| Crispness and Representation Theorem in Dedekind Categories (1997) | |||||||||||||||
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| DOI DOI Technical Report Crispness and Representation Theorem Dedekind Categories Yasuo KAWAHARA and Hithoshi FURUSAWA December Department Informatics Kyushu University Fukuoka Japan Email fkawahara furusawag kyushu Phone Crispness and Representation Theorem Dedekind Categories Yasuo KAWAHARA Lambda and Hitoshi FURUSAWA Lambda December Abstract This paper studies notions scalar relations and crispness relations Introduction Since Zadeh invention the concept fuzzy sets has been extensively investigated mathematics science and engineering The notion fuzzy relations also basic one processing fuzzy information relational structures see Pedrycz Goguen generalized the concepts fuzzy sets and relations taking values from partially ordered sets Fuzzy relational equations were initiated and applied medical models diagnosis Sanchez the other hand the theory relations namely relational calculus has long history see for more details Almost all modern formalizations relation algebras are affected the work Tarski Mac Lane and Puppe exposed categorical basis for the calculus additive relations Freyd and Scedrov veloped and summarized categorical relational calculus which they called allegories Concerning applications the relational theory graphs and programs Schmidt and Str ohlein gave simple proof representation theorem for Boolean relation algebras satisfying the Tarski rule and the point axiom They also wrote excellent text book relations and graphs with many useful examples from compute | |||||||||||||||
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