A new approach to clustering

A general formulation of data reduction and clustering processes is proposed. These procedures are regarded as mappings or transformations of the original space onto a “representation” or “code” space subjected to some constraints. Current clustering methods, as well as three other data reduction techniques, are specified within the framework of this formulation. A new method of representation of the reduced data, based on the idea of “fuzzy sets,” is proposed to avoid some of the problems of current clustering procedures and to provide better insight into the structure of the original data

The semantics of fuzzy logic

Summarized here are the results of recent research on the conceptual foundations of fuzzy logic. The focus is primarily on the principle characteristics of a model that quantifies resemblance between possible worlds by means of a similarity function that assigns a number between 0 and 1 to every pair of possible worlds. Introduction of such a function permits one to interpret the major constructs and methods of fuzzy logic: conditional and unconditional possibility and necessity distributions and the generalized modus ponens of Zadeh on the basis of related metric relationships between subsets of possible worlds

On the semantics of fuzzy logic

AbstractThis paper presents a formal characterization of the major concepts and constructs of fuzzy logic in terms of notions of distance, closeness, and similarity between pairs of possible worlds. The formalism is a direct extension (by recognition of multiple degrees of accessibility, conceivability, or reachability) of the najor modal logic concepts of possible and necessary truth.Given a function that maps pairs of possible worlds into a number between 0 and 1, generalizing the conventional concept of an equivalence relation, the major constructs of fuzzy logic (conditional and unconditioned possibility distributions) are defined in terms of this similarity relation using familiar concepts from the mathematical theory of metric spaces. This interpretation is different in nature and character from the typical, chance-oriented, meanings associated with probabilistic concepts, which are grounded on the mathematical notion of set measure. The similarity structure defines a topological notion of continuity in the space of possible worlds (and in that of its subsets, i.e., propositions) that allows a form of logical “extrapolation” between possible worlds.This logical extrapolation operation corresponds to the major deductive rule of fuzzy logic — the compositional rule of inference or generalized modus ponens of Zadeh — an inferential operation that generalizes its classical counterpart by virtue of its ability to be utilized when propositions representing available evidence match only approximately the antecedents of conditional propositions. The relations between the similarity-based interpretation of the role of conditional possibility distributions and the approximate inferential procedures of Baldwin are also discussed.A straightforward extension of the theory to the case where the similarity scale is symbolic rather than numeric is described. The problem of generating similarity functions from a given set of possibility distributions, with the latter interpreted as defining a number of (graded) discernibility relations and the former as the result of combining them into a joint measure of distinguishability between possible worlds, is briefly discussed

A Multivalued Logic Approach to Integrating Planning and Control

Intelligent agents embedded in a dynamic, uncertain environment should incorporate capabilities for both planned and reactive behavior. Many current solutions to this dual need focus on one aspect, and treat the other one as secondary. We propose an approach for integrating planning and control based on behavior schemas, which link physical movements to abstract action descriptions. Behavior schemas describe behaviors of an agent, expressed as trajectories of control actions in an environment, and goals can be defined as predicates on these trajectories. Goals and behaviors can be combined to produce conjoint goals and complex controls. The ability of multivalued logics to represent graded preferences allows us to formulate tradeoffs in the combination. Two composition theorems relate complex controls to complex goals, and provide the key to using standard knowledge-based deliberation techniques to generate complex controllers. We report experiments in planning and execution on a mobi..