In this paper, the set of all probability functions on L* is studied, where L* is the lattice of bothvalued fuzzy sets or intuitionistic fuzzy sets. It is shown that the set of all probability functions on L* endowed with two appropriate operations has a monoid structure which is also a distributive complete lattice. Also the lattice structure of the set of all probability functions on L* induced by an appropriate function on [0, 1] to itself is studied. Some lattice (dual) isomorphisms are discussed that suggests probabilities on L* could be considered in the framework of theories modeling imprecision.
Mashinchi, Mashaallah and Khaledi, Ghader
On Lattice Structure of the Probability Functions on L*,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 7,
1, Article 5.
Available at: https://digitalcommons.pvamu.edu/aam/vol7/iss1/5