Uncertainty and Indistinguishability

The concept of equality is a fundamental notion in any theory since it is essential to the ability of discerning objects. When all the properties involved are entirely precise what we obtain is the classical equality, where two individuals are considered equal if and only if they share the same set of properties. What happens, however, when imprecision arises as in the case of properties which are fulfilled only up to a degree? Then, because certain individuals will be more similar than others, the need for a gradual notion of equality arises. These considerations show that certain contexts that are pervaded with uncertainty require a more flexible concept of equality that goes beyond the rigidity of the classic one. This book explores uncertainty and its counterpart notion, indistinguishability, both from theorethical and practical points of view. Applications to the "Computing with Words" paradigm are also presented.