We show that the lattice of all ideals of a ring $R$ can be embedded in the lattice of all its fuzzyideals in uncountably many ways. For this purpose, we introduce the concept of the generalizedcharacteristic function $chi _{s}^{r} (A)$ of a subset $A$ of a ring $R$ forfixed $r , sin [0,1] $ and show that $A$ is an ideal of $R$ if, and only if, its generalizedcharacteristic function $chi _{s}^{...

and Applied Analysis 3 3. Main Results Throughout this paper, we will consider lattices as complete lattices,X will denote space, and μ is a membership function of any fuzzy set X. Definition 3.1. If m : σ L → R ∪ {∞} satisfies the following properties, then m is called a lattice measure on the lattice σ-algebra σ L . i m ∅ L0. ii For all f, g ∈ σ L such that m f , m g ≥ L0 : f ≤ g ⇒ m f ≤ m g ...

This paper showed a short characterization of embedded fuzzy sets of an interval-valued fuzzy set. We proved that any embedded fuzzy set can be expressed as a convex combination of three fuzzy sets always. We established two basic results (existence and uniqueness) in the representation as a convex combination. We showed three examples from the literature, and we showed they can be deduced by u...

Convexity theory and duality theory are important issues in math- ematical programming. Within the framework of credibility theory, this paper rst introduces the concept of convex fuzzy variables and some basic criteria. Furthermore, a convexity theorem for fuzzy chance constrained programming is proved by adding some convexity conditions on the objective and constraint functions. Finally,...

 Minimum and maximum operators are two well-known t-norm and s-norm used frequently in fuzzy systems. In this paper, two different types of fuzzy inequalities are simultaneously studied where the convex combination of minimum and maximum operators is applied as the fuzzy relational composition. Some basic properties and theoretical aspects of the problem are derived and four necessary and suffi...

We discuss the possible structures for and mutual relationships between a finite distributive lattice L, a maximal sublattice M of L and the corresponding ‘remainder’ R = L\M with the aid of Birkhoff duality, and contrast the results with the analogous situations for a general finite lattice L. @ 1999 Elsevier Science B.V. All rights reserved

in this paper, an optimization problem with a linear objective function subject to a consistent finite system of fuzzy relation inequalities using the max-product composition is studied. since its feasible domain is non-convex, traditional linear programming methods cannot be applied to solve it. we study this problem and capture some special characteristics of its feasible domain and optimal s...

A locally modular (resp. locally distributive) lattice is a lattice with a congruence relation and each of whose equivalence class has sufficiently many elements and is a modular (resp. distributive) sublattice. Both the lattice of all closed subspaces of a locally convex space and the lattice of projections of a locally finite von Neumann algebra are locally modular. The lattice of all /^-topo...