Our knowledge on an unspecified situation, is generally imperfect, either

• because we have a doubt about its validity (it is then uncertain), or
• because we feel some difficulty in expressing it clearly (it is then imprecise).

These two types of imperfection of knowledge are often closely combined. Thus, the real world appears both imprecise and uncertain.

Scarcely two elements, considered as similar, have exactly the same characteristics. For instance, two twins generally differ from one another in small details. Moreover, natural events have not always obvious boundaries, such that the transition between day and night. Even well-known data of the universe are sometimes rough, such that the period of gestation of a human being.

Moreover, our ability to understand the universe is limited by the instruments of observation used, even our eyes. So, the observations that we get upon the universe can be rough and uncertain.

With regard to imprecision, the human mind has remarkable powers of recognition and reasoning. It is naturally able to classify elements having similar properties. For instance, it can recognize a dog, assess the approximate age of somebody by watching him, identify a voice, without using a precise list of criteria.

In the same way, it can deal with data spoilt by uncertainty.