Understanding Predication in Conceptual Spaces

We argue that a cognitive semantics has to take into account the possibly partial information that a cognitive agent has of the world. After discussing Gärdenfors's view of objects in conceptual spaces, we offer a number of viable treatments of partiality of information and we formalize them by means of alternative predicative logics. Our analysis shows that understanding the nature of simple predicative sentences is crucial for a cognitive semantics

Interpretations of Association Rules by Granular Computing

We present interpretations for association rules. We first introduce Pawlak's method, and the corresponding algorithm of finding decision rules (a kind of association rules). We then use extended random sets to present a new algorithm of finding interesting rules. We prove that the new algorithm is faster than Pawlak's algorithm. The extended random sets are easily to include more than one criterion for determining interesting rules. We also provide two measures for dealing with uncertainties in association rules

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

Determining rules for closing customer service centers: A public utility company's fuzzy decision

In the present work, we consider the general problem of knowledge acquisition under uncertainty. A commonly used method is to learn by examples. We observe how the expert solves specific cases and from this infer some rules by which the decision was made. Unique to this work is the fuzzy set representation of the conditions or attributes upon which the decision make may base his fuzzy set decision. From our examples, we infer certain and possible rules containing fuzzy terms. It should be stressed that the procedure determines how closely the expert follows the conditions under consideration in making his decision. We offer two examples pertaining to the possible decision to close a customer service center of a public utility company. In the first example, the decision maker does not follow too closely the conditions. In the second example, the conditions are much more relevant to the decision of the expert