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On Lattice Structure Of The Probability Functions On L*, Mashaallah Mashinchi, Ghader Khaledi
On Lattice Structure Of The Probability Functions On L*, Mashaallah Mashinchi, Ghader Khaledi
Applications and Applied Mathematics: An International Journal (AAM)
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.