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Paraconsistent semantics for Pavelka style fuzzy sentential logic

The root of this work is on the one hand in Belnaps four valued paraconsistent logic, and on the other hand on Pavelkas papers further developed by Turunen. We do not introduce a new non-classical logic but, based on a related study of Perny and Tsoukias, we introduce paraconsistent semantics of Pavelka style fuzzy sentential logic. Restricted to Lukasiewicz t-norm, our approach and the approach of Perny and Tsoukias partly overlap; the main difference lies in the interpretation of the logical connectives implication and negation. The essential mathematical tool proved in this paper is a one-one correspondence between evidence couples and evidence matrices that holds in all injective MV-algebras. Evidence couples associate to each atomic formula p two values a and b that can be interpreted as the degrees of pros and cons for p, respectively. Four values t,f,k,u, interpreted as the degrees of the truth, falsehood, contradiction and unknownness of p, respectively, can then be calculated by means of a and b and finally, the degrees of the truth, falsehood, contradiction and unknownness of any well formed formula @a are available. The obtained logic is Pavelka style fuzzy sentential logic. In such an approach truth and falsehood are not each others complements. Moreover, we solve some open problems presented by Perny and Tsoukias.

When conflict induces the expression of incomplete preferences

Multicriteria conflict arises in pairwise comparisons, where each alternative outperforms the other one on some criterion, which imposes a trade-off. Comparing two alternatives can be difficult if their respective advantages are of high magnitude (the attribute spread is large). In this paper, we investigate to which extent conflict in a comparison situation can lead decision makers to express incomplete preferences, that is, to refuse to compare the two alternatives, or to be unable to compare them with confidence. We report on an experiment in which subjects expressed preferences on pairs of alternatives involving varying conflicts. Results show that depending on whether the participants are allowed to express incomplete preferences or not, attribute spread has a different effect: a large attribute spread increases the frequency of incomparability statements, when available, while it increases the use of indifference statements when only indifference and preference answers are permitted. These results lead us to derive some implications for preference elicitation methods involving comparison tasks.

Representing preferences using intervals

In this paper we present a general framework for the comparison of intervals when preference relations have to established. The use of intervals in order to take into account imprecision and vagueness in handling preferences is well known in the literature, but a general theory on how such models behave is lacking. In the paper we generalize the concept of interval (allowing the presence of more than two points). We then introduce the structure of the framework based on the concept of relative position and component set. We provide an exhaustive study of 2-point and 3-point intervals comparison and show the way to generalize such results to n-point intervals.

Ordered sets with interval representation and ( m , n )-Ferrers relation

Semiorders may form the simplest class of ordered sets with a not necessarily transitive indifference relation. Their generalization has given birth to many other classes of ordered sets, each of them characterized by an interval representation, by the properties of its relations or by forbidden configurations. In this paper, we are interested in preference structures having an interval representation. For this purpose, we propose a general framework which makes use of n-point intervals and allows a systematic analysis of such structures. The case of 3-point intervals shows us that our framework generalizes the classification of Fishburn by defining new structures. Especially we define three classes of ordered sets having a non-transitive indifference relation. A simple generalization of these structures provides three ordered sets that we call “d-weak orders”, “d-interval orders” and “triangle orders”. We prove that these structures have an interval representation. We also establish some links between the relational and the forbidden mode by generalizing the definition of a Ferrers relation.

Valued Hesitation in Intervals Comparison

The paper presents a valued extension of the recently introduced concept of PQIinterval order. The main idea is that, while comparing objects represented by interval of values there is a zone of hesitation between strict difference and strict similarity which could be modelled through valued relations. The paper presents suitable definitions of such valued relations fulfilling a number of interesting properties. The use of such a tool in data analysis and rough sets theory is discussed in the paper.

On the use of a multicriteria decision aiding tool for the evaluation of comfort

In this paper we present a real word application of multicriteria decision aiding for the evaluation of high speed trains comfort from passengers’s point of view. Our study is used as a feasibility analysis for the introduction of multicriteria tools in the SNCF. Our approach concerns different steps of a decision aiding procedure. We firstly define the complex notion of comfort and propose to use a hierarchical model for its representation. We then present in more detail the seating comfort by assigning value scales to its components. Our problem being a sorting problem and our data being very heterogeneous, we decide to use the ELECTRE TRI method for the aggregation of the components. The article presents how the decision parameters, such as thresholds, weights and limit profiles, of ELECTRE TRI are selected and conclude with three fictitious assignment examples.

A valued Ferrers relation for interval comparison

The paper deals with the valued comparison of intervals for decision making. Interval orders are classical preference structures where the comparison of intervals is done in an ordinal way. In this paper we focus on valued comparison where more information, especially the distance between end-points of intervals, is used in order to have more sophisticated preference structures. The generalization of an interval order as a valued structure requires the choice of de Morgan triplets. We propose a valued outranking relation for interval comparison and show that it satisfies different definitions of valued interval orders using different de Morgan triplet. The decomposition of our outranking relation into preference and indifference provides a valued preference structure where the preference is T-transitive and monotone.

The effect of bi-criteria conflict on matching-elicited preferences

We focus on multicriteria preference elicitation by matching. In this widely employed task, the decision maker (DM) is presented with two multicriteria options, a and b, and must assess the performance value on one criterion for b, left blank, so that she is indifferent between the two options. A reverse matching, which is normatively equivalent, can be created by integrating the answer to the description of b and letting the DM adjust a performance value on the previously totally specified option a. Such a procedure is called a bi-matching. Consistency requires that isopreferences resulting from the forward and backward matchings be identical, but they empirically differ in a systematic direction. In a matching task, multicriteria conflict refers to the magnitude of the advantage or disadvantage to be compensated. We investigate the effect of the multicriteria conflict, or trade-off size, on the difference of judgement between forward and backward matchings. We observed that the difference of judgement is increased both by multicriteria conflict and by asking deteriorating rather than improving judgements at both steps of the bi-matching. We derive some implications for the practice of preference elicitation.

Aggregating Interval Orders by Propositional Optimization

Aggregating preferences for finding a consensus between several agents is an important issue in many fields, like economics, decision theory and artificial intelligence. In this paper we focus on the problem of aggregating interval orders which are special preference structures allowing the introduction of tresholds for the indifference relation. We propose to solve this problem by first translating it into a propositional optimization problem, namely the Binate Covering Problem, then to solve the latter using a max-sat solver. We discuss some properties of the proposed encoding and provide some hints about its practicability using preliminary experimental results.

Representing Interval Orders by Weighted Bases: some Complexity Results

This paper is centered on the notion of interval order as a model for preferences. We introduce a family of representation languages for such orders, parameterized by a scale and an aggregation function. We show how interval orders can be represented by elements of those languages, called weighted bases. We identify the complexity of the main decision problems to be considered for exploiting such representations of interval orders (including the comparison problems and the non-dominance problem). We also show that our representation of interval orders based on weighted bases encompasses the penalty-based representation of complete preorders as a specific case.