When attempting to find the mechanism of the brain of a living being that is capable of bringing to light the most elemental symptom of intelligence, one must surely pay a great deal of attention to the concept of relation. If a domestic animal is accustomed to eat from a certain container, when it hears the particular noise it makes then it will run towards it: it associates and relates, noise-food. From our very earliest childhood we are taught to improve the devices that lead to relation, by developing in the very smallest, the most diverse kinds of connections: between things and colours, effort and prizes, between certain objects and others,... Teachers are very much aware of the importance of relation in the mental progress of a child. And the truth of the matter is that whatever activity is carried on, it is difficult to imagine any reasoning whatsoever in which relations are not present as a very basic support.
KeywordsFuzzy Relation Transitive Relation Fuzzy Graph Fuzzy Sphere Boolean Matrix
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- 1.See, for example, in this respect Kaufmann, A and Gil Aluja, J: Grafos neuronales para la economla y gestion de empresas. Ed. Pirdmide. Madrid 1995, page 18.Google Scholar
- 2.We have specifically place zeros when µ = 0 with the object of making obvious the custom of doing without the arcs in this case, when resorting to the arrow form representation.Google Scholar
- 3.In these types of square matrices we are going to use, for easy and visual effectiveness, the type of arrow form representation we show in this case.Google Scholar
- 4.We are not referring here to the case in which the intensity coincides in the relation a, with ai with that of the relation al with a,.Google Scholar
- 5.It would be advisable not to confuse “class of similarity” with “class of equivalence” or “strongly connected sub-graph”. In fact, for matrix [B], the sub-set formed byy fat, a4, as) is a class of equivalence but not a class of similarity, while in [B] it is one thing and the other.Google Scholar
- 6.Here we disregard the normal rules used for converting a fuzzy relation into a boolean relation, since we are only attempting to illustrate, by an example, the concept of pre-order.Google Scholar
- 7.We repeat the necessity to distinguish between similarity and equivalency class. The formation of maximum strongly connected sub-graphs or equivalency classes will be dealt with later on.Google Scholar
- 8.See in this respect Kaufmann, A, and Gil Aluja, J.: Nuevas técnicas para la direccidn estratégica. Publicaciones Universidad de Barcelona, Barcelona, 1991, page 117–147.Google Scholar
- 9.The development of the relations of incidence has permitted the formulation of the notion of forgotten effect. Anyone interested in this subject can consult: Kaufmann, A. and Gil Aluja, J.: Modelos para la investigaciOn de efectos olvidados. Ed Milladoiro. Santiago de Compostela, 1988.Google Scholar
- 10.Kaufmann, A. and Gil Aluja, J.: Modelos para la investigaciOn de efectos olvidados. Ed. Milladoiro. Santiago de Compostela, 1988.Google Scholar
- 11.Kaufmann, A. and Gil Aluja, J.: Técnicas operativas de gestion para el tratamiento de la incertidumbre. Ed. Hispano Europea. Barcelona 1987, pages 147–148.Google Scholar