Afr. Mat. DOI 10.1007/s13370-016-0414-3 Quotient BCK/BCI-algebras induced by soft sets Young Bae Jun 1 · Seok Zun Song 2 Received: 9 October 2014 / Accepted: 4 March 2016 © African Mathematical Union and Springer-Verlag Berlin Heidelberg 2016 Abstract The present paper deals with a new quotient structure of BCK/BCI-algebras using int-soft ideals. The fundamental homomorphism theorem of quotient BCK/BCI-algebras is established. Characterizations of commutative (implicative, positive implicative) quotient BCK/BCI-algebras are discussed. Keywords BCK/BCI-algebra · Ideal · Soft set · Int-soft ideal · Commutative (implicative, positive implicative) BCK-algebra Mathematics Subject Classification 06F35 · 03G25 · 06D72 1 Introduction For the general development of BCK/BCI-algebras, the ideal (filter) theory plays an important role. Of course, the quotient structure by ideals (filters) plays an important role also. Using the notion of fuzzy ideals (filters) in BCK/BCI-algebras, the quotient structures of BCK/BCI- algebras are discussed in [6, 9, 11, 20, 21]. Molodtsov [23] introduced the concept of soft set as a new mathematical tool for dealing with uncertainties, which are an attribute of information, that is free from the difficulties that have troubled the usual theoretical approaches. The algebraic structure of set theories dealing with uncertainties has been studied by some authors. Çaˇ gman et al. [3] introduced fuzzy parameterized (FP) soft sets and their related properties. Feng [4] considered the application of soft rough approximations in multicriteria group B Seok Zun Song szsong@jejunu.ac.kr Young Bae Jun skywine@gmail.com 1 Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea 2 Department of Mathematics, Jeju National University, Cheju 690-756, Korea 123