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NASA NTRS1985

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.↗
NASA NTRS1985

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.↗
NASA NTRS1986

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↗
NASA NTRS1991

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↗
NASA NTRS1991

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.↗
NASA NTRS1991

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.↗
NASA NTRS1991

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↗
NASA NTRS1992

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.↗
NASA NTRS1993

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↗
NASA NTRS1993

Learning fuzzy information in a hybrid connectionist, symbolic model

An instance-based learning system is presented. SC-net is a fuzzy hybrid connectionist, symbolic learning system. It remembers some examples and makes groups of examples into exemplars. All real-valued attributes are represented as fuzzy sets. The network representation and learning method is described. To illustrate this approach to learning in fuzzy domains, an example of segmenting magnetic resonance images of the brain is discussed. Clearly, the boundaries between human tissues are ill-defined or fuzzy. Example fuzzy rules for recognition are generated. Segmentations are presented that provide results that radiologists find useful.

Romaniuk, Steve G.↗
NASA NTRS1993

A fuzzy controller with nonlinear control rules is the sum of a global nonlinear controller and a local nonlinear PI-like controller

The fuzzy controllers studied in this paper are the ones that employ N trapezoidal-shaped members for input fuzzy sets, Zadeh fuzzy logic and a centroid defuzzification algorithm for output fuzzy set. The author analytically proves that the structure of the fuzzy controllers is the sum of a global nonlinear controller and a local nonlinear proportional-integral-like controller. If N approaches infinity, the global controller becomes a nonlinear controller while the local controller disappears. If linear control rules are used, the global controller becomes a global two-dimensional multilevel relay which approaches a global linear proportional-integral (PI) controller as N approaches infinity.

Ying, Hao↗
NASA NTRS1993

Certain and possible rules for decision making using rough set theory extended to fuzzy sets

Uncertainty may be caused by the ambiguity in the terms used to describe a specific situation. It may also be caused by skepticism of rules used to describe a course of action or by missing and/or erroneous data. To deal with uncertainty, techniques other than classical logic need to be developed. Although, statistics may be the best tool available for handling likelihood, it is not always adequate for dealing with knowledge acquisition under uncertainty. Inadequacies caused by estimating probabilities in statistical processes can be alleviated through use of the Dempster-Shafer theory of evidence. Fuzzy set theory is another tool used to deal with uncertainty where ambiguous terms are present. Other methods include rough sets, the theory of endorsements and nonmonotonic logic. J. Grzymala-Busse has defined the concept of lower and upper approximation of a (crisp) set and has used that concept to extract rules from a set of examples. We will define the fuzzy analogs of lower and upper approximations and use these to obtain certain and possible rules from a set of examples where the data is fuzzy. Central to these concepts will be the idea of the degree to which a fuzzy set A is contained in another fuzzy set B, and the degree of intersection of a set A with set B. These concepts will also give meaning to the statement; A implies B. The two meanings will be: (1) if x is certainly in A then it is certainly in B, and (2) if x is possibly in A then it is possibly in B. Next, classification will be looked at and it will be shown that if a classification will be looked at and it will be shown that if a classification is well externally definable then it is well internally definable, and if it is poorly externally definable then it is poorly internally definable, thus generalizing a result of Grzymala-Busse. Finally, some ideas of how to define consensus and group options to form clusters of rules will be given.

Dekorvin, Andre↗
NASA NTRS1993

Structure identification in fuzzy inference using reinforcement learning

In our previous work on the GARIC architecture, we have shown that the system can start with surface structure of the knowledge base (i.e., the linguistic expression of the rules) and learn the deep structure (i.e., the fuzzy membership functions of the labels used in the rules) by using reinforcement learning. Assuming the surface structure, GARIC refines the fuzzy membership functions used in the consequents of the rules using a gradient descent procedure. This hybrid fuzzy logic and reinforcement learning approach can learn to balance a cart-pole system and to backup a truck to its docking location after a few trials. In this paper, we discuss how to do structure identification using reinforcement learning in fuzzy inference systems. This involves identifying both surface as well as deep structure of the knowledge base. The term set of fuzzy linguistic labels used in describing the values of each control variable must be derived. In this process, splitting a label refers to creating new labels which are more granular than the original label and merging two labels creates a more general label. Splitting and merging of labels directly transform the structure of the action selection network used in GARIC by increasing or decreasing the number of hidden layer nodes.

Berenji, Hamid R.↗
NASA NTRS1993

Improvement on fuzzy controller design techniques

This paper addresses three main issues, which are somewhat interrelated. The first issue deals with the classification or types of fuzzy controllers. Careful examination of the fuzzy controllers designed by various engineers reveals distinctive classes of fuzzy controllers. Classification is believed to be helpful from different perspectives. The second issue deals with the design according to specifications, experiments related to the tuning of fuzzy controllers, according to the specification, will be discussed. General design procedure, hopefully, can be outlined in order to ease the burden of a design engineer. The third issue deals with the simplicity and limitation of the rule-based IF-THEN logical statements. The methodology of fuzzy-constraint network is proposed here as an alternative to the design practice at present. It is our belief that predicate calculus and the first order logic possess much more expressive power.

Wang, Paul P.↗
NASA NTRS1992

Strongly transitive fuzzy relations: A more adequate way to describe similarity

The notion of a transitive closure of a fuzzy relation is very useful for clustering in pattern recognition, for fuzzy databases, etc. It is based on translating the standard definition of transitivity and transitive closure into fuzzy terms. This definition works fine, but to some extent it does not fully capture our understanding of transitivity. The reason is that this definition is based on fuzzifying only the positive side of transitivity: if R(a,b) and R(b,c), then R(a,c); but transitivity also includes a negative side: if R(a,b) and not R(a,c), then not R(b,c). In classical logic, this negative statement follows from the standard 'positive' definition of transitivity. In fuzzy logic, this negative part of the transitivity has to be formulated as an additional demand. A strongly transitive fuzzy relation as the one that satisfies both the positive and the negative transitivity demands is defined, the existence of strongly transitive closure is proven, and the relationship between strongly transitive similarity and clustering are found.

Kreinovich, Vladik YA.↗
NASA NTRS1992

Comparison of crisp and fuzzy character networks in handwritten word recognition

Experiments involving handwritten word recognition on words taken from images of handwritten address blocks from the United States Postal Service mailstream are described. The word recognition algorithm relies on the use of neural networks at the character level. The neural networks are trained using crisp and fuzzy desired outputs. The fuzzy outputs were defined using a fuzzy k-nearest neighbor algorithm. The crisp networks slightly outperformed the fuzzy networks at the character level but the fuzzy networks outperformed the crisp networks at the word level.

Gader, Paul↗
NASA NTRS1992

Incomplete fuzzy data processing systems using artificial neural network

In this paper, the implementation of a fuzzy data processing system using an artificial neural network (ANN) is discussed. The binary representation of fuzzy data is assumed, where the universe of discourse is decartelized into n equal intervals. The value of a membership function is represented by a binary number. It is proposed that incomplete fuzzy data processing be performed in two stages. The first stage performs the 'retrieval' of incomplete fuzzy data, and the second stage performs the desired operation on the retrieval data. The method of incomplete fuzzy data retrieval is proposed based on the linear approximation of missing values of the membership function. The ANN implementation of the proposed system is presented. The system was computationally verified and showed a relatively small total error.

Patyra, Marek J.↗
NASA NTRS1990

Overview of Fuzzy Logic

Viewgraphs on an overview of fuzzy logic are presented. Topics covered include: fuzzy control system; fuzzy logic; fuzzy inference; fuzzy controller; and the Sendai subway system.

Ma, Xiwen↗