commonsense reasoning based on fuzzy logic

The basic idea underlying the approach outlined in this paper is that commonsense knowledge may be regarded as a collection of dispositions, that is, propositions which are preponderantly, but not necessarily always, true. Technically, a disposition may be interpreted as a proposition with implicit fuzzy quantifiers, e.g., most, almost all, usually, often, etc. For example, a disposition such as Swedes are blond may be interpreted as most Swedes are blond. For purposes of inference from commonsense knowledge, the conversion of a disposition into a proposition with explicit fuzzy quantifiers sets the stage for an application of syllogistic reasoning in which the premises are allowed to be of the form Q A's are B's, where A and B are fuzzy predicates and Q is a fuzzy quantifier. In general, the conclusion yielded by such reasoning is a proposition which may be converted into a disposition through the suppression of fuzzy quantifiers.

Zadeh, L. A.↗

Probabilistic versus fuzzy reasoning

This paper shows how to solve problems using probability theory that the fuzzy approaches claim probability cannot solve. By using the view that probabilities are a measure of belief in a proposition in a particular context, limitations imposed by the frequncy interpretations of probability are avoided. The various fuzzy approaches (fuzzy sets, fuzzy logic, possibility theory and higher order generalizations) seem to fill the gap caused by the restricted frequency interpretation. Close examination shows that the fuzzy approaches have exactly the same representation as the corresponding probabilistc approach and include similar calculi. The probabilistic approach assumes less information when the calculi differ.

Cheeseman, Peter↗

Fuzzy associative memories

Mappings between fuzzy cubes are discussed. This level of abstraction provides a surprising and fruitful alternative to the propositional and predicate-calculas reasoning techniques used in expert systems. It allows one to reason with sets instead of propositions. Discussed here are fuzzy and neural function estimators, neural vs. fuzzy representation of structured knowledge, fuzzy vector-matrix multiplication, and fuzzy associative memory (FAM) system architecture.

Kosko, Bart↗

The simplification of fuzzy control algorithm and hardware implementation

The conventional interface composition algorithm of a fuzzy controller is very time and memory consuming. As a result, it is difficult to do real time fuzzy inference, and most fuzzy controllers are realized by look-up tables. Here, researchers derive a simplified algorithm using the defuzzification mean of maximum. This algorithm takes shorter computation time and needs less memory usage, thus making it possible to compute the fuzzy inference on real time and easy to tune the control rules on line. A hardware implementation based on a simplified fuzzy inference algorithm is described.

Wu, Z. Q.↗

Applications of fuzzy logic to control and decision making

Long range space missions will require high operational efficiency as well as autonomy to enhance the effectivity of performance. Fuzzy logic technology has been shown to be powerful and robust in interpreting imprecise measurements and generating appropriate control decisions for many space operations. Several applications are underway, studying the fuzzy logic approach to solving control and decision making problems. Fuzzy logic algorithms for relative motion and attitude control have been developed and demonstrated for proximity operations. Based on this experience, motion control algorithms that include obstacle avoidance were developed for a Mars Rover prototype for maneuvering during the sample collection process. A concept of an intelligent sensor system that can identify objects and track them continuously and learn from its environment is under development to support traffic management and proximity operations around the Space Station Freedom. For safe and reliable operation of Lunar/Mars based crew quarters, high speed controllers with ability to combine imprecise measurements from several sensors is required. A fuzzy logic approach that uses high speed fuzzy hardware chips is being studied.

Lea, Robert N.↗

Expert system training and control based on the fuzzy relation matrix

Fuzzy knowledge, that for which the terms of reference are not crisp but overlapped, seems to characterize human expertise. This can be shown from the fact that an experienced human operator can control some complex plants better than a computer can. Proposed here is fuzzy theory to build a fuzzy expert relation matrix (FERM) from given rules or/and examples, either in linguistic terms or in numerical values to mimic human processes of perception and decision making. The knowledge base is codified in terms of many implicit fuzzy rules. Fuzzy knowledge thus codified may also be compared with explicit rules specified by a human expert. It can also provide a basis for modeling the human operator and allow comparison of what a human operator says to what he does in practice. Two experiments were performed. In the first, control of liquid in a tank, demonstrates how the FERM knowledge base is elicited and trained. The other shows how to use a FERM, build up from linguistic rules, and to control an inverted pendulum without a dynamic model.

Ren, Jie↗

Fuzzy logic control of telerobot manipulators

Telerobot systems for advanced applications will require manipulators with redundant 'degrees of freedom' (DOF) that are capable of adapting manipulator configurations to avoid obstacles while achieving the user specified goal. Conventional methods for control of manipulators (based on solution of the inverse kinematics) cannot be easily extended to these situations. Fuzzy logic control offers a possible solution to these needs. A current research program at SRI developed a fuzzy logic controller for a redundant, 4 DOF, planar manipulator. The manipulator end point trajectory can be specified by either a computer program (robot mode) or by manual input (teleoperator). The approach used expresses end-point error and the location of manipulator joints as fuzzy variables. Joint motions are determined by a fuzzy rule set without requiring solution of the inverse kinematics. Additional rules for sensor data, obstacle avoidance and preferred manipulator configuration, e.g., 'righty' or 'lefty', are easily accommodated. The procedure used to generate the fuzzy rules can be extended to higher DOF systems.

Franke, Ernest A.↗

Towards autonomous fuzzy control

The efficient implementation of on-line adaptation in real time is an important research problem in fuzzy control. The goal is to develop autonomous self-organizing controllers employing system-independent control meta-knowledge which enables them to adjust their control policies depending on the systems they control and the environments in which they operate. An autonomous fuzzy controller would continuously observe system behavior while implementing its control actions and would use the outcomes of these actions to refine its control policy. It could be designed to lie dormant when its control actions give rise to adequate performance characteristics but could rapidly and autonomously initiate real-time adaptation whenever its performance degrades. Such an autonomous fuzzy controller would have immense practical value. It could accommodate individual variations in system characteristics and also compensate for degradations in system characteristics caused by wear and tear. It could also potentially deal with black-box systems and control scenarios. On-going research in autonomous fuzzy control is reported. The ultimate research objective is to develop robust and relatively inexpensive autonomous fuzzy control hardware suitable for use in real time environments.

Shenoi, Sujeet↗