Intuitionistic Fuzzy Rough Graphs with Applications

Abstract

Intuitionistic fuzzy sets, neutrosophic sets, rough sets and soft sets are different mathematical tools to deal the problem of how to understand and manipulate imperfect knowledge. The intuitionistic fuzzy rough framework and soft rough neutrosophic framework are made by combining these models, which are more flexible and expressive for modeling and processing incomplete information in information systems. The notions of intuitionistic fuzzy rough sets and soft rough neutrosophic sets are applied to graph theory in this thesis. Novel hybrids models, namely, intuitionistic fuzzy rough graphs and soft rough neutrosophic influence graphs are introduced. Certain methods of their construction are developed. Further, efficient algorithms are developed to solve decision-making problems. The time complexity of the algorithms is computed. Moreover, MATLAB coding of the algorithms is given for the implementation of the proposed hybrid models.