Annals of Fuzzy Mathematics and Informatics Volume 12, No. 6, (December 2016), pp. 739–756 ISSN: 2093–9310 (print version) ISSN: 2287–6235 (electronic version) http://www.afmi.or.kr @FMI c  Kyung Moon Sa Co. http://www.kyungmoon.com Fuzzy sets in UP-algebras Jaruwat Somjanta, Natthanicha Thuekaew, Praprisri Kumpeangkeaw, Aiyared Iampan Received 6 December 2014; Revised 4 February 2015; Accepted 8 February 2015 Abstract. The aim of this paper is to introduce and study fuzzy UP-subalgebras, fuzzy UP-ideals and fuzzy UP-filters of UP-algebras and investigate some of its properties. The notions of upper t-(strong) level subsets and lower t-(strong) level subsets are introduced from some fuzzy sets, and its characterizations are given. 2010 AMS Classification: 03G25 Keywords: UP-algebra, Fuzzy UP-subalgebra, Fuzzy UP-ideal, Fuzzy UP-filter, Upper t-(strong) level subset, Lower t-(strong) level subset. Corresponding Author: Aiyared Iampan (aiyared.ia@up.ac.th) 1. Introduction and preliminaries Among many algebraic structures, algebras of logic form important class of algebras. Examples of these are BCK-algebras [6], BCI-algebras [7], BCH-algebras [4], KU-algebras [18], SU-algebras [14] and others. They are strongly connected with logic. For example, BCI-algebras introduced by Is´ eki [7] in 1966 have connections with BCI-logic being the BCI-system in combinatory logic which has application in the language of functional programming. BCK and BCI-algebras are two classes of logical algebras. They were introduced by Imai and Is´ eki [6, 7] in 1966 and have been extensively investigated by many researchers. It is known that the class of BCK-algebras is a proper subclass of the class of BCI-algebras. A fuzzy subset f of a set S is a function from S to a closed interval [0, 1]. The concept of a fuzzy subset of a set was first considered by Zadeh [25] in 1965. The fuzzy set theories developed by Zadeh and others have found many applications in the domain of mathematics and elsewhere. After the introduction of the concept of fuzzy sets by Zadeh [25], several re- searches were conducted on the generalizations of the notion of fuzzy set and ap- plication to many logical algebras such as: In 2000, Jun [8] introduced the notion of M -BCK/BCI-algebras and M -fuzzy subalgebras for a set M , and investigated