<p>There are numerous uses for trapezoidal intuitionistic fuzzy sets (TraIFSs), which include membership and non-membership functions in the form of trapezoidal fuzzy sets (TraFSs), for handling data that is ambiguous. The TraIFS distance based similarity metrics are designed to illustrate the similarities among various categories of sensitive fuzzy data. Nonetheless, certain current similarity metrics fail to satisfy the similarity axioms. Moreover, in other circumstances, they could not be utilized effectively. In this article, a novel distance based similarity measure between any two trapezoidal intuitionistic fuzzy numbers (TraIFNs) is defined and some of its important properties are proved and validated by numerical examples. It consists of two interrelated modules. In the first module consists of distance based similarity measure between TraIFNs and it is used for ranking procedure. For the second module, Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is used for real life application problems under TraIFN environment. The effectiveness of the proposed distance based similarity measure between TraIFNs is examined by solving the real life applications such as multi-criteria decision making (MCDM) method, pattern recognition problems and also compared over familiar existing methods. Finally, we obtain a general conclusions and future scope of the proposed method.</p>

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A distance based similarity measure on trapezoidal intuitionistic fuzzy numbers and its applications

  • P. Dhanasekaran,
  • S. Kalidasan

摘要

There are numerous uses for trapezoidal intuitionistic fuzzy sets (TraIFSs), which include membership and non-membership functions in the form of trapezoidal fuzzy sets (TraFSs), for handling data that is ambiguous. The TraIFS distance based similarity metrics are designed to illustrate the similarities among various categories of sensitive fuzzy data. Nonetheless, certain current similarity metrics fail to satisfy the similarity axioms. Moreover, in other circumstances, they could not be utilized effectively. In this article, a novel distance based similarity measure between any two trapezoidal intuitionistic fuzzy numbers (TraIFNs) is defined and some of its important properties are proved and validated by numerical examples. It consists of two interrelated modules. In the first module consists of distance based similarity measure between TraIFNs and it is used for ranking procedure. For the second module, Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) method is used for real life application problems under TraIFN environment. The effectiveness of the proposed distance based similarity measure between TraIFNs is examined by solving the real life applications such as multi-criteria decision making (MCDM) method, pattern recognition problems and also compared over familiar existing methods. Finally, we obtain a general conclusions and future scope of the proposed method.