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Ignacio MONTES
                        Research: Description
Book Chapters
JCR Papers
PhD
Description
Conference papers
After finishing the degree on Mathematics, I started my PhD at the UNIMODE Research Unit of the University of Oviedo (Spain). Between 2010 and 2014, I was granted by the Spanish Ministry of Science and Education with a FPU grant. During this period, I made three research stays: Between 2014 and 2015, I made a postdoctoral stay at the Technologic University of Compiegne with a Laboratory of Excellence (LABEX) grant:
 My research can be split in three main topics:
  1. Stochastic Ordering: In Probability Theory, Stochastic Orders are the methods that allow to compare uncertain quantities. The most known and used stochastic order that can be found in the literature is stochastic dominance, which is based in the comparison of cumulative distribution functions. Another alternative is statistical preference, which is based on the joint distribution and therefore takes into account the dependence between the quantities to be compared.
    My research in this topic is mainly based on the study of these two stochastic orders, their properties, connections and possible extensions to the multivariate framework. For these aims, I usually make use of the Theory of Copulas, which uses a simple function called copula to capture all the information about the dependence.


  2. Imprecise Probabilities: This is the generic term used to refer to all the mathematical models that serve as an alternative and extension of the usual Probability Theory when we deal with imprecise or incomplete information. It includes as particular cases 2- and n-monotone previsions, belief functions, possibility measures, p-boxes or random sets. You can find here the website of the Society of Imprecise Probabilities: Theory and Applications (SIPTA), here a very nice survey done by Enrique Miranda, and here and here some recent books.
    In this framework, my research focuses on the theoretical part of IP. In particular, I am interested in how to define stochastic orders when dealing with imprecise information and the extension of dependence models when dealing with lower probabilities. Also, I have made some works related to conditioning and distorsion models.


  3. Fuzzy Set Theory: Fuzzy sets were introduced by Zadeh as a more flexible model than crisp sets, which is particularly useful when dealing with linguistic information. A fuzzy set assigns a value to each element on the universe, called membership degree, which is interpreted as the degree in which the element fulfills the characteristic described by the set. Of course, crisp sets are particular cases of fuzzy sets, since every element either belongs (i.e., has membership degree 1) or does not (membership degree equals 0) to the set. Since their introduction, fuzzy sets have become a very popular research topic, and nowadays several international journals, conferences and societies are devoted to them. Here you can finde the website of the European Society for Fuzzy Logic and Technology (EUSFLAT) and here the website of the International Fuzzy Systems Association (IFSA).
    My research in this field is related to some theorical generalities and the extensions of fuzzy sets like intuitionistic fuzzy sets.
Here you can see my Google Scholar profile.