Mathematics and Statistics Vol. 14(1), pp. 98 - 105
DOI: 10.13189/ms.2026.140109
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A Multi-fuzzy Set Theoretic Framework for Unanimity Measures

Priyanka P ^1,*, Sabu Sebastian ², Ramakrishnan T V ¹, Bijumon R ³, Rejeesh C John ⁴, Haseena C ¹, Gafoor I ^1
1 Department of Mathematical Sciences, Kannur University, Kannur, 670567, India
² Department of Mathematics, Nirmalagiri College, Nirmalagiri, Kannur, Kerala, 670701, India
³ Department of Mathematics, Mahatma Gandhi College, Iritty, Kannur, Kerala, 670703, India
⁴ Department of Statistics, Nirmalagiri College, Nirmalagiri, Kannur, Kerala, 670701, India

ABSTRACT

This paper introduces and explores a range of distance measures defined on multi-fuzzy sets, emphasizing both their mathematical foundations and applicability to real-world decision environments. Classical distance metrics such as Minkowski, Hamming, and Euclidean measures are extended to the multi-fuzzy context, and their behaviour is analysed at both the set and element levels. The proposed formulations are rigorously analyzed at both the set level and element level to capture variations in structure and similarity more precisely. The study further examines how these measures are affected when multi-fuzzy sets are transformed via crisp functions or adjusted using fuzzy weight matrices. The Minkowski distance in the original multi-fuzzy sets dominates or bounds the corresponding distance in the multi-fuzzy weighted sets via fuzzy matrix transformation. In addition to these classical extensions, this paper introduces new deviation-based and normalised measures aimed at quantifying unanimity and consensus within group decision-making processes. By extending classical statistical notions such as mean, variance, and standard deviation into the multi-fuzzy domain, the authors develop refined methods for assessing agreement among individual judgments. These are further strengthened through the use of weighted criteria to reflect varying importance. A numerical case study is provided to demonstrate the practical effectiveness of the proposed approach in real-world consensus evaluation. By improving the accuracy of collective decision-making models, the research contributes to transparent, equitable, and evidence-based decision support systems in fields such as education, healthcare, and policy analysis. The study is primarily theoretical and validated through a limited case study; future work may involve empirical validation across larger datasets or multi–fuzzy–neutrosophic extensions.

KEYWORDS
Multi-fuzzy Set, Multi-fuzzy Measure, σ−distance Measure, Measure of Unanimity

Cite This Paper in IEEE or APA Citation Styles
(a). IEEE Format:
[1] Priyanka P , Sabu Sebastian , Ramakrishnan T V , Bijumon R , Rejeesh C John , Haseena C , Gafoor I , "A Multi-fuzzy Set Theoretic Framework for Unanimity Measures," Mathematics and Statistics, Vol. 14, No. 1, pp. 98 - 105, 2026. DOI: 10.13189/ms.2026.140109.

(b). APA Format:
Priyanka P , Sabu Sebastian , Ramakrishnan T V , Bijumon R , Rejeesh C John , Haseena C , Gafoor I (2026). A Multi-fuzzy Set Theoretic Framework for Unanimity Measures. Mathematics and Statistics, 14(1), 98 - 105. DOI: 10.13189/ms.2026.140109.