Functions and \(\alpha I\)-compactness on fuzzy topological spaces (Q1313065)

The authors introduce \(\alpha I\)-compactness and characterize it in terms of fuzzy regular semiopen, fuzzy semiopen, and fuzzy \(\beta\)-open \(\alpha\)-shadings. In a fuzzy extremely disconnected space, \(\alpha I\)- compactness is shown equivalent to \(\alpha\)-compactness as well as \(\alpha\)-near compactness, \(\alpha\)-almost compactness, and the property of being \(\alpha S\) closed. They study images and preimages of \(\alpha I\)-compact sets under various weakenings of fuzzy continuity and openness. \(\alpha^*I\)-compactness is also defined and analogous results for the \(\alpha^*\) case are noted throughout the paper.