Decision-Making Approach with Fuzzy Type-2 Soft Graphs

Abstract EN

Molodtsov’s theory of soft sets is free from the parameterizations insufficiency of fuzzy set theory.

Type-2 soft set as an extension of a soft set has an essential mathematical structure to deal with parametrizations and their primary relationship.

Fuzzy type-2 soft models play a key role to study the partial membership and uncertainty of objects along with underlying and primary set of parameters.

In this research article, we introduce the concept of fuzzy type-2 soft set by integrating fuzzy set theory and type-2 soft set theory.

We also introduce the notions of fuzzy type-2 soft graphs, regular fuzzy type-2 soft graphs, irregular fuzzy type-2 soft graphs, fuzzy type-2 soft trees, and fuzzy type-2 soft cycles.

We construct some operations such as union, intersection, AND, and OR on fuzzy type-2 soft graphs and discuss these concepts with numerical examples.

The fuzzy type-2 soft graph is an efficient model for dealing with uncertainty occurring in vertex-neighbors structure and is applicable in computational analysis, applied intelligence, and decision-making problems.

We study the importance of fuzzy type-2 soft graphs in chemical digestion and national engineering services.