Refining aggregation operations in finite ordinal scales
نویسندگان
چکیده
We discuss how to aggregate multiple criteria evaluations belonging to qualitative, linearly ordered scales. Qualitative aggregation operations such as min or max can be refined by discrimin and leximin orderings, in agreement with the Pareto ordering of vector evaluations. Further refinements of discrimin orderings, as well as the generalization of discrimin and lexirnin to functions other than min or max, are presented. Lastly, it is pointed out that a generalized leximin is not sufficient for describing any aggregation structure. However, the definition of aggregation structures in qualitative scales amounts, in practice, to the specification of a small number of positionings of aggregation results.
منابع مشابه
Meaningful aggregation functions mapping ordinal scales into an ordinal scale: a state of the art
We present an overview of the meaningful aggregation functions mapping ordinal scales into an ordinal scale. Three main classes are discussed, namely order invariant functions, comparison meaningful functions on a single ordinal scale, and comparison meaningful functions on independent ordinal scales. It appears that the most prominent meaningful aggregation functions are lattice polynomial fun...
متن کاملAggregation on Finite Ordinal Scales by Scale Independent Functions
We define and investigate the scale independent aggregation functions that are meaningful to aggregate finite ordinal numerical scales. Here scale independence means that the functions always have discrete representatives when the ordinal scales are considered as totally ordered finite sets. We also show that those scale independent functions identify with the so-called order invariant function...
متن کاملNegations and aggregation operators based on a new hesitant fuzzy partial ordering
Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negati...
متن کاملOn the use of aggregation operations in information fusion processes
This position paper discusses the role of the existing body of fuzzy set aggregation operations in various kinds of problems where the process of fusion of items coming from several sources is central. Several kinds of membership functions can be useful according to the nature of the information to be merged: numerical vs. ordinal inputs, preferences vs. uncertain data, observations vs. constra...
متن کاملMedian-based aggregation operators for prototype construction in ordinal scales
This article studies aggregation operators in ordinal scales for their application to clustering (more specifically, to microaggregation for statistical disclosure risk). In particular, we consider these operators in the process of prototype construction. This study analyzes main aggregation operators for ordinal scales [plurality rule, medians, Sugeno integrals (SI), and ordinal weighted means...
متن کامل