Jin-xuan Fang

On fixed point theorems in fuzzy metric spaces

Abstract The purpose of this paper is to give some new fixed point theorems for contractive type mappings in fuzzy metric spaces. The results presented improve and generalize some recent results.

On the level convergence of a sequence of fuzzy numbers

Abstract In this paper we first give a simplified proof of the existence theorem of supremum and infimum in fuzzy number space E 1 established by Wu and Wu (J. Math. Anal. Appl. 210 (1997) 499) and improve the expressions of the supremum and infimum. As a straightforward corollary of this result, we obtain a necessary and sufficient condition under which, for a bounded sequence of fuzzy numbers { u n }, the pair of functions sup n u n − ( λ ) and sup n u n + ( λ ) can determine a fuzzy number. Secondly, we give a necessary and sufficient condition for a sequence of fuzzy numbers { u n } to be levelwise convergent in E 1 , and generalize some important theorems in real number spaces to fuzzy number spaces. Finally, we prove the existence of supremum and infimum for the level-continuous fuzzy-valued function on a closed interval and give a necessary and sufficient condition under which its supremum and infimum can be attained.

Residual operations of left and right uninorms on a complete lattice

Uninorms are an important generalization of triangular norms and conorms, having a neutral element lying anywhere in the unit interval. In this paper, we introduce the concepts of left and right uninorms on a complete lattice. We discuss the residual operations of left and right uninorms, and study some basic properties of the residual operations of infinitely @?-distributive left (right) uninorms and pseudo-uninorms.

Residual coimplicators of left and right uninorms on a complete lattice

Uninorms are an important generalization of triangular norms and conorms, having a neutral element lying anywhere in the unit interval, and left and right uninorms are a non-commutative extension of uninorms. In this paper, we further study left and right uninorms on a complete lattice. First we introduce the concepts of residual coimplicators of left and right uninorms. Then we discuss some basic properties of the residual coimplicators of infinitely @?-distributive left (right) uninorms and pseudo-uninorms. Finally we investigate the relations between residual implicators and residual coimplicators of left (right) uninorms.

A note on fixed point theorems of Hadzci´c

Abstract In this paper we give a fixed point theorem for multi-valued probabilistic (φ)-contraction mappings on a Menger space. As a special case, a fixed point theorem for multi-valued (φ)-contraction mappings on a fuzzy metric space is obtained. The results presented improve and generalize in a sense some recent fixed point theorems proved by Hadžic.

On nonlinear equations for fuzzy mappings in probabilistic normed spaces

In this paper, we introduce the concept of probabilistic Ψ-contractor couple, which simplifies and weakens that of probabilistic Φ-g-contractor given by Cho et al. (Fuzzy Sets and Systems 110 (2000) 115-122). By using this concept, we study the existence and iteration convergence of solutions for set-valued nonlinear operator equations and nonlinear equations of fuzzy mappings in Menger PN-spaces. The results presented in this paper improve and extend the corresponding results of Cho et al. in a sense.

Generalization of Kolmogoroff' s theorem to L-topological vector spaces

In this paper, the concept of L-fuzzy normed linear spaces is introduced and some of its properties are studied. Then we give a necessary and sufficient condition for L-topological vector spaces to be L-fuzzy normable. This is a generalization of Kolmogoroffs theorem in the classical topological vector spaces to L-topological vector spaces.

A note on the completions of fuzzy metric spaces and fuzzy normed spaces

In this paper, we point out that the completion theorem of fuzzy metric spaces given by Lee et al. (Fuzzy Sets and Systems 106 (1999) 469-473) is incorrect and prove a new completion theorem.

On ∞-contractions in probabilistic and fuzzy metric spaces

In this paper, by means of weakening conditions of the gauge function ?, a new fixed point theorem for probabilistic ?-contraction in Menger probabilistic metric spaces with a t-norm of H-type is established. This theorem improves and generalizes the recent results of ?iric (2010) 4, Jachymski (2010) 12 and Xiao et al. (2013) 25. By using the theorem, we also obtain some important corollaries and the fixed point theorems for ?-contraction in fuzzy metric spaces.

Some properties of the level convergence topology on fuzzy number space En

In this paper, we study topological structure of level convergence on fuzzy number space En and give a characterization of compact subsets in (En,τ(l)), where τ(l) is the level convergence topology on En.