Rough set approach to multiple criteria classification with imprecise evaluations and assignments

Dominance-based Rough Set Approach (DRSA) has been introduced to deal with multiple criteria classification (also called multiple criteria sorting, or ordinal classification with monotonicity constraints), where assignments of objects may be inconsistent with respect to dominance principle. In this paper, we consider an extension of DRSA to the context of imprecise evaluations of objects on condition criteria and imprecise assignments of objects to decision classes. The imprecisions are given in the form of intervals of possible values. In order to solve the problem, we reformulate the dominance principle and introduce second-order rough approximations. The presented methodology preserves well-known properties of rough approximations, such as rough inclusion, complementarity, identity of boundaries and precisiation. Moreover, the meaning of the precisiation property is extended to the considered case. The paper presents also a way to reduce decision tables and to induce decision rules from rough approximations.     

Categorical Abstract Algebraic Logic: Structurality,protoalgebraicity, and correspondence

The notion of an ? ‐matrix as a model of a given π ‐institution ? is introduced. The main difference from the approach followed so far in Categorical Abstract Algebraic Logic (CAAL) and the one adopted here is that an ? ‐matrix is considered modulo the entire class of morphisms from the underlying N ‐algebraic system of ? into its own underlying algebraic system, rather than modulo a single fixed (N,N ′)‐logical morphism. The motivation for introducing ? ‐matrices comes from a desire to formulate a correspondence property for N ‐protoalgebraic π ‐institutions closer in spirit to the one for sentential logics than that considered in CAAL before. As a result, in the previously established hierarchy of syntactically protoalgebraic π ‐institutions, i. e., those with an implication system, and of protoalgebraic π ‐institutions, i. e., those with a monotone Leibniz operator, the present paper interjects the class of those π ‐institutions with the correspondence property, as applied to ? ‐matrices. Moreover, this work on ? ‐matrices enables us to prove many results pertaining to the local deduction‐detachment theorems, paralleling classical results in Abstract Algebraic Logic formulated, first, by Czelakowski and Blok and Pigozzi. Those results will appear in a sequel to this paper. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Linguistic modelling and information coarsening based on prototype theory and label semantics

The theory of prototypes provides a new semantic interpretation of vague concepts. In particular, the calculus derived from this interpretation results in the same calculus as label semantics proposed by Lawry. In the theory of prototypes, each basic linguistic label L has the form ‘about P’, where P is a set of prototypes of L and the neighborhood size of the underlying concept is described by the word ‘about’ which represents a probability density function δ on [0,+∞). In this paper we propose an approach to vague information coarsening based on the theory of prototypes. Moreover, we propose a framework for linguistic modelling within the theory of prototypes, in which the rules are concise and transparent. We then present a linguistic rule induction method from training data based on information coarsening and data clustering. Finally, we apply this linguistic modelling method to some benchmark time series prediction problems, which show that our linguistic modelling and information coarsening methods are potentially powerful tools for linguistic modelling and uncertain reasoning.     

Heavy flavor baryon spectra via QCD sum rules

In this talk, we give a short review of our recent works on studying the singly heavy baryon, doubly heavy baryon, and triply heavy baryon spectra from QCD sum rules.     

Strong coupling constants of light pseudoscalar mesons with heavy baryons in QCD

We calculate the strong coupling constants of light pseudoscalar mesons with heavy baryons within the light cone QCD sum rules method. It is shown that sextet–sextet, sextet–antitriplet and antitriplet–antitriplet transitions are described by one universal invariant function for each class. A comparison of our results on the coupling constants with the predictions existing in literature is also presented.     

Hierarchical and conditional combination of belief functions induced by visual tracking

In visual tracking, sources of information are often disrupted and deliver imprecise or unreliable data leading to major data fusion issues. In the Dempster-Shafer framework, such issues can be addressed by attempting to design robust combination rules. Instead of introducing another rule, we propose to use existing ones as part of a hierarchical and conditional combination scheme. The sources are represented by mass functions which are analysed and labelled regarding unreliability and imprecision. This conditional step divides the problem into specific sub-problems. In each of these sub-problems, the number of constraints is reduced and an appropriate rule is selected and applied. Two functions are thus obtained and analysed, allowing another rule to be chosen for a second (and final) fusion level. This approach provides a fast and robust way to combine disrupted sources using contextual information brought by a particle filter. Our experiments demonstrate its efficiency on several visual tracking situations.     

World-line approach to the Bern-Kosower formalism in two-loop Yang-Mills theory

Based on the world-line formalism with a sewing method, we derive the Yang-Mills effective action in a form useful to generate the Bern-Kosower-type master formulae for gluon scattering amplitudes at the two-loop level. It is shown that four-gluon (φ⁴ type sewing) contributions can be encapsulated in the action with three-gluon (φ³ type) vertices only, the total action thus becoming a simple expression. We then derive a general formula for a two-loop Euler-Heisenberg type action in a pseudo-abelian su(2) also studied.     

Distribution‐free precedence control charts with improved runs‐rules

Distribution‐free (nonparametric) control charts are helpful in applications where we do not have enough information about the underlying distribution. The Shewhart precedence charts is a class of Phase I nonparametric charts for location. One of these charts, called the median precedence chart (Med chart hereafter), uses the median of the test sample as the charting statistic, whereas another chart, called the minimum precedence chart (Min chart hereafter), uses the minimum. In this paper, we first study the comparative performance of the Min and the Med charts, respectively, in terms of their in‐control and out‐of‐control run‐length properties in an extensive simulation study. It is seen that neither chart is best as each has its strength in certain situations. Next, we consider enhancing their performance by adding some supplementary runs‐rules. It is seen that the new charts present very attractive run‐length properties, that is, they outperform their competitors in many situations. A summary and some concluding remarks are given. Copyright © 2016 John Wiley & Sons, Ltd.     

An in silico expert system for the identification of eye irritants

This report describes development of an in silico, expert rule-based method for the classification of chemicals into irritants or non-irritants to eye, as defined by the Draize test. This method was developed to screen data-poor cosmetic ingredient chemicals for eye irritancy potential, which is based upon exclusion rules of five physicochemical properties – molecular weight (MW), hydrophobicity (log P), number of hydrogen bond donors (HBD), number of hydrogen bond acceptors (HBA) and polarizability (Pol). These rules were developed using the ADMET Predictor software and a dataset of 917 eye irritant chemicals. The dataset was divided into 826 (90%) chemicals used for training set and 91 (10%) chemicals used for external validation set (every 10th chemical sorted by molecular weight). The sensitivity of these rules for the training and validation sets was 72.3% and 71.4%, respectively. These rules were also validated for their specificity using an external validation set of 2011 non-irritant chemicals to the eye. The specificity for this validation set was revealed as 77.3%. This method facilitates rapid screening and prioritization of data poor chemicals that are unlikely to be tested for eye irritancy in the Draize test.