An approach to fixed point theory based on the notion of fuzzy order is proposed. Such an approach extends both the fixed point theory in ordered sets and the fixed point theory in metric spaces. This since the fuzzy orders are strictly related with the quasi-metrics as defined by A. K. Seda in [10]. The aim is to give new tools for logic programming and for approximate reasoning.

The transitivity of fuzzy relations with respect to a subset of quasi-linear functions in the unit interval is studied. A new construction of transitive relations with respect to an archimedean t-norm is proposed.

In the present work, we introduce and study completely generalized quasi-variational inequality problem for fuzzy mappings. By using the definitions of strongly accretive and retraction mappings, we propose an iterative algorithm for computing the approximate solutions of this class of variational inequalities. We prove that approximate solutions obtained by the proposed algorithm converge to t...

In this communication, we establish some existence theorem for a new class of generalized mixed vector quasi-variationallike inequalities with fuzzy mappings in topological vector spaces by using the KKM-Fan Theorem and an equivalent fixed point theorem.

In this paper we prove common fixed point theorems for a class of fuzzy mappings in Smyth-complete quasi-metric spaces. Well-known theorems are special case of our results.

In this paper, we show that every selective groupoid induced by a fuzzy subset is a pogroupoid, and we discuss several properties in quasi ordered sets by introducing the notion of a framework.

The notion of generalized locally bounded $I$-topological vectorspaces is introduced. Some of their important properties arestudied. The relationship between this kind of spaces and thelocally bounded $I$-topological vector spaces introduced by Wu andFang [Boundedness and locally bounded fuzzy topological vectorspaces, Fuzzy Math. 5 (4) (1985) 87$-$94] is discussed. Moreover, wealso use the fam...