Aggregated Fuzzy Answer Set Programming

Abstract

In the previous chapter we introduced FASP, an extension of ASP that allows to solve continuous problems in a concise, declarative manner. We have also shown that FASP can sometimes be limited in its flexibility, however. For example, the fuzzy graph coloring program Pfgc introduced in Sect. 3.3 on page 46 allowed a continuous range of gray values as colors, but was unable to find a suitable graph coloring for graph G(b) depicted in Fig. 3.1 on the preceding page. This is not ideal, as a coloring that colors node a white, node b black, and node c gray may be better than having no solution at all. The inadmissibility is due to the constraint constr, which for G(b) removes solutions in which nodes have a similarity that is strictly greater than 0. A possible alternative is to allow solutions in which the similarity degree of two adjacent nodes may be greater than 0. Of course, solutions in which this degree is as small as possible are still preferred. This idea can be implemented by allowing that the last rule, constr, may not always be completely satisfied.