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Szmidt E. , Kacprzyk J. , Bujnowski P.

Control and Cybernetics

2022

tom Vol. 51, No. 2

249--266

We discuss some aspects of similarity measures in the context of Atanassov’s intuitionistic fuzzy sets (IFSs, for short). IFSs, proposed in 1983, are a relatively new tool for the modeling and simulation and, because of their construction, present us with new challenges as far the similarity measures are concerned. Specifically, we claim that the distances alone are not a proper measure of similarity for the IFSs. We stress the role of a lack of knowledge concerning elements (options, decisions, etc.) and point out the role of the opposing (complementing) elements. We also pay attention to the fact that it is not justified to talk about similarity when one has not enough knowledge about the compared objects/elements. Some novel measures of similarity are presented.

On the existence of (k,k-1) - kernels in directed graphs

75%

Bród D. , Włoch A. , Włoch I.

Journal of Mathematics and Applications

2006

tom Vol. 28

7-12

We calI a subset J of vertices of a digraph D as a (k, k-1) - kerneI of D, for a fixed k ≥ 2, if all distanees between vertices from J are at Ieast k and the distance from each vertex not belonging to J to the set J is at most k - 1. Some theorems concerning the existence of (k, k - 1) - kernels are proved. The resuIts generalize the well - known Riehardson theorem [9], which says: A digraph without odd circuits has a kernel.

Advanced Morphological Distances Based on Dilation and Erosion

75%

Dražić S.

Fundamenta Informaticae

2019

tom Vol. 164, nr 1

17--39

Distances based on morphological operations have shown good performance in a number of applications. Still, the existing erosion and dilation distance for gray scale images can not be computed in all situations. Furthermore, it is possible that dissimilarity between objects which are compared grows strongly, but the value of a mentioned distance does not change. We present a proposition with the necessary and sufficient conditions for computing these morphological distances and discuss drawbacks that they possess. In addition, we propose novel morphological distances, which can be computed in all situations and provide results with desirable properties. The applicability of novel morphological distances is presented in illustrative examples, including their applicability to real data.

Political colonization quantified : urbanonymy landscape seen as a network of street-sign posts

51%

Místecký M.

Acta onomastica

2019

tom 60

nr 1

74-84

The goal of the article is to present two quantitative methods of assessing the degree of political colonization of municipal space by official urbanonymy. This is done in order to provide a tool which will enable the researchers to test hypotheses and measure the property with needed exactitude. To this end, four municipal units from the Moravian-Silesian region, the Czech Republic, have been selected – namely, the former village of Ostrava-Hošťálkovice, the intra-estate city quarter of Ostrava-Pustkovec, the village of Dolní Lhota, and the medium-sized city of Studénka. The methods presented are street-sign distances (SSD), which map the density of the street sign-carrying objects, and street-sign irradiation (SSI), which measures the number of street signs placed on individual objects. It has been proved that both metrics may furnish some information about the way the public space is colonized in the chosen settlement units, and some interpretations were provided on their bases. In order to draw a general picture of political colonization, two things need to be carried out – more indexes should be brought into the game, and more municipalities investigated.

Cílem článku je představit dvě metody, které vymezují míru politické kolonizace městského prostoru oficiální urbanonymií. Cílem je poskytnout nástroje, pomocí nichž bude možné testovat hypotézy a měřit danou vlastnost s potřebnou přesností. Za tímto účelem byly z Moravskoslezského kraje v České republice vybrány čtyři sídelní jednotky – bývalá vesnice Ostrava-Hošťálkovice, městská část Ostrava-Pustkovec, která je umístěna mezi sídlišti, vesnice Dolní Lhota a středně velké město Studénka. Metody, které zde budou prezentovány, jsou vzdálenosti uličních označníků (SSD), jež zachycují hustotu objektů s uličními názvy, a iradiace uličních označníků (SSI), která zachycuje počet označníků na jednom objektu. Bylo prokázáno, že obě metriky jsou s to poskytnout informace o tom, jak byl prostor ve vybraných sídelních jednotkách kolonizován, a na jejich základě bylo vypracováno několik interpretací. Aby bylo možné o politické kolonizaci pojednat obšírněji, je třeba se zaměřit na dva aspekty – jednak vzít v potaz více indexů, jednak prozkoumat více sídelních jednotek.