Open AccessFuzzy Translations of A Fuzzy Set in UP-Algebras
Author(s) -
Aiyared Iampan
Publication year - 2017
Publication title -
journal of the indonesian mathematical society
Language(s) - English
Resource type - Journals
eISSN - 2460-0245
pISSN - 2086-8952
DOI - 10.22342/jims.23.2.371.1-19
Subject(s) - mathematics , fuzzy subalgebra , fuzzy logic , prime (order theory) , algebra over a field , fuzzy set , fuzzy number , type (biology) , fuzzy classification , fuzzy mathematics , type 2 fuzzy sets and systems , set (abstract data type) , pure mathematics , discrete mathematics , combinatorics , artificial intelligence , computer science , ecology , biology , programming language
In this paper, we apply the concept of fuzzy translations of a fuzzy set to UP-algebras.For any fuzzy set $\mu$ in a UP-algebra,the concepts of fuzzy $\alpha$-translations of $\mu$ of type \textrm{I} and of fuzzy $\beta$-translations of $\mu$ of type \textrm{II} are introduced, their basic properties are investigated and some useful examples are discussed.The concepts of prime fuzzy sets and of weakly prime fuzzy sets in UP-algebras are also studied.Moreover, we discuss the concepts of extensions and of intensions of a fuzzy set in UP-algebras.