(epsilon, epsilon V q) -OSMOTIC VALUES WITH APPLICATIONS IN BCK/BCI-ALGEBRAS

The notions of (epsilon, epsilon V q)-osmotic S-value and ((epsilon) over bar,(epsilon) over bar V (q) over bar)-osmotic S-value are introduced, and related properties are investigated. Relations between osmotic S-value and (epsilon, epsilon V q)-osmotic S-value ((epsilon) over bar,(epsilon) over bar V (q) over bar)-osmotic S-value) are considered. Conditions for a number in the unit interval [0,1] to be an osmotic S-value (resp., (epsilon, epsilon V q)-osmotic S-value and ((epsilon) over bar,(epsilon) over bar V (q) over bar)-osmotic S-value) are provided. Conditions for level sets to be S-energetic set and/or subalgebra are discussed.