Reasoning under fuzzy uncertainty arises in many applications including planning and scheduling in fuzzy environments. In many real-world applications, it is necessary to define fuzzy uncertainty over qualitative uncertainty, where fuzzy values are assigned over the possible outcomes of qualitative uncertainty. However, current fuzzy logic programming frameworks support only reasoning under fuzzy uncertainty. Moreover, disjunctive logic programs, although used for reasoning under qualitative uncertainty it cannot be used for reasoning with fuzzy uncertainty. In this paper we combine extended and normal fuzzy logic programs [30, 23], for reasoning under fuzzy uncertainty, with disjunctive logic programs [7, 4], for reasoning under qualitative uncertainty, in a unified logic programming framework, namely extended and normal disjunctive fuzzy logic programs. This is to allow directly and intuitively to represent and reason in the presence of both fuzzy uncertainty and qualitative uncertainty. The syntax and semantics of extended and normal disjunctive fuzzy logic programs naturally extends and subsumes the syntax and semantics of extended and normal fuzzy logic programs [30, 23] and disjunctive logic programs [7, 4]. Moreover, we show that extended and normal disjunctive fuzzy logic programs can be intuitively used for representing and reasoning about scheduling with fuzzy preferences.
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