The chapter advocates the interest of distinguishing between negative and positive preferences in the processing of flexible queries. Negative preferences express what is (more or less, or completely) impossible or undesirable, and by complementation, they specify flexible constraints restricting feasible or tolerated values. Positive preferences are less compulsory, and rather express wishes; they specify attribute values that would be really satisfactory. Because they are often expressed independently, negative and positive preferences may be inconsistent. Consistency is then restored by giving priority to negative preferences, since they express genuine constraints. The chapter discusses the handling of bipolar queries, that is, queries involving negative and positive preferences, in the framework of possibility theory. Both ordinary queries expressed in terms of flexible requirements and case-based queries referring to examples and counterexamples are considered in this perspective.
Key Terms in this Chapter
Case-Based Reasoning: Inference or problem-solving technique based on the similarity between the current problem and previously solved ones that are stored in a repository. Its principle relies on the idea that the more similar two problems, the more similar their solution.
Flexible Query: Query to a database interpreted as a flexible constraint on items to be retrieved.
Bipolarity: Cognitive phenomenon whereby reasoning and decision processes are described in terms of positive and negative aspects, often separately.
Asymmetric Bipolarity: Bipolarity is asymmetric when the positive and the negative parts of the information are not in reflection with respect to each other and are obtained from independent sources
Possibility Theory: A theory of uncertainty dedicated to the gradual modeling of incomplete information, similar to probability theory, but where maximum and minimum is used in place of sum and product.
Twofold Fuzzy Set: A special kind of interval-valued fuzzy set (in which membership grades are only known to belong to intervals). The upper and lower bounds are respectively defined as the possibility and the necessity of membership, hence satisfy the usual constraints of possibility necessity-pairs; if the lower bound is positive, the upperbound is 1.
Flexible Constraint: Constraint in which satisfaction is a matter of degree and can be partially relaxed if necessary so as to ensure the feasibility of a problem.
Preference Modeling: Formal methods for the description of the user’s attitude when ranking objects in terms of merit.