L-fuzzifying antimatroids
What is it about?
This paper introduces the concept of L-fuzzifying antimatroid associated with an L-fuzzifying family of feasible sets. Several relevant fundamental properties are obtained. We also propose the concept of L-fuzzifying rank functions for L-fuzzifying antimatroids, and then investigate their axiomatic characterizations. Finally, we shed light upon the bijective correspondence between an L-fuzzifying antimatroid and its L-fuzzifying rank function.
Why is it important?
Crisp antimatroid is a combinatorial abstraction of convexity. It also can be incorporated into the greedy algorithm in order to seek the optimal solutions. Nevertheless, this kind of significant classical structure has inherent limitations in addressing fuzzy optimization problems and abstracting fuzzy convexities. This paper concerns the fuzzification of antimatroids as well as some basic properties and axiomatizations by means of fuzzy logic language. To some extend, our work may facilitate to establish some potential links among fuzzy convexities, fuzzy posets and other subjects, and enrich their theoretical outcomes.