Managing the uncertainty: from probability to fuzziness, neutrosophy and soft sets

The present paper reviews and compares the main theories reported in the literature for managing the existing real life uncertainty by listing their advantages and disadvantages. Starting with a comparison of the bivalent logic (including probability) and fuzzy logic, proceeds to a brief description of the primary generalizations of fuzzy sets (FSs) including interval valued FSs, type-۲ FSs, intuitionistic FSs, neutrosophic sets, etc. Alternative theories related to fuzziness are also examined including grey system theory, rough sets and soft sets. The conclusion obtained at the end of this discussion is that there is no ideal model for managing the uncertainty; it all depends upon the form, the available data and the existing knowledge about the problem under solution. The combination of all the existing models, however, provides a sufficient framework for efficiently tackling several types of uncertainty appearing in real life.

Keywords:

Uncertainty‎ , ‎Fuzzy set (FS)‎ , ‎Interval valued FS (IVFS)‎ , ‎Type-۲ FS‎ , ‎Intuitionistic FS (IFS)‎ , ‎Neutrosophic set (NS)‎ , ‎Rough set‎ , ‎Soft set‎ , ‎Grey system (GS)‎