Document Type : Original Manuscript


1 Hatef Higher Education Institute, P.O. Box 9816848165, Zahedan, Iran.

2 Department of Mathematics, University of Sistan and Baluchestan, P.O. Box 98167- 45845, Zahedan, Iran.

3 Department of Mathematics, Shahid Beheshti University, P.O. Box 1983969411, Tehran, Iran.

4 Department of Mathematics, Education, Gyeongsang National University, P.O. Box 52828, Jinju, Korea.


Based on subalgebras and filters in hoops, the notions of S-quasi-valuation maps and F-quasi-valuation maps are introduced, and related properties are investigated. Relations between S-quasi-valuation maps and F-quasi-valuation maps are introduced. Using F-quasi-valuation map, a (pseudo) metric space is indued, and we show that the operations “⊙”, “→” and “∧” in a hoop are uniformly continuous.