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.
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Abstract: In the paper [P.K. Maji, R. Biswas, A.R. Roy, Fuzzy soft sets, J. Fuzzy Math. 9 (3) (2001) 589–602], Maji et al. introduced the concept of fuzzy soft sets as a generalization of the standard soft sets, and presented an application of fuzzy soft sets in a decision making problem. The aim of this paper is to apply fuzzy soft set for dealing with several kinds of theories in hyper BCK -algebras. The notions of fuzzy soft hyper BCK -ideal, fuzzy soft weak hyper BCK -ideal, fuzzy soft s -weak hyper BCK -ideal and fuzzy soft strong hyper BCK -ideal…are introduced, and related properties and relations are investigated.
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