SCALAR MULTIPLICATION AND RELATED MEASURES FOR INTERVAL-VALUED INTUITIONISTIC FUZZY MATRICES

Abstract

In this paper, we study several measures and algebraic properties of interval-valued intuitionistic fuzzy matrices. We define the Hamming, generalized Hamming, Euclidean, and generalized Euclidean measures and prove their main properties. We also show that these measures remain unchanged when both matrices are transposed. Next, we introduce scalar multiplication using a pair of parameters and examine its associativity and distributive properties. We then establish several identities and inequalities relating this operation to the Hamming and Euclidean measures. Examples illustrate how scalar multiplication works and help explain the theoretical results. These findings extend the algebraic framework of interval-valued intuitionistic fuzzy matrices and offer a starting point for studying further operations and their relationships with matrix measures.

Keywords

• Intuitionistic fuzzy set
• interval valued intuitionistic fuzzy set
• interval valued intuitionistic fuzzy matrix

Supporting Institution

No financial support for the research, authorship, or publication of this article.

Ethical Statement

Gökhan Çuvalcıoğlu serves as Editor-in-Chief of Journal of Universal Mathematics. To ensure an independent evaluation, the peer review process and editorial decision for this manuscript were handled by an editor who is not among its authors.

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