Berstel and Pin have characterized local languages by introducing local automaton. In this paper fuzzy local language is introduced and the fuzzy local languages recognized by partial fuzzy local automata in max-min and min-max compositions are studied. Some closure properties of fuzzy local languages are provided. Mathematics Subject Classification: 68Q45

Hierarchical structures and uncertainty measures are two main aspects in granular computing, approximate reasoning and cognitive process. Typical hesitant fuzzy sets, as a prime extension of fuzzy sets, are more flexible to reflect the hesitance and ambiguity in knowledge representation and decision making. In this paper, we mainly investigate the hierarchical structures and uncertainty measure...

Katsaras 1 defined a fuzzy norm on a vector space to construct a fuzzy vector topological structure on the space. Some mathematicians have defined fuzzy norms on a vector space from various points of view 2–4 . In particular, Bag and Samanta 5 , following Cheng and Mordeson 6 , gave an idea of fuzzy norm in such a manner that the corresponding fuzzy metric is of Kramosil and Michálek type 7 . T...

In this paper, we introduce some important properties of intuitionistic fuzzy soft topological spaces and define the intuitionistic fuzzy soft closure and interior of an intuitionistic fuzzy soft set. Furthermore, intuitionistic fuzzy soft continuous mapping are given and structural characteristics are discussed and studied.

It is shown the complete equivalence between the theory of continuous (enumeration) fuzzy closure operators and the theory of (effective) fuzzy deduction systems in Hilbert style. Moreover, it is proven that any truth-functional semantics whose connectives are interpreted in [0,1] by continuous functions is axiomatizable by a fuzzy deduction system (but not by an effective fuzzy deduction syste...

we show that the category of convergence approach spaces is a simultaneously reective and coreective subcategory of the category of latticevalued limit spaces. further we study the preservation of diagonal conditions, which characterize approach spaces. it is shown that the category of preapproach spaces is a simultaneously reective and coreective subcategory of the category of lattice-valued p...

OBJECTIVE To investigate the effect of bracket-ligature combination on the amount of orthodontic space closure over three months. DESIGN Randomized clinical trial with three parallel groups. SETTING A hospital orthodontic department (Chesterfield Royal Hospital, UK). PARTICIPANTS Forty-five patients requiring upper first premolar extractions. METHODS Informed consent was obtained and pa...

in this paper, we introduce a new concept of fuzzy generalizedcontraction and give a fixed point result for such mappings in the setting of fuzzy m-complete metric spaces. we also give an affirmative partial answer to a question posed by wardowski [d. wardowski, fuzzy contractive mappings and fixed points in fuzzy metric spaces, fuzzy set syst., {bf 222}(2013), 108-114].some examples are also g...

we consider the concept of fuzzy quasi-contractions initiated by '{c}iri'{c} in the setting of fuzzy metric spaces and establish fixed point theorems for quasi-contractive mappings and for fuzzy $mathcal{h}$-contractive mappings on m-complete fuzzy metric spaces in the sense of george and veeramani.the results are illustrated by a representative example.

This chapter tries to answer the fundamental question of what main contributions of fuzzy clustering to the theory of cluster analysis from theoretical viewpoints. While fuzzy clustering is thought to be clearly useful by users of this technique, others think that the concept of fuzziness is not needed in clustering. Thus the usefulness of fuzzy clustering is not trivial. The discussion here is...