LATTICE-VALUED POSSIBILISTIC ENTROPY MEASURE
Since almost fifty years, Shannon entropy measure has been used as a very powerful tool when quantifying and processing the amount of randomness contained in probability distributions. In this paper we propose a lattice-valued entropy measure H ascribing to each lattice-valued possibilistic distribution pi the value H (pi) defined as the expected value (in the sense of lattice-valued Sugeno integral with infimum in the role of t-norm) of certain nonincreasing function of the values ascribed to the elements of the basic space by the possibilistic distribution pi in question. The main result reads that, for completely distributive complete lattices, the entropy value ascribed to possibilistically independent product of a finite number of lattice-valued possibilistic distributions is defined by the supremum of the entropy values ascribed to particular distributions.
entropy measure lattice-valued possibilistic distribution complete lattice product of possibilistic distribution