A trapezoidal fuzzy TOPSIS method for solving decision-making problems under uncertainty

Authors

  • Appasamy Saraswathi * Department of Mathematics, SRM Institute of Science and Technology, Kattankulathur – 603 203, Tamilnadu, India. https://orcid.org/0000-0003-0529-4346
  • P Nedumaran Department of Mathematics, Guru Nanak College, Chennai, Tamilnadu, India.

https://doi.org/10.48313/uda.v2i3.75

Abstract

A fuzzy set is a mathematical construct that assigns a membership grade to each element within a universe of discourse, representing the degree to which the element belongs to the set. This approach extends classical binary logic by allowing continuous values between 0 and 1, making it a natural framework for handling uncertainties and vague concepts often expressed in natural language. Fuzzy sets are particularly powerful in modeling real- world scenarios where ambiguity and imprecision are inherent, such as in human decision-making, linguistic expressions, and complex systems. In order to analyze the ranking using the problems of transgender people, we developed a Fuzzy Multiple Criteria Decision Making (FMCDM) problem in this paper. We used the Technique for Order Performance by Similarity to the Ideal Solution (TOPSIS) and the new concept of positive and Negative Ideal Solutions (NIS), along with the weights of criteria in linguistic terms. The suggested approach gives us a practical means of addressing the fuzzy multiple attribute group decision-making problem. Therefore, an extension of the TOPSIS method is proposed using a Trapezoidal Fuzzy Number (TpFN), where the correlation information among factors provided by experts is in the form of uncertain linguistic terms and is transformed into a TpFN. At the conclusion of this paper, an example is provided to illustrate the steps involved in the suggested method.

Keywords:

Positive ideal solutions and negative ideal solutions, Trapezoidal fuzzy numbers, Transgender and fuzzy TOPSIS decision making

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Published

2025-09-16

Issue

Vol. 2 No. 3 (2025): Uncertainty Discourse and Applications

Section

Articles

How to Cite

Saraswathi, A., & Nedumaran, P. (2025). A trapezoidal fuzzy TOPSIS method for solving decision-making problems under uncertainty. Uncertainty Discourse and Applications, 2(3), 227-244. https://doi.org/10.48313/uda.v2i3.75

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