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In this paper, we explore the solution of functional equations I(x,T(y,z)) = T(I(x,y),I(x,z)) and I(x,y) = I(N(y),N(x)) satisfied simultaneously, where T is a strict t-norm, I a fuzzy implication and N a strong negation. Under the assumptions of I continuous except the points (0, 0) and (1, 1), we get the full characterizations of the solutions for this functional equations.
Consistency of preferences is related to rationality, which is associated with the transitivityproperty. Many properties suggested to model transitivity of preferences are inappropriate for reciprocal preference relations. In this paper, a functional equation is put forward to model the ldquocardinal consistency in the strength of preferencesrdquo of reciprocal preference relations. We show that...
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.
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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