Qualitative thematic maps are graphic representations of the process of areal differentiation, a process recognized as one of the hallmarks of the geographer’s craft and one of geography’s grand traditions. Traditionally the process can best be described as classification based on Boolean Set Theory wherein the area bounded by the cartographic line is considered to be in that class for the targ...

We characterize a fuzzy lattice through a fuzzy partial order relation, define ideals and filters of fuzzy lattices, characterize an ideal of fuzzy lattice using its level set and its support and show that a subset of a fuzzy lattice is an ideal if and only if its support is an ideal. Similarly, we show the same for its level set. Lastly, we define some kinds of ideals and filters of fuzzy latt...

In this paper, a new approach is prposed for ordering fuzzy numbers based on bi-symmetrical weighted distance. The proposed method considers the bi-symmetrical weighted function and the bisymmetrical weighted distance of fuzzy numbers to rank fuzzy numbers. Some examples to compare the advantage of this approch with the existing metric index ranking methods is illustrated. The process to rank t...

The Finagle point (Wuffle et al., 1989), the yolk (McKelvey, 1986; Ferejohn et al., 1984) and the epsilon-core (Wooders, 1983; Salant and Goodstein, 1990; Tovey, 2010; Feld and Grofman, 1991) are three solution concepts that have been proposed to predict the outcome of majority voting in the Euclidean spatial model. Relationships among these three concepts are investigated in (Bra̋uninger, 2007)...

the concepts of fuzzy semi-ideals of r with respect to h≤r and generalized fuzzy quotient rings are introduced. some properties of fuzzy semiideals are discussed. finally, several isomorphism theorems for generalized fuzzy quotient rings are established.

The doped topological insulator ${A}_{x}{\mathrm{Bi}}_{2}{\mathrm{Se}}_{3}$, with $A={\mathrm{Cu},\mathrm{Sr},\mathrm{Nb}}$, becomes a nematic superconductor below ${T}_{c}\ensuremath{\approx}3$--4 K. associated electronic director is described by an angle $\ensuremath{\alpha}$ and experimentally manifested in the elliptical shape of in-plane critical magnetic field ${H}_{c2}$. Because threefol...

The notion of bipolar fuzzy subalgebras and bipolar fuzzy ideals of a BCK/BCI-algebra is introduced, and several properties are investigated. Relations between a bipolar fuzzy subalgebra and a bipolar fuzzy ideal are given. A condition for bipolar fuzzy subalgebra to be a bipolar fuzzy ideal is provided, and the characterizations of a bipolar fuzzy ideal are stated. The concept of equivalence r...

This work presents the first projection-free algorithm to solve stochastic bi-level optimization problems, where objective function depends on solution of another problem. The proposed $\textbf{S}$tochastic $\textbf{Bi}$-level $\textbf{F}$rank-$\textbf{W}$olfe ($\textbf{SBFW}$) can be applied streaming settings and does not make use large batches or checkpoints. sample complexity SBFW is shown ...

We study a system comprising a spheroidal particle with permittivity epsilon 2 and conductivity sigma 2 immersed in a host medium with permittivity epsilon 1 and conductivity sigma 1 in the ac external electric field with a strength Epsilon 0 and frequency omega. We determined conditions when orientation of a spheroidal particle with a finite electric conductivity at t --> infinity coincides wi...