Varieties of Linguistic Intuitionistic Fuzzy Distance Measures for Linguistic Intuitionistic Fuzzy TOPSIS Method

A Leonishiya; John Robinson

doi:10.17485/IJST/v16i33.640-icrsms

Article

Varieties of Linguistic Intuitionistic Fuzzy Distance Measures for Linguistic Intuitionistic Fuzzy TOPSIS Method

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Indian Journal of Science and Technology

DOI: 10.17485/IJST/v16i33.640-icrsms

Year: 2023, Volume: 16, Issue: 33, Pages: 2653-2662

Original Article

Varieties of Linguistic Intuitionistic Fuzzy Distance Measures for Linguistic Intuitionistic Fuzzy TOPSIS Method

A Leonishiya^1*, John Robinson¹

¹Department of Mathematics, Bishop Heber College, Affiliated to Bharathidasan University, 620017, Tiruchirappalli

*Corresponding Author
Email: [email protected]

Received Date:22 June 2023, Accepted Date:23 June 2023, Published Date:08 September 2023

This work is licensed under a Creative Commons Attribution 4.0 International License.

Abstract

Objective: In this paper we propose various Linguistic Intuitionistic Fuzzy Distance Measures (LIFDMs) for Linguistic Intuitionistic Fuzzy Sets (LIFSs) which are then utilized in the Linguistic Intuitionistic Fuzzy-Technique of Order Preference by Similarity to Ideal Solution (LIF-TOPSIS) method of Decision Support Systems (DSS). Methods: Some novel distance measures including membership, non-membership degrees and the linguistic index and distance measures based on Hausdorff metric are proposed in this work and related theorems are proved. Findings: The proposed distance measures are used to find the weights involved in the TOPSIS method. Numerical illustration is presented for the LIF-TOPSIS method and comparisons are made with existing ranking method and the ranking methods obtained from the different distance measures. The comparison study reveals the consistency of the ranking of the best alternative from the final ranking of the alternatives through the proposed distance measures. Novelty: Most of the researchers have done decision making with Linguistic Intuitionistic Fuzzy Sets, where the best alternatives are chosen using traditional distance measures involving only the intuitionistic fuzzy number or using some other calculations. In this paper we have proposed varieties of distance measures involving intuitionistic characterization and the linguistic characterization and proved that those distance measures are metrices. Using these different metrices we have derived different weight vectors for LIF-TOPSIS and the results give consistent decision for the discussed numerical illustration.

Keywords: Linguistic Intuitionistic Fuzzy Sets (LIFSs); LIF-TOPSIS; Decision Support System (DSS); MAGDM; Linguistic Distance Measures

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Copyright

© 2023 Leonishiya & Robinson. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Published By Indian Society for Education and Environment (iSee)