On the use of the Choquet integral with fuzzy numbers in multiple criteria decision support

International audienceThis paper presents a multiple criteria decision support approach in order to build a ranking and suggest a best choice1 on a set of alternatives. The partial evaluations of the alternatives on the points of view can be fuzzy numbers. The aggregation is performed through the use of a fuzzy extension of the Choquet integral. We detail how to assess the coefficients of the aggregation operator by using alternatives which are well-known to the decision maker, and which originate from his domain of expertise

R UBIS: A bipolar-valued outranking method for the choice problem

International audienceThe main concern of this article is to present the RUBIS method for tackling the choice problem in the context of multiple criteria decision aiding. Its genuine purpose is to help a decision maker to determine a single best decision alternative. Methodologically we focus on pairwise comparisons of these alternatives which lead to the concept of bipolar-valued outranking digraph. The work is centred around a set of five pragmatic principles which are required in the context of a progressive decision aiding methodology. Their thorough study and implementation in the outranking digraph lead us to define a choice recommendation as an extension of the classical digraph kernel concept

Dealing with non-metric dissimilarities in fuzzy central clustering algorithms

Clustering is the problem of grouping objects on the basis of a similarity measure among them. Relational clustering methods can be employed when a feature-based representation of the objects is not available, and their description is given in terms of pairwise (dis)similarities. This paper focuses on the relational duals of fuzzy central clustering algorithms, and their application in situations when patterns are represented by means of non-metric pairwise dissimilarities. Symmetrization and shift operations have been proposed to transform the dissimilarities among patterns from non-metric to metric. In this paper, we analyze how four popular fuzzy central clustering algorithms are affected by such transformations. The main contributions include the lack of invariance to shift operations, as well as the invariance to symmetrization. Moreover, we highlight the connections between relational duals of central clustering algorithms and central clustering algorithms in kernel-induced spaces. One among the presented algorithms has never been proposed for non-metric relational clustering, and turns out to be very robust to shift operations. (C) 2008 Elsevier Inc. All rights reserved

Descriptive Profiles for Sets of Alternatives in Multiple Criteria Decision Aid

International audienceIn the context of Multiple Criteria Decision Aid, a decision-maker may be faced at any time with the task of analyzing one or several sets of alternatives, irrespective of the decision he is about to make. As in this case the alternatives may express contrasting gains and losses on the criteria on which they are evaluated, and while the sets that are presented to the decision-maker may potentially be large, the task of analysing them becomes a difficult one. Therefore the need to reduce these sets to a more concise representation is very important. Classically, profiles that describe sets of alternatives may be found in the context of the sorting problem, however they are either given beforehand by the decision-maker or determined from a set of assignment examples. We would therefore like to extend such profiles, as well as propose new ones, in order to characterize any set of alternatives. For each of them, we present several approaches for extracting them, which we then compare with respect to their performance

Perspectival Disagreement

UID/FIL/00183/2013A phenomenon called perspectival disagreement is laid out and modelled on the basis of modifications to known consensus measures for qualitative representations of preferences and transitive values by binary relations. Cases of perspectival disagreement are of general philosophical interest, because they allow for the possibility that two or more agents judge the value positions of other agents differently even when their assessments are based on the same evidence. Various examples of perspectival disagreement are given, generalizations are discussed, and it is argued that any representation by cardinal utilities also gives rise to some form of perspectivity. Although the examples strongly suggest that this phenomenon occurs in real life, it is concluded in the end that it does not pose any fundamental threat to representations of preferences and values as binary relations. Instead, position-sensitive measures of disagreement ought to be taken as a modelling option for cases in which the relative importance of preference changes matters to an agent.authorsversionpublishe

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

An Interactive Approach Based on Alternative Achievement Scale and Alternative Comprehensive Scale for Multiple Attribute Decision Making under Linguistic Environment

The aim of this paper is to develop an interactive approach for multiple attribute decision making with incomplete weight information under linguistic environment. Some of the concepts are defined, such as the distance between two 2-tuple linguistic variables, the expectation level of alternative, the achievement scale, the alternative comprehensive scale under linguistic environment. Based on these concepts, we establish some linear programming models, through which the decision maker interacts with the analyst. Furthermore, we establish a practical interactive approach for selecting the most desirable alternative(s). The interactive process can be realized by giving and revising the achievement scale and comprehensive scale of alternatives till the achievement scale and the comprehensive scale are achieved to the decision maker’s request. Finally, an illustrative example is also given.The author is very grateful to the associated editor and two anonymous referees for their insightful and constructive comments and suggestions that have led to an improved version of this paper. This work was partly supported by the National Natural Science Foundation of China (No. 90924027, No. 71101043), National Basic Research Program of China (973 Program, No. 2010C B951104), Key Program of National Social Science Foundation of China (No. 10AJY005), College Philosophy and Social Science Research Project of Jiangsu Province under Grant 2011SJD630007.Xu, Y.; Wang, H.; Palacios Marqués, D. (2013). An Interactive Approach Based on Alternative Achievement Scale and Alternative Comprehensive Scale for Multiple Attribute Decision Making under Linguistic Environment. International Journal of Computational Intelligence Systems. 6(1):87-95. https://doi.org/10.1080/18756891.2013.756226S87956