Wyniki wyszukiwania - BazTech

Ograniczanie wyników

3 Fundamenta Informaticae

Powiadomienia systemowe

Sesja wygasła!
Sesja wygasła!
Sesja wygasła!

Znaleziono wyników: 3

Liczba wyników na stronie

Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: rough inclusion

Sortuj według:

Ogranicz wyniki do:

On the Compactness Property of Mereological Spaces

Polkowski Lech

Fundamenta Informaticae

2020

Vol. 172, nr 1

73--95

Continuing our work on mass-based rough mereologies, we make use of the Stone representation theorem for complete Boolean algebras and we exhibit the existence of a finite base in each mereological space. Those bases in turn allow for the introduction of distributed mereologies; regarding each element of the base as a mereological space, we propose a mechanism for fusing those mereological spaces into a global distributed mereological space. We define distributed mass-assignments and rough inclusions pointing to possible applications.

Introducing Mass-based Rough Mereology in a Mereological Universe with Relations to Fuzzy Logics and a Generalization of the Łukasiewicz Logical Foundations of Probability

Polkowski Lech

Fundamenta Informaticae

2019

Vol. 166, nr 3

227--249

We investigate a model for rough mereology based reasoning in which things in the universe of mereology are endowed with positive masses. We define the mass based rough inclusion and establish its properties. This model does encompass inter alia set theoretical universes of finite sets with masses as cardinalities, probability universes with masses as probabilities of possible events, sets of satisfiable formulas with values of satisfiability, measurable bounded sets in Euclidean n -spaces with n -dimensional volume as mass, in particular complete Boolean algebras of regular open or closed sets – the playground for spatial reasoning and geographic information systems. We define a mass-based rough mereological theory (in short mRM-theory). We demonstrate affinities of the mass-based rough mereological mRM-theory with classical many-valued (‘fuzzy’) logics of Łukasiewicz, Gödel and Goguen and we generalize the theses of logical foundations of probability as given by Łukasiewicz. We give an abstract version of the Bayes theorem which does extend the classical Bayes theorem as well as the proposed by Łukasiewicz logical version of the Bayes formula. We also establish an abstract form of the betweenness relation which has proved itself important in problems of data analysis and behavioral robotics. We address as well the problem of granulation of knowledge in decision systems by pointing to the most general set of conditions a thing has to satisfy in order to be included into a formally defined granule of knowledge, the notion instrumental in our approach to data analysis. We address the problem of applications by pointing to our work on intelligent robotics in which the mass interpreted as the relative area of a planar region is basic for definition of a rough inclusion on regular open/closed regions as well as in definition of the notion of betweenness crucial for a strategy for navigating teams of robots.

Rough Granular Computing in Modal Settings : Generalised Approximation Spaces

Wolski M., Gomolińska A.

Fundamenta Informaticae

2016

Vol. 148, nr 1/2

157--172

The paper studies the rough granular computing paradigm within the conceptual settings of multi-modal logic. The main idea is to express a generalised approximation space (U; I; κ), where U is the universe of objects, I is an uncertainty function, and κ is a rough inclusion function, in terms of binary relations, and then to consider the corresponding modal operators. The new modal structure obtained in this way is rich enough to define closure and interior operators corresponding to the classical rough approximation operators and their well-known uni-modal generalisations. In contrast to the standard modal interpretation of rough set approximations, in the new settings one can directly deal with information granules and their properties, which is crucial for granular computing paradigm. More precisely, we are provided with means of describing features of objects and information granules, as well as inclusion degrees between granules.