On the Preservation of Monotonicity by Extended Mappings

Abstract Images of fuzzy relations provide powerful access to fuzzifications of properties of and/or relationships between fuzzy sets. As an important example, images of fuzzy orderings canonically lead to a concept of ordering of fuzzy sets. This contribution studies in which way the partial (i.e. componentwise) monotonicity of an n-ary mapping transfers to its extension to fuzzy sets

Model of the Computer Simulation System for Managing Geospace under Uncertainty Conditions

Cilj - Cilj istraživanja je razvoj modela, implementacija prototipa i verifikacija računarskog simulacionog sistema koji omogućuje rad sa nepreciznim geoprostornim podacima u realnim uslovima, i proširivanje postojećiim sistemima, razvoja novih algoritama za obradu, novih modela za reprezentaciju procesa i njihovu integraciju. Metodologija - Za modeliranje neodređenosti i nepreciznosti u podacima i procesima korišćen je fazi pristup. Za razvoj softverskog sistema korišćen je objektni pristup (UML 2.0.), model višeslojne distribuirane softverske arhitekture, kombinacija više objektno orijentisanih programskih jezika, i standardi iz oblasti prostornih podataka i procesa. Verifikacija je izvršena na primeru ekstrakcije prostornih osobina na osnovu rasterskih mapa, i implementirana su dva prostorna procesa u skladu sa definisanim modelima. Rezultati - Predloženi su modeli tačkastih (fazi tačka), pravolinijskih (fazi duž) i jednostavnih površinskih (fazi trougao, fazi krug) nepreciznih objekata pomoću fazi skupova. Date su definicije i osobine osnovnih prostornih operacija (prostorna merenja, prostorne funkcije i prostorne relacije). Dat je predlog za modeliranje geoprostornih procesa i algoritam za odreĎivanje fazi konveksnog omotača koji se odlikuje smanjenom računskom složenošću u odnosu na postojeće algoritme. Ograničenja istraživanja/implikacije – Sistem ne obuhvata standardizovan format za razmenu nepreciznih prostornih podataka. To znači da se format razmene mora implementirati u softveru. Praktične implikacije - Predloženi modeli mogu se, pre svega, koristiti u geografskim informacionim sistemima, ali i u analizi slike, te drugim zadacima koji zahtevaju modelovanje realnog prostora (robotika i slično). Originalnost/vrednost – Originalni doprinosi su sledeći: novi modeli tačkastih (fazi tačka), pravolinijskih (fazi duž) i jednostavnih površinskih (fazi trougao, fazi krug) objekata, novi modeli osnovnih prostornih operacija (prostorna merenja, prostorne funkcije i prostorne relacije) i novi algoritam za odreĎivanje fazi konveksnog omotača koji se odlikuje smanjenom računskom složenošću u odnosu na postojeće algoritme.Purpose- The purpose is model development, software prototype implementation and verification of the computer simulation system which provides support for imprecise data processing under real conditions, as well as extensions to existing systems, development of novel algorithms for data processing, new models for processes’ representation and their integration. Design/methodology/approach - Fuzzy approach is used for modelling uncertainties and imprecision. For the software system’s development object approach (UML 2.0), multi-tiered distributed software architecture, combination of several object programming languages, and standards for geospatial data and processes are deployed. Verification is carried out by the example of spatial features extraction from raster maps which is applied to two spatial processes compliant to the proposed model. Findings- Models for point (fuzzy point), line (fuzzy line) and simple planar (fuzzy triangle, fuzzy circle) imprecise objects are proposed. The definitions and basic features of spatial operations (spatial measurements, spatial functions and spatial relations) are given. A proposal for modelling geospatial processes is given and the algorithm for fuzzy convex hull characterized by reduced computational complexity. Research limitations/implications - The system does not comprise standardized format for imprecise data interchange. This means that interchange format should be implemented within the software. Practical implications - The proposed models can be used, primarily for geographic information systems, but they can be also deployed in image analysis as well as tasks requiring modelling of the real space (robotics, etc.). Originality/Value - The main original contributions are: novel models for point (fuzzy point), line (fuzzy line) and simple planar (fuzzy triangle, fuzzy circle) imprecise objects, novel models for imprecise spatial operations (spatial measurements, spatial functions and spatial relations), and the algorithm for fuzzy convex hull characterized by reduced computational complexity

Model of the Computer Simulation System for Managing Geospace under Uncertainty Conditions

