Crisp and lattice-valued ambiguous representations of one continuous semilattice in another one are introduced and operation of taking pseudo-inverse of the above relations is defined. It is shown that continuous semilattices and their ambiguous representations, for which taking pseudo-inverse is involutive, form categories. Self-dualities and contravariant equivalences for these categories are obtained. Possible interpretations and applications to processing of imperfect information are discussed.

中文翻译：

---

半格、不完全信息和谓词变换器的二义性表示

介绍了一个连续半格在另一个半格中的清晰和格值模糊表示，并定义了取上述关系的伪逆运算。结果表明，取伪逆是对合的连续半格及其模糊表示形成范畴。获得了这些类别的自对偶和逆变等价。讨论了处理不完善信息的可能解释和应用。