Data granulation by the principles of uncertainty

Researches in granular modeling produced a variety of mathematical models, such as intervals, (higher-order) fuzzy sets, rough sets, and shadowed sets, which are all suitable to characterize the so-called information granules. Modeling of the input data uncertainty is recognized as a crucial aspect in information granulation. Moreover, the uncertainty is a well-studied concept in many mathematical settings, such as those of probability theory, fuzzy set theory, and possibility theory. This fact suggests that an appropriate quantification of the uncertainty expressed by the information granule model could be used to define an invariant property, to be exploited in practical situations of information granulation. In this perspective, a procedure of information granulation is effective if the uncertainty conveyed by the synthesized information granule is in a monotonically increasing relation with the uncertainty of the input data. In this paper, we present a data granulation framework that elaborates over the principles of uncertainty introduced by Klir. Being the uncertainty a mesoscopic descriptor of systems and data, it is possible to apply such principles regardless of the input data type and the specific mathematical setting adopted for the information granules. The proposed framework is conceived (i) to offer a guideline for the synthesis of information granules and (ii) to build a groundwork to compare and quantitatively judge over different data granulation procedures. To provide a suitable case study, we introduce a new data granulation technique based on the minimum sum of distances, which is designed to generate type-2 fuzzy sets. We analyze the procedure by performing different experiments on two distinct data types: feature vectors and labeled graphs. Results show that the uncertainty of the input data is suitably conveyed by the generated type-2 fuzzy set models.Comment: 16 pages, 9 figures, 52 reference

A Dual Hesitant Fuzzy Multigranulation Rough Set over Two-Universe Model for Medical Diagnoses

In medical science, disease diagnosis is one of the difficult tasks for medical experts who are confronted with challenges in dealing with a lot of uncertain medical information. And different medical experts might express their own thought about the medical knowledge base which slightly differs from other medical experts. Thus, to solve the problems of uncertain data analysis and group decision making in disease diagnoses, we propose a new rough set model called dual hesitant fuzzy multigranulation rough set over two universes by combining the dual hesitant fuzzy set and multigranulation rough set theories. In the framework of our study, both the definition and some basic properties of the proposed model are presented. Finally, we give a general approach which is applied to a decision making problem in disease diagnoses, and the effectiveness of the approach is demonstrated by a numerical example

An overview of decision table literature 1982-1995.

This report gives an overview of the literature on decision tables over the past 15 years. As much as possible, for each reference, an author supplied abstract, a number of keywords and a classification are provided. In some cases own comments are added. The purpose of these comments is to show where, how and why decision tables are used. The literature is classified according to application area, theoretical versus practical character, year of publication, country or origin (not necessarily country of publication) and the language of the document. After a description of the scope of the interview, classification results and the classification by topic are presented. The main body of the paper is the ordered list of publications with abstract, classification and comments.

A spectroscopic census of the M82 stellar cluster population

We present a spectroscopic study of the stellar cluster population of M82, the archetype starburst galaxy, based primarily on new Gemini-North multi-object spectroscopy of 49 star clusters. These observations constitute the largest to date spectroscopic dataset of extragalactic young clusters, giving virtually continuous coverage across the galaxy; we use these data to deduce information about the clusters as well as the M82 post-starburst disk and nuclear starburst environments. Spectroscopic age-dating places clusters in the nucleus and disk between (7, 15) and (30, 270) Myr, with distribution peaks at ~10 and ~140 Myr respectively. We find cluster radial velocities in the range (-160, 220) km/s (wrt the galaxy centre) and line of sight Na I D interstellar absorption line velocities in (-75, 200) km/s, in many cases entirely decoupled from the clusters. As the disk cluster radial velocities lie on the flat part of the galaxy rotation curve, we conclude that they comprise a regularly orbiting system. Our observations suggest that the largest part of the population was created as a result of the close encounter with M81 ~220 Myr ago. Clusters in the nucleus are found in solid body rotation on the bar. The possible detection of WR features in their spectra indicates that cluster formation continues in the central starburst zone. We also report the potential discovery of two old populous clusters in the halo of M82, aged >8 Gyr. Using these measurements and simple dynamical considerations, we derive a toy model for the invisible physical structure of the galaxy, and confirm the existence of two dominant spiral arms.Comment: Accepted for publication in the Astrophysical Journa

Some views on information fusion and logic based approaches in decision making under uncertainty

Decision making under uncertainty is a key issue in information fusion and logic based reasoning approaches. The aim of this paper is to show noteworthy theoretical and applicational issues in the area of decision making under uncertainty that have been already done and raise new open research related to these topics pointing out promising and challenging research gaps that should be addressed in the coming future in order to improve the resolution of decision making problems under uncertainty