In spite of increasing studies and investigations in the field of aggregation operators, there are two fundamental problems remaining unsolved: aggregation of L-fuzzy settheoretic notions and their justification. In order to solve these problems, we will formulate aggregation operators and their special types on partially ordered sets with universal bounds, and introduce their categories. Furth...

We prove a related fixed point theorem for n mappings which arenot necessarily continuous in n fuzzy metric spaces using an implicit relationone of them is a sequentially compact fuzzy metric space which generalizeresults of Aliouche, et al. [2], Rao et al. [14] and [15].

Let (X, ) be a partially ordered set and d be a metric on X such that (X, d) is a complete metric space. Assume that X satisfies; if a non-decreasing sequence xn → x in X , then xn x, for all n. Let F be a set valued mapping from X into X with nonempty closed bounded values satisfying; (i) there exists κ ∈ (0, 1) with D(F (x), F (y)) ≤ κd(x, y), for all x y, (ii) if d(x, y) < ε < 1 for some y ∈...

Existence of fixed point in partially ordered sets has been considered recently in 1–17 . Tarski’s theorem is used in 9 to show the existence of solutions for fuzzy equations and in 11 to prove existence theorems for fuzzy differential equations. In 2, 6, 7, 10, 13 some applications to ordinary differential equations and to matrix equations are presented. In 3– 5, 17 some fixed point theorems a...

‎the purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed $g$-monotone property in partially ordered metric spaces‎. ‎also‎, ‎we present a result on the existence and uniqueness of coupled common fixed points‎. ‎the results presented in the paper generalize and extend several well-known results in the literature‎.

In the present paper, we show the existence of a coupled fixed point for a non-decreasing mapping in partially ordered complete metric space using a partial order induced by an appropriate function φ. We also define the concept of weakly related mappings on an ordered space. Moreover common coupled fixed points for two and three weakly related mappings are also proved in the same space.

Introduction § 0. Preliminaries: fuzzy sets 125 § 1. Fuzzy topological spaces: the basic categories of fuzzy topology 127 § 2. Fundamental interrelations between the category Top of topological 135 spaces and the categories of fuzzy topology § 3. Local structure of fuzzy topological spaces 138 § 4. Convergence structures in fuzzy spaces 140 § 5. Separation in fuzzy spaces 143 § 6. Normality and...