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 relative tolerance relation of rough set in incomplete information

University is an educational institution that has objectives to increase student retention and also to make sure students graduate on time. Student learning performance can be predicted using data mining techniques e.g. the application of finding essential association rules on student learning base on demographic data by the university in order to achieve these objectives. However, the complete data i.e. the dataset without missing values to generate interesting rules for the detection system, is the key requirement for any mining technique. Furthermore, it is problematic to capture complete information from the nature of student data, due to high computational time to scan the datasets. To overcome these problems, this paper introduces a relative tolerance relation of rough set (RTRS). The novelty of RTRS is that, unlike previous rough set approaches that use tolerance relation, non-symmetric similarity relation, and limited tolerance relation, it is based on limited tolerance relation by taking account into consideration the relatively precision between two objects and therefore this is the first work that uses relatively precision. Moreover, this paper presents the mathematical properties of the RTRS approach and compares the performance and the existing approaches by using real-world student dataset for classifying university’s student performance. The results show that the proposed approach outperformed the existing approaches in terms of computational time and accuracy

Weighted logics for artificial intelligence : an introductory discussion

International audienceBefore presenting the contents of the special issue, we propose a structured introductory overview of a landscape of the weighted logics (in a general sense) that can be found in the Artificial Intelligence literature, highlighting their fundamental differences and their application areas

The e-mail game revisited - Modeling rough inductive reasoning

I study the robustness of Rubinstein´s (1989) E-Mail Game results towards rough inductive reasoning. Rough induction is a form of boundedly rational reasoning where a player does not carry out every inductive step. The information structure in the E-Mail game is generalized and the conditions are characterized under which Rubinstein´s results hold. Rough induction generates a payoff dominant equilibrium where the expected payoffs change continously in the probability of "faulty" communication. The article follows one of Morris´(2001a) reactions to the E-Mail game "that one should try to come up with a model of boundedly rational behavior that delivers predictions that are insensitive to whether there is common knowledge or a large number of levels of knowledge".