Abstract
The concept of fuzzy supra soft topological spaces was presented by Abd El-latif [2]. He derived their fundamental properties in detail. In this paper, we investigated more properties to the concept of fss-compact spaces based on the finite intersection property and the fuzzy supra irresolute open soft functions and got some new important results. The concept of fssalmost compact spaces is introduced as a generalization to that's in [2]. Furthermore, many of its interested properties are provided. We introduced the notion of fss-generalized closed sets and use it to introduce another type of compactness, named fss-generalized compactness. Also, we introduced some fundamental definitions and theorems of these concepts.