Study of T-norms and Quantum Logic Functions on BL-algebra and Their Relationships to the Classical Probability Structures

Ahmed  AL-Adilee; Habeeb Kareem  Abdullah; Hawraa A.  AL-Challabi

doi:10.24996/ijs.2020.61.3.15

Authors

Ahmed AL-Adilee Department of Math., Faculty of Education, University of Kufa, Kufa, Iraq.
Habeeb Kareem Abdullah Department of Math., Faculty of Education for Girls, University of Kufa, Kufa, Iraq.
Hawraa A. AL-Challabi Department of Math., Faculty of Education for Girls, University of Kufa, Kufa, Iraq

DOI:

https://doi.org/10.24996/ijs.2020.61.3.15

Keywords:

BL-algebra, T-norms, Quantum Logic Functions, Probability Space, States

Abstract

This paper is concerned with the study of the T-norms and the quantum logic functions on BL-algebra, respectively, along with their association with the classical probability space. The proposed constructions depend on demonstrating each type of the T-norms with respect to the basic probability of binary operation. On the other hand, we showed each quantum logic function with respect to some binary operations in probability space, such as intersection, union, and symmetric difference. Finally, we demonstrated the main results that explain the relationships among the T-norms and quantum logic functions. In order to show those relations and their related properties, different examples were built.