Wyniki wyszukiwania - BazTech

1

Betweenness, Łukasiewicz Rough Inclusions, Euclidean Representations in Information Systems, Hyper-granules and Conflict Resolution

Polkowski L. T., Nowak B.

Fundamenta Informaticae

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2016

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Vol. 147, nr 2/3

337--352

EN

In this work, we approach the problem of data analysis from a new angle: we investigate a relational method of separation of data into disjoint sub–data employing a modified betweenness relation, successfully applied by us in the area of behavioral robotics, and, we set a scheme for applications to be studied. The effect of the action by that relation on data is selection of a sub–data, say, ‘kernel’ with the property that each thing in it is a convex combination, in a sense explained below, of some other things in the kernel. One can say that kernel thus exhibited is ‘self–closed’. Algorithmically, this is achieved by means of a new construct, called by us a ‘dual indiscernibility matrix’. On the other hand, the complement to kernel consists of things in the data, which have some attribute values not met in any other thing. It is proper to call this complement to kernel the residuum. We examine both the kernel and the residuum from the point of view of quality of classification into decision classes for a few standard data sets from the UC Irvine Repository finding the results very satisfactory. Conceptually, our work is set in the framework of rough set theory and rough mereology and the main tool in inducing of the betweenness relation is the Łukasiewicz rough inclusion. Apart from the classification problem, we propose some strategies for conflict resolution based on concepts introduced in this work, and in this way we continue conflict analysis in rough set framework initiated by Zdzisław Pawlak.

2

Stability of Optimal Parameters for Classifier Based on Simple Granules of Knowledge

Artiemjew P.

Technical Sciences / University of Warmia and Mazury in Olsztyn

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2011

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nr 14(1)

57-69

EN

Searching for optimal parameters of a classifier based on simple granules of knowledge investigated recently by the author (ARTIEMJEW 2010) raises a question about stability of optimal parameters. In this article, we will check dependence of stability of the optimal radius of granulation on random damage of decision system. The results of experiments show the dependence of stability on size of damage and strategies of treating missing values. This kind of research aims at finding methods of protecting decision systems which are vulnerable to damage against decreasing their classification effectiveness, which means preserving classifying possibilities similar to undamaged decision systems.

PL

Przeprowadzone w ostatnim czasie badania (ARTIEMJEW 2010) zmierzające do wyszukiwania optymalnych parametrów klasyfikacji modułów decyzyjnych opartych na prostych granulach wiedzy zrodziły pytanie o stabilność optymalnych parametrów klasyfikacji. W pracy sprawdzono zależność stabilności optymalnych promieni granulacji od losowego uszkadzania systemu decyzyjnego. Wyniki badań wskazały jednoznacznie, że istnieje zależność między stabilnością a wielkością uszkodzenia i strategiami traktowania wartości uszkodzonych. Tego typu badania mają na celu szukanie metod zabezpieczania systemów decyzyjnych, które są podatne na uszkodzenia, przed zmniejszaniem ich efektywności klasyfikacyjnej. Celem było zachowanie możliwości klasyfikacyjnych zbliżonych do efektywności nieuszkodzonych systemów decyzyjnych.

3

A Logic-Algebraic Approach to Graded Inclusion

Gomolińska A.

Fundamenta Informaticae

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2011

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Vol. 109, nr 3

265-279

EN

In this article we continue searching for functions which might be used as measures of inclusion of information granules in information granules. Starting with a 3-valued logic having an adequate logical matrix, we show how to derive a corresponding graded inclusion function. We report on the results of examination of several best known 3-valued logics in this respect. We also give some basic properties of the inclusion functions obtained.

4

Rough Mereology: A Rough Set Paradigm for Unifying Rough Set Theory and Fuzzy Set Theory

Polkowski L.

Fundamenta Informaticae

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2003

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Vol. 54, nr 1

67-88

EN

In this work, we would like to discuss rough inclusions defined in Rough Mereology - a paradigm for approximate reasoning introduced by Polkowski and Skowron [20] - as a basis for common models for rough as well as fuzzy set theories. We would like to adhere to the point of view that tolerance (or, similarity) is the leading motif common to both theories and in this area paths between the two lie. To this end, we demonstrate that rough inclusions (which represent a hierarchy of tolerance relations) induce rough set theoretic approximations as well as partitions and equivalence relations in the sense of fuzzy set theory. For completeness sake, we also discuss granulation mechanisms based on rough inclusions with applications to Rough-Neuro Computing and Computing with Words. These considerations are also carried out in specialized cases of Menger's as well as Łukasiewicz's rough inclusions introduced in the paper.