Affiliations: [a] Research Institute for Natural Sciences, Department of Mathematics, Hanyang University, Seoul, Korea
| [b] Department of Mathematics, University of Alabama, Tuscaloosa, AL, USA
| [c] Department of Mathematics Education, Dongguk University, Seoul, Korea
Correspondence:
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Corresponding author. Sun Shin Ahn, Department of Mathematics Education, Dongguk University, Seoul, Korea. E-mail: sunshine@dongguk.edu.
Abstract: In this paper, we introduce the notions of an almost φ-fuzzy subalgebra and an almost φ-fuzzy semi-ideal in groupoids by using the concept of a function. This concepts are generalizations of a fuzzy subalgebra and a fuzzy ideal in groupoids respectively. We discuss some relations between almost φ-fuzzy subalgebras and vanishing, level subsets. By introducing the notions of (μ, φ)-extremes, e-ideals, we obtain several properties of almost φ-fuzzy subalgebras. The relations between almost φ-fuzzy semi-ideals and (μ, φ)-special elements are discussed. Finally we discuss fuzzy algebraic structures of almost φ-fuzzy semi-ideals by diagrams.
