Efficient design of experiment for exponential regression models

In this paper robust and efficient designs are derived for several exponential decay models. These models are widely used in chemistry, pharmacokinetics or microbiology. We propose a maximin approach, which determines the optimal design such that a minimum of the D-efficiencies (taken over a certain range for the nonlinear parameters) becomes maximal. Analytic solutions are derived if optimization is performed in the class of minimal supported designs. In general the optimal designs with respect to the maximin criterion have to be determined numerically and some properties of these designs are also studied. --exponential regression model,D-optimal design,robust design,maximin design,pharmacokinetics,microbiology

Testing Relativity at High Energies Using Spaceborne Detectors

(ABRIDGED) The Gamma-ray Large Area Space Telescope (GLAST) will measure the spectra of distant extragalactic sources of high energy gamma-rays. GLAST can look for energy dependent propagation effects from such sources as a signal of Lorentz invariance violation (LIV). Such sources should also exhibit high energy spectral cutoffs from pair production interactions with low energy photons. The properties of such cutoffs can also be used to test LIV. Detectors to measure gamma-ray polarization can look for the depolarizing effect of space-time birefingence predicted by loop quantum gravity. A spaceborne detector array looking down on Earth to study extensive air showers produced by ultrahigh energy cosmic rays can study their spectral properties and look for a possible deviation from the predicted GZK effect as another signal of LIV.Comment: 14 pages, Text of invitated talk presented at the "From Quantum to Cosmos: Fundamental Physics Studies from Space" meeting. More references adde

Computing with Comparative Linguistic Expressions and Symbolic Translation for Decision Making: ELICIT Information

Many real-world decision making (DM) problems present changing contexts in which uncertainty or vagueness appear. Such uncertainty has been often modeled based on the linguistic information by using single linguistic terms. Dealing with linguistic information in DM demands processes of computing with words whose main characteristic is to emulate human beings reasoning processes to obtain linguistic outputs from linguistic inputs. However, often single linguistic terms are limited or do not express properly the expert’s knowledge, being necessary to elaborate richer linguistic expressions easy to understand and able to express greater amount of knowledge, as it is the case of the comparative linguistic expressions based on hesitant fuzzy linguistic terms sets. Nevertheless, current computational models for comparative linguistic expressions present limitations both from understandability and precision points of view. The 2-tuple linguistic representation model stands out in these aspects because of its accuracy and interpretability dealing with linguistic terms, both related to the use of the symbolic translation, although 2-tuple linguistic values are still limited by the use of single linguistic terms. Therefore, the aim of this article is to present a new fuzzy linguistic representation model for comparative linguistic expressions that takes advantage of the goodness of the 2-tuple linguistic representation model and improve the interpretability and accuracy of the results in computing with words processes, resulting the so-called extended comparative linguistic expressions with symbolic translation. Taking into account the proposed model, a new computing with words approach is presented and then applied to a DM case study to show its performance and advantages in a real case by comparing with other linguistic decision approaches.Spanish Ministry of Economy and Competitiveness through the Spanish National Research Projects TIN2015-66524-P and PGC2018-099402-B-I00 and the Postdoctoral Fellowship Ramón y Cajal (RYC-2017-21978)

Uncertainty Measures of Extended Hesitant Fuzzy Linguistic Term Sets

A hesitant fuzzy linguistic term set (HFLTS) is defined as a subset of ordered consecutive linguistic terms, and it has been successfully applied to deal with experts hesitation in decision-making problems when experts have to provide their assessments. This concept has been recently extended to manage ordered consecutive and nonconsecutive linguistic terms, called extendedHFLTS (EHFLTS), which is used in linguistic group decision-making problems to represent the group opinion without loss of information. This paper is focused on studying how to measure the uncertainty presented by the information of an EHFLTS and also of an HFLTS. To do so, a new comprehensive entropy measure for EHFLTSs, which considers two types of uncertainty, fuzziness and hesitation, is proposed. The constructionmethods of the two types of entropy are studied and a comprehensive entropy formula is defined. Finally, a comparative study is carried out to analyze the results obtained from the proposed entropy measures.National Natural Science Foundation of China under Grant 71371107, Spanish National Research Project TIN2015-66524-P, Spanish Ministry of Economy and Finance Postdoctoral fellow (IJCI-2015-23715) and Education Research and Development Foundation