Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

Neural networks and fuzzy logic are two bio-mimetic techniques that are used to provide approximations to real-world problems. While for some people this biological plausibility provides some justification for their use, for others the important point is that, regardless of their origins, both approaches are known to be robust alternatives to conventional deterministic and programmed models. Ho...

We reformulate Mesiar’s hypothesis [Possibility measures, integration and fuzzy possibility measures, Fuzzy Sets and Systems 92 (1997) 191196], which as such was shown to be untrue by Murofushi [Two-valued possibility measures induced by σ-finite σ-additive measures, Fuzzy Sets and Systems 126 (2002) 265268]. We prove that a two-valued σ-maxitive measure can be induced by a σ-additive measure u...

Cutting, Bruno, Brady, and Moore (1992) investigated the properties of Massaro's (1987) fuzzy-logical model of perception (FLMP) and other models. Among their results, they found that FLMP and an additive model fit the data of individuals' judgments of depth about equally well, that the additive model fit the group data better, and that FLMP fit random data better. Massaro and Cohen (1993) ques...

The G_DACG (Genetic Discovery of Additive Cartesian Granule feature models) constructive induction algorithm is presented as a means of automatically identifying rulebased Cartesian granule feature models from example data. G_DACG combines the powerful search capabilities of genetic programming with a rather novel and cheap fitness function based upon the semantic separation of learnt concepts ...

The family of k-additive measures has been introduced as a midterm between probabilities and general fuzzy measures and finds a wide number of applications in practice. However, its structure is different from other families of fuzzy measures and is certainly more complex (for instance, its vertices are not always {0, 1}valued), so it has not been yet fully studied. In this paper we present som...

The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation