In this paper, we take a GL-quantale as the truth value table to study a new rough set model—L-valued fuzzy rough sets. The three key components of this model are: an L-fuzzy set A as the universal set, an L-valued relation of A and an L-fuzzy set of A (a fuzzy subset of fuzzy sets). Then L-valued fuzzy rough sets are completely characterized via both constructive and axiomatic approaches. 

A concept of weak $f$-property for a set-valued mapping is introduced‎, ‎and then under some suitable assumptions‎, ‎which do not involve any information‎ ‎about the solution set‎, ‎the lower semicontinuity of the solution mapping to‎ ‎the parametric‎ ‎set-valued vector equilibrium-like problems are derived by using a density result and scalarization method‎, ‎where the‎ ‎constraint set $K$...

Continuity of the mapping from initial endowments and utilities to equilibria is an essential property for a desirable model of an economy – without continuity, small errors in the observation of parameters of the economy may lead to entirely different predicted equilibria. We show that for the linear case of Fisher’s market model, the (unique) vector of equilibrium prices, p = p(m,U) is a cont...

This paper provides a systematic solvability analysis for (generalized) variational inequalities on separable Hilbert lattices. By contrast to a large part of the existing literature, our approach is lattice-theoretic, and is not based on topological …xed point theory. This allows us to establish the solvability of certain types of (generalized) variational inequalities without requiring the in...

In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...

interval-valued intuitionistic fuzzy sets (ivifss) are widely used to handle uncertainty and imprecision in decision making. however, in more complicated environment, it is difficult to express the uncertain information by an ivifs with considering the decision-making preference. hence, this paper proposes a group generalized interval-valued intuitionistic fuzzy soft set (g-givifss) which conta...

The aim of this paper is to introduce and study set- valued homomorphism on lattices and T-rough lattice with respect to a sublattice. This paper deals with T-rough set approach on the lattice theory. The result of this study contributes to, T-rough fuzzy set and approximation theory and proved in several papers. Keywords: approximation space; lattice; prime ideal; rough ideal; T-rough set; set...