| Crispness in Dedekind Categories (2007) | |||||||||||||||
Abstract | |||||||||||||||
| . This paper studies notions of scalar relations and crispness of relations. 1 Introduction Just after Zadeh's invention of the concept of fuzzy sets [19], Goguen [5] generalized the concepts of fuzzy sets and relations to taking values on arbitrary lattices. On the other hand, the theory of relations, namely relational calculus, has been investigated since the middle of the nineteen century, see [13, 16, 17] for more details. Almost all modern formalisations of relation algebras are affected by the work of Tarski [18]. Mac Lane [12] and Puppe [15] exposed a categorical basis for the calculus of additive relations. Freyd and Scedrov [2] developed and summarized categorical relational calculus, which they called allegories. In relational calculus one calculates with relations in an element-free style, which makes relational calculus a very useful framework for the study of mathematics [8] and theoretical computer science [1, 7, 11] and also a useful tool for applications. Some element... | |||||||||||||||
Publication details | |||||||||||||||
| |||||||||||||||