We prove the existence of fuzzy common fixed point of two mappings satisfying a generalized contractive condition in complete ordered spaces. Our results provide extension as well as substantial improvements of several well-known results in the existing literature and initiate the study of fuzzy fixed point theorems in ordered spaces. © 2010 Elsevier Ltd. All rights reserved.

Ordered fuzzy numbers as generalization of convex fuzzy numbers are defined together with four algebraic operations. For defuzzification operators, that play the main role when dealing with fuzzy controllers and fuzzy inference systems, new representation formulae are given. Step ordered fuzzy numbers are considered. Approximation method based on forward neural networks is presented for determi...

In this paper, we present equivalent characterizations of L-closure systems on lower bounded complete L-ordered sets and complete L-lattices, respectively. These results demonstrate the feasibility of notion of fuzzy closure system developed in our previous work (L.-K. Guo, G.-Q. Zhang, Q.-G. Li: Fuzzy closure systems on L-ordered sets. Math. Log. Quart. 57 (3) (2011), 281-291.). Also we develo...

We introduce and use the concept of (∈γ ,∈γ ∨qδ)-fuzzy (left, right, bi-) ideals to study the structural properties of a non-associative algebraic ordered structure. We characterize an intra-regular ordered AGgroupoid by these generalized fuzzy ideals. 2010 AMS Classification: 06F05, 20M12, 08A72

At the first, we revise the Kosinski’s definition of the sum of ordered fuzzy numbers. The associativity of revised sum is investigated here. In addition, we show that the multiple revised sum of finite sequence of trapezoidal ordered fuzzy numbers depends on its summands ordering. .AMS Classification: 03E72

In this paper we introduce a procedure, based on the Max-Min clustering method, that identiies a xed order of training pattern presentation for Fuzzy ARTMAP. This procedure is referred to as the Ordering Algorithm, and the combination of this procedure with Fuzzy ARTMAP is referred to as Ordered Fuzzy ARTMAP. Experimental results demonstrate that Ordered Fuzzy ARTMAP exhibits a generalization p...

In this paper, we introduce some new classes of proximal contraction mappings and establish  best proximity point theorems for such kinds of mappings in a non-Archimedean fuzzy metric space. As consequences of these results, we deduce certain new best proximity and fixed point theorems in partially ordered non-Archimedean fuzzy metric spaces. Moreover, we present an example to illustrate the us...

In this paper we introduce a procedure, based on the max-min clustering method, that identifies a fixed order of training pattern presentation for fuzzy adaptive resonance theory mapping (ARTMAP). This procedure is referred to as the ordering algorithm, and the combination of this procedure with fuzzy ARTMAP is referred to as ordered fuzzy ARTMAP. Experimental results demonstrate that ordered f...

Diversity of opinion is an empirical fact often appearing in social networks. In the paper known statistical methods of evaluation is substituted by fuzzy concepts, namely Step Ordered Fuzzy Numbers (SOFN). SOFN are extentions of Ordered Fuzzy numbers (OFN) introduced by Kosiński, Prokopowicz and Ślȩzak in 2002. In 2011 Kacprzak and Kosiński observed that SOFN may be equipped with a lattice str...