Taking intuitionistic fuzzy sets as the structures of truth values, we propose the notions of intuitionistic fuzzy context-free grammars (IFCFGs, for short) and pushdown automata with final states (IFPDAs). Then we investigate algebraic characterization of intuitionistic fuzzy recognizable languages including decomposition form and representation theorem. By introducing the generalized subset c...

the starting point of this paper is given by priestley’s papers, where a theory of representation of distributive lattices is presented. the purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. in this way, some results of priestley’s papers are extended. in the main theorem, we show that the category of finite fuzzy priestley space...

In a companion paper [9] we used fuzzy context-free grammars in order to model grammatical errors resulting in erroneous inputs for robust recognizing and parsing algorithms for fuzzy context-free languages. In particular, this approach enables us to distinguish between small errors (“tiny mistakes”) and big errors (“capital blunders”). In this paper we present some algorithms to recognize fuzz...

In this paper, we define the notion of (dual) multi-fuzzy normedspaces and describe some properties of them. We then investigate Ulam-Hyers stability of Jensen's functional equation for mappings from linear spaces into  multi-fuzzy normed spaces. We establish an asymptotic behavior of the Jensen equation in the framework of multi-fuzzy normed spaces.

Fuzzy automata have long been accepted as a generalization of nondeterministic finite automata. A closer examination, however, shows that the fundamental property—nondeterminism—in nondeterministic finite automata has not been well embodied in the generalization. In this paper, we introduce nondeterministic fuzzy automata with or without -moves and fuzzy languages recognized by them. Furthermor...

Some properties of fuzzy formal languages associated to Chomsky, Petri and Lindenmayer formal languages will be presented. Generalized alpha cuts lead to the generation of sets of crisp languages of different type within their hierarchies of origin. A fuzzy formal language may serve as a model for several apparently different phenomena of the real world.

The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...

Handwritten character recognition of Urdu script based languages is one of the most difficult task due to complexities of the script. Urdu script based languages has not received much attestation even this script is used more than 1/6th of the population. The complexities in the script makes more complicated the recognition process. The problem in handwritten numeral recognition is the shape si...