Fuzzy Qualitative Reasoning with Words

Computing in its traditional sense involves manipulation of numbers for the most part. Symbolic computation has been developed in the meantime especially in Artificial Intelligence, but often without preserving the capability of interfacing the symbolic processing of information with numerical data. By contrast, humans employ mostly words and qualitative descriptions when providing assessments of situations, or reasoning about complex physical or human systems, even if a part of the data refers to numerical scales. For a long time, fuzzy sets have been advocated by Zadeh (1973) as a methodology for interfacing numerical data about the world (which are often imprecisely perceived), with linguistic categories or classes used in reasoning. In particular, it is the case for fuzzy rules or fuzzy algorithms where words are interpreted as the labels of fuzzy sets. There are different kinds of situations where the underlying reasoning process can be handled within the framework of a limited vocabulary. When developing his approach to approximate reasoning, Zadeh (1979) was already separating the combination/projection machinery acting at the levels of the fuzzy set membership functions, from the knowledge representation and linguistic approximation steps which respectively turn the linguistic input information into possibility distributions and restate the obtained conclusions into a prescribed vocabulary understandable by the user. The fuzzy set framework should supply the right tools for mixing a symbolic treatment to be performed at the level of the linguistic labels with facilities for permanently interfacing them with their fuzzy set semantics along the reasoning process. Indeed, fuzzy sets restore gradual transitions between categories on continuous universes, which would be lost if the interface between labels and data were provided by crisp sets only. In this paper, we investigate the feasibility of such a view on a particular type of reasoning: the order of magnitude reasoning in terms of closeness and negligibility relations. The same line of research has been explored on more general patterns of approximate reasoning by Dubois, Foulloy, Galichet and Prade (1997).