Algorithms to Detect and Rectify Multiplicative and Ordinal Inconsistencies of Fuzzy Preference Relations

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.Consistency, multiplicative and ordinal, of fuzzy preference relations (FPRs) is investigated. The geometric consistency index (GCI) approximated thresholds are extended to measure the degree of consistency for an FPR. For inconsistent FPRs, two algorithms are devised (1) to find the multiplicative inconsistent elements, and (2) to detect the ordinal inconsistent elements. An integrated algorithm is proposed to improve simultaneously the ordinal and multiplicative consistencies. Some examples, comparative analysis, and simulation experiments are provided to demonstrate the effectiveness of the proposed methods

Reaching social consensus family budgets: The Spanish case

The study of family budgets has been traditionally used to analyse consumers’ behaviour and estimate cost-of-living since the end of 19th century. Generally speaking, the computation of the budgets has been based on two different methodologies, the prescriptive and the descriptive method. Both present several drawbacks like the comparison among different areas, family types and over time. This paper proposes a new methodology for reaching family budgets, namely social consensus family budgets, to overcome such problems and examine the main features of the novel approach. The suggested method uses the minimization of the differences with respect to the consumer’s preferences to obtain a solution that summarizes single behaviour into a social preference. This approach is especially conceived for preferences on possibly related-expenditure groups. In addition, several algorithms are introduced to compute the social family budgets. Finally, the contribution includes the Spanish case as an example of reaching some social consensus family budgets in order to show the operational character and intuitive interpretation of the proposal approach.Este trabajo forma parte del proyecto de investigación con financiación nacional: MEC-FEDER Grant ECO2016-77900-

Preference fusion and Condorcet's Paradox under uncertainty

Facing an unknown situation, a person may not be able to firmly elicit his/her preferences over different alternatives, so he/she tends to express uncertain preferences. Given a community of different persons expressing their preferences over certain alternatives under uncertainty, to get a collective representative opinion of the whole community, a preference fusion process is required. The aim of this work is to propose a preference fusion method that copes with uncertainty and escape from the Condorcet paradox. To model preferences under uncertainty, we propose to develop a model of preferences based on belief function theory that accurately describes and captures the uncertainty associated with individual or collective preferences. This work improves and extends the previous results. This work improves and extends the contribution presented in a previous work. The benefits of our contribution are twofold. On the one hand, we propose a qualitative and expressive preference modeling strategy based on belief-function theory which scales better with the number of sources. On the other hand, we propose an incremental distance-based algorithm (using Jousselme distance) for the construction of the collective preference order to avoid the Condorcet Paradox.Comment: International Conference on Information Fusion, Jul 2017, Xi'an, Chin