Figure 2 - uploaded by Regivan H N Santiago
Content may be subject to copyright.
According to Example 10, to evaluate Z " Y ´ X¨X Y by Constrained Interval Arithmetic (CIA)
Source publication
The impreciseness of numeric input data can be expressed by intervals. On the other hand, the normalization of numeric data is a usual process in many applications. How do we match the normalization with impreciseness on numeric data? A straightforward answer is that it is enough to apply a correct interval arithmetic, since the normalized exact va...
Contexts in source publication
Context 1
... we need to optimize: θpλ x , λ y q " pλ y ` 1q´p3λ1q´ 1q´p3λ x ´ 1q 2 pλ y ` 1q on r0, 1sˆr01sˆ1sˆr0, 1s (see Figure 2). ...
Context 2
... if Z " X ¨ Y or Z " X Y , the process can become complex, since the global minimum and maximum of θ can occur in the interior of the box (see Figure 2 from Example 10) and one needs to use the optimization process to find them. If we increase the number of variables, for instance Z " XYK, the optimization process becomes more complex. ...
Similar publications
The Average Silhouette Width (ASW) is a popular cluster validation index to estimate the number of clusters. The question whether it also is suitable as a general objective function to be optimized for finding a clustering is addressed. Two algorithms (the standard version OSil and a fast version FOSil) are proposed, and they are compared with exis...
Citations
... Therefore, historical data need to undergo preprocessing. Approximate piecewise linearization and normalization (Santiago et al., 2020) are employed for processing, reducing the dimensionality of highdimensional data and linearizing historical data. Using a 15-min time period, the maximum and minimum values within each period form the upper and lower limits of the interval. ...
With the construction and development of the new energy system, the integrated energy system (IES) has garnered significant attention as a crucial energy carrier in recent years. Therefore, to address the scheduling challenges of IES influenced by uncertainty in source load and mitigate the conservatism of scheduling schemes while enhancing clustering accuracy, a method for day-ahead top-note scheduling of IES is proposed. First, by improving dynamic time warping (DTW) for hierarchical clustering of wind, solar, and load data in IES, typical scenarios of IES are derived. Second, using the interval method to model wind, solar, and load data in IES along with their coupled devices and considering the conservatism issue of interval optimization, the established IES interval model undergoes affine processing. Finally, with the goal of minimizing the operating costs of IES, a day-ahead interval affine scheduling model is established, which is solved using the CPLEX Solver and INTLAB toolbox, and scheduling schemes for all typical scenarios are provided. Through comparative analysis of calculation examples, it is found that the method proposed in this paper can enhance clustering accuracy and reduce the conservatism of system scheduling schemes.
... In contrast to the Boundary-based Interval Standardization (BIS) and the Min-Max-based interval normalization (Min-Max) algorithms provided by [11], DIS allows dynamic standardization of interval sets. Additionally, different from the Probabilitybased Interval Normalization (PIN) algorithm [12], the object of DIS scaling is the bias of original data, which can reduce the variation in the distribution shape of an original dataset. ...
... The original values of the indicators need to be standardized to align them with the same baseline. The most widely used interval standardization methods include the BIS algorithm [11], the Min-Max algorithm [11], and the PIN algorithm [12]. ...
... In Section 3.1, we have developed a dynamic interval standardization method called DIS. In order to verify the superiority of DIS over other interval standardization methods, we compare DIS with BIS, Min-Max, and PIN [11,12]. To verify the superiority of the fusion model MFD-DFR over other fusion models, we compare MFD-DFR with the existing fusion models [16,18,19]. ...
Data fusion technology plays a pivotal role in aggregating, storing, and mining multi-source data to extract its joint value through the construction of a unified fusion representation model. However, we argue that mainstream methods are limited to precise data, which may not satisfy practical application requirements, as data collected from an information source often exhibits imprecision and uncertainty. In this paper, we develop a Multi-source Fuzzy Data-driven Dynamic Fusion Representation (MFD-DFR) model. This model effectively addresses the challenges related to heterogeneity, dynamics, and quality optimization that arise during the fusion of fuzzy data. To achieve this goal, we first adopt intervals as a means of description to capture the inherent uncertainty in single-source information. We then present a Dynamic Interval Standardization (DIS) algorithm, a novel approach that dynamically deals with the heterogeneity of multi-source fuzzy data without relying on the storage of historical sample data. We next propose a fusion representation model for standardized intervals that improves the quality of single-source fuzzy data through confidence interval estimation. The experimental results convincingly demonstrate that the MFD-DFR model outperforms alternative models in terms of data classification and clustering. We also show the effectiveness of our proposed DIS algorithm in expediting the convergence speed of gradient descent algorithms.
This paper discuss on Interval Arithmetic by Moore under two main principles: inclusion isotonicity and quick computations under algebraic cost. In 1999, to overcome Moore difficulties Lodwick introduced constrained interval arithmetic. This paper discuss on Lodwick’s theory under these principles.
