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Granular computing is a essential mathematical tool in artificial intelligence. An incomplete information system is an important model and its basic structures are information structures. This paper investigates information structures in an incomplete information system from granular computing viewpoint, i.e., information structures are viewed as granular structures. Information structures in an incomplete information system are first described through set vectors. Then, dependence between information structures is depicted, and information distance for calculating the difference between information structures is proposed. Next, properties of information structures in an incomplete information system are given. Finally, group and lattice characterizations of information structures in an incomplete information system are obtained. These results will be helpful for establishing a framework of granular computing in information systems.

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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 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.