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 π the value H(π) 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 π 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.