Overlap functions

Abstract

a b s t r a c tIn this paper we address a key issue in scenario classification, where classifying concepts show a natural overlapping. In fact, overlapping needs to be evaluated whenever classes are not crisp, in order to be able to check if a certain classification structure fits reality and still can be useful for our declared decision making purposes. In this paper we address an object recognition problem, where the best classification with respect to background is the one with less overlapping between the class object and the class background. In particular, in this paper we present the basic properties that must be fulfilled by overlap functions, associated to the degree of overlapping between two classes. In order to define these overlap functions we take as reference properties like migrativity, homogeneity of order 1 and homogeneity of order 2. Hence we define overlap functions, proposing a construction method and analyzing the conditions ensuring that t-norms are overlap functions. In addition, we present a characterization of migrative and strict overlap functions by means of automorphisms.

A new fuzzy reasoning method based on the use of the Choquet integral

“…We must point out that in this work we apply t-norms to compute this step but functions satisfying different properties could be used, like overlap functions that are non-associative [22,23,24]. 2.…”

Paired Structures and other opposites-based models

“…is not being a priori imposed, although certain circumstances, constraints or generalizations, might suggest specific adaptations, particularly in the management of predicates (see, e.g., [5]). …”

Some properties of implications via aggregation functions and overlap functions

“…From the construction method of overlap functions by means of rational functions 10 we can also state the following example. …”