Abstract
Outranking methods are a family of techniques concerned with ranking the preference for alternatives based on the criteria values that describe them. The breadth of applications taking inference from such preference ranking analysis includes the areas of business, health, environment, marketing, and public services. In the context of databases, the ranking issue is closely associated with data retrieval, including the ranking of matches to queries. This chapter describes the rudiments of fuzzy outranking methods, with particular attention to one such approach, namely fuzzy PROMETHEE, compounded further with the different structures of defined fuzziness of the criteria values also considered. Alternative fuzzy PROMETHEE approaches are described, with one used in two real-life applications. The results presented, with emphasis on their graphical representation, offer insights into the appropriate application of such fuzzy outranking methods.
Key Terms in this Chapter
Preference Ranking Organization Method for Enrichment Evaluation (PROMETHEE): It is a multicriteria decision-making technique.
Outranking Relation: It is a relation to identify preference between two alternatives. An alternative a1 outranks a2 if and only if there is sufficient evidence to believe that a1 is better than a2 or at least a1 is as good as a2.
Ranking: Ranking is the process of ordering alternatives in relation to others. The resultant list arranged is called a rank order; an individual alternative has a rank position.
Flow Values: Within PROMETHEE, they are preference function values on alternatives used to rank the alternatives, including criteria that quantify the preference of alternatives on a specific criterion, outgoing and incoming values that discern positive and negative preferences, and net values that offer an overall quantification of preference over all the criteria.
Alternative: It is an abstract or real object or action that can be chosen. It is one of a number of objects or options considered for preference ranking, each described by values over a series of criteria.
Membership Function: It is a function that quantifies the grade of membership of a variable to a linguistic term. Reasonable functions are often piecewise linear functions, such as triangular and trapezoidal functions.
Multicriteria Decision Making (MCDM): MCDM is the general subject whereby alternatives are considered over a number of different criteria.
Defuzzification: It is the general term for the process of the creation of a crisp value as a surrogate for an existing fuzzy value. A number of defuzzification techniques are known, including centre-of-area, centre of gravity, and mean of maximums.
Preference Function: It is a function to standardize (remove scale effects) the difference between two alternative’s values over a single criterion.
Criterion: A criterion is a feature or standard that the preference for alternatives is based on, which has a known direction for improving preference.