Cilj - Cilj istraživanja je razvoj modela, implementacija prototipa i verifikacija računarskog simulacionog sistema koji omogućuje rad sa nepreciznim geoprostornim podacima u realnim uslovima, i proširivanje postojećiim sistemima, razvoja novih algoritama za obradu, novih modela za reprezentaciju procesa i njihovu integraciju. Metodologija - Za modeliranje neodređenosti i nepreciznosti u podacima i procesima korišćen je fazi pristup. Za razvoj softverskog sistema korišćen je objektni pristup (UML 2.0.), model višeslojne distribuirane softverske arhitekture, kombinacija više objektno orijentisanih programskih jezika, i standardi iz oblasti prostornih podataka i procesa. Verifikacija je izvršena na primeru ekstrakcije prostornih osobina na osnovu rasterskih mapa, i implementirana su dva prostorna procesa u skladu sa definisanim modelima. Rezultati - Predloženi su modeli tačkastih (fazi tačka), pravolinijskih (fazi duž) i jednostavnih površinskih (fazi trougao, fazi krug) nepreciznih objekata pomoću fazi skupova. Date su definicije i osobine osnovnih prostornih operacija (prostorna merenja, prostorne funkcije i prostorne relacije). Dat je predlog za modeliranje geoprostornih procesa i algoritam za odreĎivanje fazi konveksnog omotača koji se odlikuje smanjenom računskom složenošću u odnosu na postojeće algoritme. Ograničenja istraživanja/implikacije – Sistem ne obuhvata standardizovan format za razmenu nepreciznih prostornih podataka. To znači da se format razmene mora implementirati u softveru. Praktične implikacije - Predloženi modeli mogu se, pre svega, koristiti u geografskim informacionim sistemima, ali i u analizi slike, te drugim zadacima koji zahtevaju modelovanje realnog prostora (robotika i slično). Originalnost/vrednost – Originalni doprinosi su sledeći: novi modeli tačkastih (fazi tačka), pravolinijskih (fazi duž) i jednostavnih površinskih (fazi trougao, fazi krug) objekata, novi modeli osnovnih prostornih operacija (prostorna merenja, prostorne funkcije i prostorne relacije) i novi algoritam za odreĎivanje fazi konveksnog omotača koji se odlikuje smanjenom računskom složenošću u odnosu na postojeće algoritme.Purpose- The purpose is model development, software prototype implementation and verification of the computer simulation system which provides support for imprecise data processing under real conditions, as well as extensions to existing systems, development of novel algorithms for data processing, new models for processes’ representation and their integration. Design/methodology/approach - Fuzzy approach is used for modelling uncertainties and imprecision. For the software system’s development object approach (UML 2.0), multi-tiered distributed software architecture, combination of several object programming languages, and standards for geospatial data and processes are deployed. Verification is carried out by the example of spatial features extraction from raster maps which is applied to two spatial processes compliant to the proposed model. Findings- Models for point (fuzzy point), line (fuzzy line) and simple planar (fuzzy triangle, fuzzy circle) imprecise objects are proposed. The definitions and basic features of spatial operations (spatial measurements, spatial functions and spatial relations) are given. A proposal for modelling geospatial processes is given and the algorithm for fuzzy convex hull characterized by reduced computational complexity. Research limitations/implications - The system does not comprise standardized format for imprecise data interchange. This means that interchange format should be implemented within the software. Practical implications - The proposed models can be used, primarily for geographic information systems, but they can be also deployed in image analysis as well as tasks requiring modelling of the real space (robotics, etc.). Originality/Value - The main original contributions are: novel models for point (fuzzy point), line (fuzzy line) and simple planar (fuzzy triangle, fuzzy circle) imprecise objects, novel models for imprecise spatial operations (spatial measurements, spatial functions and spatial relations), and the algorithm for fuzzy convex hull characterized by reduced computational complexity

Fitting aggregation operators to data

Theoretical advances in modelling aggregation of information produced a wide range of aggregation operators, applicable to almost every practical problem. The most important classes of aggregation operators include triangular norms, uninorms, generalised means and OWA operators.With such a variety, an important practical problem has emerged: how to fit the parameters/ weights of these families of aggregation operators to observed data? How to estimate quantitatively whether a given class of operators is suitable as a model in a given practical setting? Aggregation operators are rather special classes of functions, and thus they require specialised regression techniques, which would enforce important theoretical properties, like commutativity or associativity. My presentation will address this issue in detail, and will discuss various regression methods applicable specifically to t-norms, uninorms and generalised means. I will also demonstrate software implementing these regression techniques, which would allow practitioners to paste their data and obtain optimal parameters of the chosen family of operators.<br /