Affiliations: [a] Department of Mathematics Education, Gyeongsang National University, Jinju, Korea
| [b] Department of Mathematics, Jeju National University, Jeju, Korea
| [c] Department of Mathematics, Natural Science of College, Gyeongsang National University, Jinju, Korea
Correspondence:
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Corresponding author. Seok-Zun Song, Department of Mathematics, Jeju National University, Jeju, Korea, E-mail: [email protected].
Abstract: As a foundation to study the similarity measure with applications in pattern recognition, (normalized) Hamming distances and (normalized) Euclidean distances between hyper structures based on two and three parameters are established. An example to show that these distances are not metrics in general is provided, and conditions for these distances to be metrics are considered. The notions of length fuzzy ideals with four types are introduced, and related properties and their relations are investigated. Relations between length fuzzy ideals and length fuzzy subalgebras are investigated. Conditions for a length fuzzy subalgebra to be a length fuzzy ideal are provided. Characterizations of a length fuzzy ideal are considered.
