Consistency of crisp and fuzzy preference relations

In this paper we point out some difficulties in developing rationality measures of fuzzy preference relations, as defined by Cutello and Montero in a previous paper. In particular, we analyze some alternative approaches, taking into account that consistency can not be viewed as an univoque concept in a fuzzy framework, neither in the crisp context, where consistency should not be necessarily represented in terms of linear orders

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

Managing Incomplete Preference Relations in Decision Making: A Review and Future Trends

In decision making, situations where all experts are able to efficiently express their preferences over all the available options are the exception rather than the rule. Indeed, the above scenario requires all experts to possess a precise or sufficient level of knowledge of the whole problem to tackle, including the ability to discriminate the degree up to which some options are better than others. These assumptions can be seen unrealistic in many decision making situations, especially those involving a large number of alternatives to choose from and/or conflicting and dynamic sources of information. Some methodologies widely adopted in these situations are to discard or to rate more negatively those experts that provide preferences with missing values. However, incomplete information is not equivalent to low quality information, and consequently these methodologies could lead to biased or even bad solutions since useful information might not being taken properly into account in the decision process. Therefore, alternative approaches to manage incomplete preference relations that estimates the missing information in decision making are desirable and possible. This paper presents and analyses methods and processes developed on this area towards the estimation of missing preferences in decision making, and highlights some areas for future research

Preference Modelling

This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with "compact representation of preferences" introduced for special purpoes. We end the paper with some concluding remarks

Multi-criteria group decision making with a partialranking-based ordinal consensus reaching process for automotive development management

The consensus reaching process (CRP) aims at reconciling the conflicts between individual preferences when eliciting collective preferences. The ordinal CRP based on the positional orders of alternatives in linear rankings is straightforward and robust; however, for partial rankings involving preference, indifference and incomparability relations, there is no explicit positional order but are binary relations. This study focuses on partial rankings that may occur when using the ORESTE (organısation, rangement et Synthese de donnees relarionnelles, in French) method for making decisions, and designs an ordinal CRP pertaining to the binary relations of alternatives. Concretely, we propose an enhanced ordinal consensus measure with two hierarchies to measure the agreement levels between individual partial rankings. Consensus degrees are calculated based on the frequency distribution of binary relation types, which can avoid subjective axiomatic assumptions on the relations themselves. Besides, a consensus threshold determination method close to cognitive expression is developed. A feedback mechanism is designed to aid experts to modify preferences towards group consensus. An example about the evaluation of automotive design schemes is presented to validate the proposed ordinal CRP. A ranking result that allows the incomparability relations of design schemes is obtained after the information exchange among experts

Estimating unknown values in reciprocal intuitionistic preference relations via asymmetric fuzzy preference relations

Intuitionistic preference relations are becoming increasingly important in the field of group decision making since they present a flexible and simple way to the experts to provide their preference relations, while at the same time allowing them to accommodate a certain degree of hesitation inherent to all decision making processes. In this contribution, we prove the mathematical equivalence between the set of asymmetric fuzzy preference relations and the set of reciprocal intuitionistic fuzzy preference relations. This result is exploited to tackle the presence of incomplete reciprocal intuitionistic fuzzy preference relation in decision making by developing a consistency driven estimation procedure via the corresponding equivalent incomplete asymmetric fuzzy preference relation

On Incomplete Fuzzy and Multiplicative Preference Relations In Multi-Person Decision Making

This research work has been developed with the financing of FEDER funds in FUZZYLING-II Project TIN2010- 17876, the Andalusian Excellence Projects TIC-05299 and TIC-5991 and the mobility grant program awarded by the University of Granada ’s International Office.2nd International Conference on Information Technology and Quantitative Management, ITQM 2014Rapid changes in the business environment such us the globalization as well as the increasing necessity to make crucial decisions involving a huge range of alternatives in short period of time or even in real time have made that computerized group decision support systems become very useful tools. However in the majority of the cases the panel of experts cannot provide all the information about their preferences due to different reasons such as lack of knowledge, time etc. Therefore different approaches have been presented to deal with the missing preferences in group decision making contexts. In this paper we review and analyse the state-of-the-art research efforts carried out on this topic for incomplete fuzzy preference relations and multiplicative preference relations.FEDER funds in FUZZYLING-II Project TIN2010- 17876Andalusian Excellence Projects TIC-05299 and TIC-5991Mobility grant program awarded by the University of Granada ’s International Offic