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In aggregation problems different types of information items can occur. In spite of such diversity, it is possible to reinterpret them approximately in a unique formal setting by means of profiles: an extension of fuzzy set membership functions. Then the original aggregation problem can be modelled by an appropriate profile aggregation. Therefore, in this paper we concentrate on and reconsider some...
In this paper we study possible extensions of classical difference structures when fuzzy relations are involved. In this framework quaternary fuzzy relations arise. Three models are introduced, based on three different interpretations of fuzzy implications. Functional forms of the quaternary fuzzy relation are determined by solutions of functional equations.
This paper gives an overview on some classes of binary connectives that play a key role in fuzzy logic. We start with left-continuous triangular norms, by recalling some facts about the nilpotent minimum and its extensions. Some standard construction methods are also described. We also deal with two possible extensions of t-norms: the classes of uninorms and nullnorms.
In this paper we completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent classes, the characterization and construction is carried out by solving a functional equation for additive generators of strict t-norms. We also study cases when the construction results in a smooth generator.
In this paper we completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent classes, the characterization and construction is carried out by solving a functional equation for additive generators of strict t-norms. We also study cases when the construction results in a smooth generator.
We investigate the problem of aggregation of fuzzy preference structures in multicriteria decision making. Starting from monocriterion weak preferences, there are two ways to define global strict preference, indifference and incomparability. We prove that, under very mild conditions, the only aggregation for which those two ways result in the same global preference structure is dictatorial.
Preference modelling is a fundamental part of several applied fields but at the same time it has its own interesting theoretical problems. There exists a well-known axiomatic approach to fuzzy preference structures. In this axiomatic framework, general constructions of strict preference, indifference and incomparability relations associated with a fuzzy large preference relation are established via...
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