Document Type: Original Manuscript
Hatef Higher Education Institute, P.O. Box 9816848165, Zahedan, Iran.
Department of Mathematics, University of Sistan and Baluchestan, P.O. Box 98167- 45845, Zahedan, Iran.
Department of Mathematics, Shahid Beheshti University, P.O. Box 1983969411, Tehran, Iran.
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.