6533b7d3fe1ef96bd1260c75

RESEARCH PRODUCT

Fuzzy functions: a fuzzy extension of the category SET and some related categories

Hans-e. PorstUlrich HöhleAlexander P. Sostak

subject

Discrete mathematicsFuzzy classificationL-relationFuzzy topologylcsh:MathematicsFuzzy setlcsh:QA299.6-433Fuzzy subalgebralcsh:AnalysisFuzzy groupType-2 fuzzy sets and systemslcsh:QA1-939DefuzzificationAlgebraFuzzy mathematicsL-fuzzy functionFuzzy numberFuzzy set operationsGeometry and TopologyFuzzy categoryMathematics

description

<p>In research Works where fuzzy sets are used, mostly certain usual functions are taken as morphisms. On the other hand, the aim of this paper is to fuzzify the concept of a function itself. Namely, a certain class of L-relations F : X x Y -> L is distinguished which could be considered as fuzzy functions from an L-valued set (X,Ex) to an L-valued set (Y,Ey). We study basic properties of these functions, consider some properties of the corresponding category of L-valued sets and fuzzy functions as well as briefly describe some categories related to algebra and topology with fuzzy functions in the role of morphisms.</p>

yearjournalcountryeditionlanguage
2000-10-01
10.4995/agt.2000.3028https://dx.doi.org/10.4995/agt.2000.3028