Abstract:
Vagueness arises in several complex issues of engineering, science and many other
fields. These issues cannot be resolved using crisp mathematical methods. Rough
set theory is an approach for dealing with the inaccurate and ambiguous knowledge.
Because of the confinement of human’s learning to comprehend the perplexing issues,
it is exceptionally hard to apply one kind of uncertainty technique to address such
issues. Consequently, it is important to build hybrid models by combining the benefits
of numerous other diverse mathematical models dealing with uncertainty. In this
dissertation, the concepts and methods of fuzzy sets, rough sets and soft sets are
applied to construct rough fuzzy digraphs and soft rough fuzzy digraphs. Several
new concepts, concerning these digraphs are introduced. Also various properties of
these two models are discussed in detail. Some real world problems are also presented
and solved through these graphical models. Furthermore, efficient algorithms are
designed to solve these problems and the time complexity of these algorithms are also
computed.
