Introduction: In radiotherapy with external surrogates, exact information of tumor position is one of the key factors that improves treatment delivery. Many dynamic tumors in thorax region of patient move mainly due to respiration and are known as intra-fractional motion error that must be compensated, as well. One of clinical strategy is using Stereotactic Body Radiation Thera...

The aim of this paper is to study the properties of t-cut set, strong t-cut set, t-quasi-cut set, strong t-quasi-cut set and ∈ ∨q-cut set of a fuzzy set μ. For any intuitionistic fuzzy A =< μA, νA > and α, β ∈ [0, 1], we define and study the properties of upper (α, β) cut setA(α,β), strong upper (α, β) cut setA(α, β) ̇ , lower (α, β) cut set A, strong lower (α, β) cut set A (α, β) ̇ , upper (α, β...

In this paper, some types of fuzzy filters a strong Sheffer stroke non-associative MV-algebra (for short, NMV-algebra) are introduced. By presenting new properties filters, we define prime filter in algebraic structure. Then (prime) NMV-algebra determined and features proved. Finally, built quotient by filter.

Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theo...

In this note first we define the notions of fuzzy positive implicativehyper BCK-ideals of types 1,2,3 and 4. Then we prove some theorems whichcharacterize the above notions according to the level subsets. Also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperBCK-ideals and fuzzy positive implicative hyper BCK-ideals of types 5,6,7and 8. Then, we define the no...