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Some Advances in Mathematical Models for Preference Relations

Matteo Brunelli, Some Advances in Mathematical Models for Preference Relations. TUCS Dissertations 136. Turku Centre for Computer Science, 2011.

Abstract:

Preference relations, and their modeling, have played a crucial role in both social sciences and applied mathematics. A special category of preference relations is represented by cardinal preference relations, which are nothing other than relations which can also take into account the degree of relation. Preference relations play a pivotal role in most of multi criteria decision making methods and in the operational research. This thesis aims at showing some recent advances in their methodology. Actually, there are a number of open issues in this field and the contributions presented in this thesis can be grouped accordingly.

The first issue regards the estimation of a weight vector given a preference relation. A new and efficient algorithm for estimating the priority vector of a reciprocal relation, i.e. a special type of preference relation, is going to be presented. The same section contains the proof that twenty methods already proposed in literature lead to unsatisfactory results as they employ a conflicting constraint in their optimization model.

The second area of interest concerns consistency evaluation and it is possibly the kernel of the thesis. This thesis contains the proofs that some indices are equivalent and that therefore, some seemingly different
formulae, end up leading to the very same result. Moreover, some numerical simulations are presented. The section ends with some consideration of a new method for fairly evaluating consistency.

The third matter regards incomplete relations and how to estimate missing comparisons. This section reports a numerical study of the methods already proposed in literature and analyzes their behavior in different situations.

The fourth, and last, topic, proposes a way to deal with group decision making by means of connecting preference relations with social network analysis.

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BibTeX entry:

@PHDTHESIS{phdBrunelli11a,
  title = {Some Advances in Mathematical Models for Preference Relations},
  author = {Brunelli, Matteo},
  number = {136},
  series = {TUCS Dissertations},
  school = {Turku Centre for Computer Science},
  year = {2011},
  ISBN = {978-952-12-2596-3},
}

Belongs to TUCS Research Unit(s): Institute for Advanced Management Systems Research (IAMSR)

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