The notions of a S fuzzy ∧ sub semi lattice, a S fuzzy ideal and a S fuzzy prime ideal of a bounded lattice with truth values in a bounded ∧ sub semi lattice S are introduced which generalize the existing notions with truth values in a unit interval of real numbers. Finally, S fuzzy prime ideal theorem is proved. 2010 AMS Classification: 03G10, 46H10, 06D50, 08A72

1 (t) then the tangent vector ^ T ips direction as can be shown by its dot product with ^ T. Rewriting equation 13 as ^ T (t) = (x 0 (t); y 0 (t)) + (?y 00 (t); x 00 (t))d k ^ Tk + (y 0 (t); ?x 0 (t))k ^ Tk 0 d k ^ Tk 2 and substituting it into ^ T (t) ^ T(t) = " (x 0 (t); y 0 (t)) + (?y 00 (t); x 00 (t))d k ^ Tk + (y 0 (t); ?x 0 (t))k ^ Tk 0 d k ^ Tk 2 # (x 0 (t); y 0 (t)) = (x 0 (t) 2 + y 0 (...

We prove that there is no sparse hard set for P under logspace computable bounded truth-table reductions unless P=L. In case of reductions computable in NC, the collapse goes down to P=NC. We parameterize this result and obtain a generic theorem allowing us to vary the sparseness condition, the space bound and the number of queries of the truth-table reduction. Another instantiation yields that...

interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

Keywords--Fuzzy numbers, Convexity, Preinvexity, Generalized convexity, Fuzzy mappings. 1. I N T R O D U C T I O N Let R n deno te t he n -d imens iona l Euc l idean space. T h e suppor t , supp (p), of a fuzzy set # : R n ~ I = [0, 1] is def ined as s u p p ( # ) = { x e R n ] # ( x ) > 0} . A fuzzy set # : R n ~ I is cal led fuzzy convex if i t is quas i concave in c o m m o n sense on its su...