An Intuitionistic Fuzzy Hamming and Euclidean Hesitance Distance Measure for Environmental Sustainability Decision-Making

M Kaviyarasu; Nasreen Kausar

doi:10.67334/cds31202638

Authors

M Kaviyarasu Department of mathematics, Vel Tech Rangarajan Dr. Sagunthala R&D Institute of Science and Technology Avadi, Chennai, India Author https://orcid.org/0000-0002-4709-1857
Nasreen Kausar Department of Mathematics, Faculty of Arts and Science, Balikesir University, Balikesir, Turkey Author https://orcid.org/0000-0002-8659-0747

DOI:

https://doi.org/10.67334/cds31202638

Keywords:

Intuitionistic fuzzy set, Euclidean Hesitance distance measure, Hamming Hesitance distance measure, Decision-Making, Environmental Sustainability

Abstract

Intuitionistic fuzzy distance measures play a fundamental role in modeling uncertainty in multi-criteria decision-making; however, most existing measures do not explicitly exploit hesitation information, which may limit their ability to distinguish alternatives under uncertain conditions. To address this limitation, this study introduces two novel intuitionistic fuzzy distance measures, namely the Euclidean hesitance distance and the Hamming hesitance distance. Unlike conventional approaches that primarily rely on membership and non-membership degrees, the proposed measures explicitly incorporate hesitation, providing a more comprehensive representation of uncertainty and ambiguity. Their mathematical properties are formally established to ensure theoretical consistency and applicability in decision-making environments. To demonstrate their practical usefulness, the proposed measures are applied to an environmental sustainability assessment problem, where evaluations are often characterized by incomplete, vague, and conflicting information. A systematic algorithm is developed to compute and compare the sustainability performance of multiple regions using both distance measures. The application illustrates how incorporating hesitation information enhances the representation of uncertainty and supports a more informative evaluation process. The proposed framework extends the methodological foundations of intuitionistic fuzzy distance measures and provides an effective tool for sustainability assessment and other decision-making problems involving uncertain and ambiguous information.

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