This paper presents a study of the suitability for FPGA design of full custom based CORDIC implementations. Since all these methods are based on redundant arithmetic, the FPGA implementation of the required operators to perform the different CORDIC methods has been evaluated. Efficient mappings on FPGA have been performed leading to the fastest implementations. It is concluded that the redundan...

We analyze different types of aggregation operators based on the use of probabilities, weighted averages (WAs) and generalized aggregation operators. We present the generalized probabilistic weighted averaging (GPWA) operator. It is a new aggregation operator that unifies the WA and the probability in the same formulation considering the degree of importance that each concept has in the analysi...

The cloud model, which can synthetically describe the randomness and fuzziness of qualitative concepts and implement uncertain transformations between a qualitative concept and its quantitative instantiations, has attracted considerable attention from researchers studying multi-criteria group decision-making problems involving linguistic information. In this paper, some operations of clouds and...

Historically, the prominence of the commensurator was due in large part to its density in the arithmetic setting being closely related to the abundance of Hecke operators attached to arithmetic lattices. These operators are fundamental objects in the theory of automorphic forms associated to arithmetic lattices (see Shimura [38] for example). More recently, the commensurator of various classes ...

The use of geographical entities with fuzzy spatial extent, called here fuzzy geographical entities (FGE’s), in Geographical Information Systems requires the existence of operators capable of processing them. This paper focuses on the computation of areas of FGE’s. Two methods are considered, one crisp due to Rosenfeld (1984), which will be shown to be limited in its applicability, and the othe...

Chiclana et al. [Chiclana, F., Herrera-Viedma, E., Herrera, F., Alonso, S. (2007). European Journal of Operational Research 182, 383–399] provided some IOWA operators for aggregating the individual fuzzy preference elations. The aim of this work is further to study their desired properties under group decision making problem with fuzzy preference relations. First, it is proved that the collecti...

Let XΓ = Γ\H∗ be the modular curve associated to a congruence subgroup Γ of level N with Γ1(N) ≤ Γ ≤ Γ0(N), and let X = XΓ,Q be its canonical model over Q. The main aim of this paper is to show that the endomorphism algebra End0Q(JX) of its Jacobian JX/Q is generated by the Hecke operators Tp, with p N , together with the “degeneracy operators” DM,d, D t M,d, for dM |N . This uses the fundament...

We study the lattice of local operators in Hyland’s Effective Topos. We show that this lattice is a free completion under internal sups indexed by the natural numbers object, generated by what we call basic local operators. We produce many new local operators and we employ a new concept, sight, in order to analyze these. We show that a local operator identified by A.M. Pitts in his thesis, give...

In this paper we study extensions of the arithmetic operators +, −, ·, ÷ to the lattice L of closed subintervals of the unit interval. Starting from a minimal set of axioms that these operators must fulfill, we investigate which properties they satisfy. We also investigate some classes of t-norms on L which can be generated using these operators; these classes provide natural extensions of the ...

Wavelet transforms have been widely applied to image and video compression but they also have the ability to compress operators. A result is that there is great potential for producing fast algorithms for the processing of wavelet compressed image and video data. We examine the implementation of a set of fundamental image operations including pixel-wise arithmetic operators and arbitrary linear...