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

Öz

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.

Anahtar Kelimeler

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

Destekleyen Kurum

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

Etik Beyan

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.

Kaynakça

1. K. T. Atanassov, Intuitionistic fuzzy sets, VII ITKR’s Session, Sofia, June 1983 (Deposed in Central Sci.-Techn. Library of Bulg. Acad. of Sci., No. 1697/84) (in Bulgarian), (1983).
2. K. T. Atanassov, Intuitionistic fuzzy sets and interval valued intuitionistic fuzzy sets, Advanced Studies in Contemporary Mathematics, Vol.28, No.2, pp.167-176 (2018).
3. K. T. Atanassov, G. Gargov, Interval valued intuitionistic fuzzy sets, Fuzzy Sets and Systems, Vol.31, No.3, pp.343-349 (1989).
4. Y. Wang, Y. J. Lei, A technique for constructing intuitionistic fuzzy entropy, Control and Decision, Vol.22, No.12, pp.1390-1394 (2007).
5. C. P. Wei et al., Entropy, similarity measure of interval-valued intuitionistic fuzzy sets and their applications, Information Sciences, Vol.181, pp.4273-4286 (2011).
6. Z. S. Xu, A method based on distance measure for interval-valued intuitionistic fuzzy group decision making, Information Sciences, Vol.180, pp.181-190 (2010).
7. L. A. Zadeh, Fuzzy sets, Information and Control, Vol.8, pp.338-353 (1965).
8. Q. Zhang et al., Some new entropy measures for interval-valued intuitionistic fuzzy sets based on distances and their relationships with similarity and inclusion measures, Information Sciences, Vol.283, pp.55-69 (2014).