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Decision-Making Approach with Fuzzy Type-2 Soft Graphs

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  • Sundas Shahzadi
  • Musavarah Sarwar
  • Muhammad Akram
  • Lemnaouar Zedam

Abstract

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.

Suggested Citation

  • Sundas Shahzadi & Musavarah Sarwar & Muhammad Akram & Lemnaouar Zedam, 2020. "Decision-Making Approach with Fuzzy Type-2 Soft Graphs," Journal of Mathematics, Hindawi, vol. 2020, pages 1-25, November.
    • Handle: RePEc:hin:jjmath:8872446
    DOI: 10.1155/2020/8872446
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