Fuzzy Preference Model Research Articles

Logical foundation of fuzzy preferential systems with application to the electre decision aid methods

In this paper we introduce split truth/falseness semantics for a multi-valued logical processing of fuzzy preference modelling. Our approach takes as starting point the standard framework of fuzzy outranking relations as proposed by the French multi-criteria decision aid community. Formal links between a given relational credibility calculus and associated truth polarization techniques will be discussed. The main result is the establishment of a multi-valued logical framework which allows us to naturally postpone any necessary defuzzification step to the end of the decision problem. Scope and purpose In this paper we propose an innovative multi-valued logical framework for processing fuzzy preferential information as is common in the context of multi-criteria preference modelling. Our results concern a methodological and computational enhancement of the Electre decision aid methods as promoted by the French school of decision aid around the work of B. Roy and D. Bouyssou (Roy. Méthodologie Multicritère d'Aide à la Décision. Paris: Economica, 1985; Roy and Bouyssou. Aide Multicritère à la Décision: Methodes et cas. Paris: Economica, 1993). The main achievement concerns the implementation of a logically coherent defuzzification technique in order to make commute logical reasoning and defuzzification of preferential information.

Structure of left-continuous triangular norms with strong induced negations (I) Rotation construction

ABSTRACT A new algebraic construction -called rotation- is introduced in this paper which from any left-continuous triangular norm which has no zero divisors produces a left-continuous but not continuous triangular norm with strong induced negation. An infinite number of new families of such triangular norms can be constructed in this way which provides a huge spectrum of choice for e.g. logical and set theoretical connectives in non-classical logic and in fuzzy theory. On the other hand, the introduced construction brings us closer to the understanding the structure of these connectives and the corresponding logics. From the application point of view, results of this paper can be especially useful in the field of non-classical logic, fuzzy sets, and fuzzy preference modeling.

Fuzzy Ranking for Concept Evaluation in Configuration Design for Mass Customization

Aiming at configuration design for mass customization, this paper develops a fuzzy ranking methodology for concept evaluation The fuzzy preference relation is applied to modeling the fuzziness on the level of a single critenon as well as on a global level. The ranking approach integrates linguistic terms and fuzzy numbers into the fuzzy preference model so as to characterize both intangible and tangible criteria. In addition, the information content is employed to synchronize diverse measures of design criteria into a common metric and con nect customer satisfaction to the technical capabilities of a design. Moreover, the fuzzy line segment is employed to fuzzify the cnsp meas urements of tangible criteria in order to be compatible with the universe of discourse defined for the intangible criteria. Furthermore, a more rigorous procedure for determining subjective customer preferences, Saaty's analytic hierarchy process, is applied to the fuzzy analysis

On the equiponderate equation xa+xb+x=xc+xd+1 and a representation of weight quadruplets

The equation xa+xb+x=xc+xd+1 considered in this paper is a particular equiponderate equation. The number and location of the roots (w.r.t. x = 1) of this equation are determined in case (a,b,c,d)∈]0,1[4. Based on these results, it is shown that any weight quadruplet, a basic tool in fuzzy preference modelling, admits an interesting expression in terms of Frank t-norms with reciprocal parameters.

An axiomatic approach to fuzzy preference modelling

We propose an axiomatic approach to the definition of fuzzy strict preference P, indifference I and incomparability J associated with a fuzzy preference relation R. Expression for P, I and J are given via solving two systems of functional equations.