We develop a theory of stratified $LM$-filters which generalizes the theory of stratified $L$-filters. Our stratification condition explicitly depends on a suitable mapping between the lattices $L$ and $M$. If $L$ and $M$ are identical and the mapping is the identity mapping, then we obtain the theory of stratified $L$-filters. Based on the stratified $LM$-filters, a general theory of lattice-v...

We prove that certain Lipschitz properties of the inverse F-1 of a set-valued map F are inherited by the map (f+F)~x when / has vanishing strict derivative. In this paper, we present an inverse mapping theorem for set-valued maps F acting from a complete metric space I toa linear space Y with a (translation) invariant metric. We prove that, for any function f: X -> Y with "vanishing strict deri...

in this paper, the notions of $(t,s)$-composition matrix and$(t,s)$-interval-valued intuitionistic fuzzy equivalence matrix areintroduced where $(t,s)$ is a dual pair of triangular module. theyare the generalization of composition matrix and interval-valuedintuitionistic fuzzy equivalence matrix. furthermore, theirproperties and characterizations are presented. then a new methodbased on $tilde{...