tag:blogger.com,1999:blog-59957920802053650742011-08-18T19:42:16.243+02:00Still totally `Under construction'Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.comBlogger131100tag:blogger.com,1999:blog-5995792080205365074.post-9620816923848075092011-02-21T23:26:00.001+01:002011-03-01T22:33:18.114+01:00

P. Terán (201x). Fuzzy Sets and Systems, in press.I think this is a nice paper. It combines many things and, being a 42-page manuscript to prove one theorem, it brings an `epic' culmination to part of my earlier research.The general framework is that of convex combination spaces, an attempt by Ilya Molchanov and myself (2006 below) at an axiomatic treatment of expectation in metric spaces taking

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-19825446267751889942010-09-23T21:19:00.008+02:002010-09-29T23:59:56.446+02:00

P. Terán (2010). In: Combining Soft Computing and Statistical Methods in Data Analysis (C.Borgelt et al., editors), 611--618. Springer, Berlin.[Proceedings of the 5th Intl. Conf. on Soft Methods in Statistics and Probability][Invited session Probabilistic aspects of fuzzy sets]Abstract: We show that two probabilistic interpretations of fuzzy sets via random sets and large deviation principles

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-5012967085638492422009-06-18T21:08:00.013+02:002009-12-14T14:21:05.907+01:00

P. Terán (2010). Journal of Mathematical Analysis and Applications 363, 569-578.A well-known technique for stochastic optimization problems in which one aims to optimize the expected value of a function is called the Sample Average Approximation (SAA). The expectation is replaced by the average over a sample, and the solution of the SAA problem is close to that of the original one. But if the

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-10816245348202373092009-04-20T23:54:00.005+02:002009-04-21T01:28:37.464+02:00

P. Terán (2007). Fuzzy Sets and Systems 158, 973-986.For some reason, I never wrote an entry for this paper when I started this blog.It appeared in the FSS special issue Selected papers from IFSA 2005, 11th World Congress of International Fuzzy Systems Association, for which 7 papers were selected out of the 340 conference communications (I made it into the 2% cut, showing that events with

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-10024965768373783682009-04-07T19:44:00.008+02:002010-10-01T23:23:38.737+02:00

P. Terán (2008). Test 17, 505-514.Trying to understand when the Herer expectation of a random set falls into the abstract definition of expectation in A law of large numbers in a metric space with a convex combination operation unexpectedly triggered a line of research on the Herer expectation itself.This paper characterizes those separable Banach spaces where the Herer expectation is identical

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-50246554146418466602009-04-03T20:40:00.009+02:002010-06-30T12:04:42.667+02:00

P. Terán (2010). Journal of Convex Analysis 17, 277-292.Although there is no probability in it, this paper is in fact part of a strand of research in random set theory. The driving question is as follows: what is the relationship between the Aumann and the Herer expectation of a random set? Since Aumann's definition relies on integration in Banach spaces whereas Herer's is geometric, the mere

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-20814018855660537922008-05-07T19:12:00.008+02:002009-04-03T22:04:27.723+02:00

P. Terán (2008). In: Soft Methods for Handling Variability and Imprecision, 289--296. Springer, Berlin.[Proceedings of the 4th Intl. Conf. on Soft Methods in Statistics and Probability]An interesting question is what happens to random variables when the probability measure is replaced by a non-additive measure. That topic has been intermitently studied in the fuzzy literature for over 20 years,

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-13109114661117641082008-01-24T12:34:00.000+01:002008-01-24T12:53:33.333+01:00

P. Terán (2002). Ph. D. Thesis.This is my thesis, defended 10 March 2003. It's in Spanish, so it won't be so helpful to most people. The title is `Approximation and convergence theorems for random sets and random functions'.Some parts of it never appeared in paper form (mostly but not only, the less better ones).The main lines are:-Korovkin-type approximation theorems for set-valued and

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-39482700973157867362007-11-13T19:12:00.001+01:002010-10-01T23:28:40.826+02:00

P. Terán (2008). Fuzzy Sets and Systems 159, 343-360.This paper was conceived and written in late 2001 and early 2002. For years, I stubbornly tried to have it published in a Statistics & Probability journal. A tale of this epic yet unfruitful quest was told in my personal blog (in Spanish).I finally quit and submitted it to FSS, where I knew knowledgeable reviewers would be used.Young people do

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-87300472181903134982007-10-31T15:28:00.003+01:002009-06-19T00:18:33.175+02:00

P. Terán (2008). Statistics and Probability Letters 78, 42-49.While spending a night in the (South) Tenerife Airport, and that means a lot of time to kill, I read a JMAA paper by Alexander Shapiro and Huifu Xu where they obtained a strong law of large numbers for subdifferentials of random functions as a tool for consistency analysis of stationary points in non-convex non-smooth stochastic

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-74803603313111468142007-10-26T13:40:00.001+02:002008-11-24T12:17:37.528+01:00

P. Terán (2008). Proceedings of the American Mathematical Society. 136, 4417-4425.The starting point is Zvi Artstein's 1983 paper on distributions of random sets. Among other things, he proved that, if a sequence of distributions of random compact sets converges weakly in the Hausdorff metric, their cores (or sets of distributions of selections) also converge in the Hausdorff metric defined in

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-72303887810684944772007-10-18T18:02:00.003+02:002009-04-07T20:11:59.305+02:00

P. Terán, I. Molchanov (2006). In Soft methods for integrated uncertainty modelling (J.Lawry, E.Miranda, A.Bugarin, S.Li, M.A.Gil, P. Grzegorzewski, O. Hryniewicz, editors), 153-160. Springer, Berlin.[Proceedings of the 3rd Intl. Conf. on Soft Methods in Statistics and Probability] [Invited session Probability of imprecisely valued random elements with applications]We tried to draw some

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0tag:blogger.com,1999:blog-5995792080205365074.post-21249614970604944622007-10-15T17:59:00.000+02:002008-01-24T12:54:16.875+01:00

A fact about modern scientific research, and one researchers may want to ponder, is that no-one cares about you. Just as tons and tons of new papers are being printed and published right as I speak, you should know that Pallas Athena will visit no-one in dreams to tell them to read your paper.In the old days, researchers went to the university library to browse through a small number of journals,

Pedro Teránhttp://www.blogger.com/profile/17225528247201190873noreply@blogger.com0