We present pumping lemmas for five classes of functions definable by fragments weighted automata over the min-plus semiring, max-plus semiring and natural numbers. As a corollary we show that hierarchy unambiguous, finitely-ambiguous, polynomially-ambiguous automata, full class is strict semirings.

In this paper we consider general t-norm in the definition of fuzzy normed linear space which is introduced by the authors in an earlier paper. It is proved that if t-norm is chosen other than ”min” then decomposition theorem of a fuzzy norm into a family of crisp norms may not hold. We study some basic results on finite dimensional fuzzy normed linear spaces in general t-norm setting. 2010 AMS...

Each fuzzy set can be represented by a nested system of ordinary sets—its a-cuts. There is an extensive literature on fuzzy sets devoted to problems of the following kind: is it possible to reduce operations with fuzzy sets to operations with their a-cuts? Is it possible to reduce properties of fuzzy relations to properties of their a-cuts? More generally, can a fuzzy concept be represented by ...

in this work, we define fuzzy soft ($fs$) matrices and theiroperations which are more functional to make theoretical studies inthe $fs$-set theory. we then define products of $fs$-matrices andstudy their properties. we finally construct a $fs$-$max$-$min$decision making method which can be successfully applied to theproblems that contain uncertainties.

The main goal of this paper is to introduce and study fuzzy multiset regular grammar to show that fuzzy multiset finite automata and fuzzy multiset regular grammars are equivalent. We also study fuzzy multiset linear grammars and fuzzy multiset regular grammars in normal form. Furthermore, we show the equivalence of fuzzy multiset regular grammars, fuzzy multiset left linear grammars, fuzzy mul...

Recently, two types of simulations (forward and backward simulations) and four types of bisimulations (forward, backward, forward-backward, andbackward-forwardbisimulations) between fuzzyautomatahavebeen introduced. If there is at least one simulation/bisimulation of some of these types between the given fuzzy automata, it has been proved that there is the greatest simulation/bisimulation of th...