Fuzzy Logic for Incidence Geometry
The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | The Scientific World Journal |
| Online Access: | http://dx.doi.org/10.1155/2016/9057263 |
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| _version_ | 1832551481903939584 |
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| author | Alex Tserkovny |
| author_facet | Alex Tserkovny |
| author_sort | Alex Tserkovny |
| collection | DOAJ |
| description | The paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid’s first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points. |
| format | Article |
| id | doaj-art-add350413c4b4f19a93a064746eeac84 |
| institution | Kabale University |
| issn | 2356-6140 1537-744X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | The Scientific World Journal |
| spelling | doaj-art-add350413c4b4f19a93a064746eeac842025-02-03T06:01:22ZengWileyThe Scientific World Journal2356-61401537-744X2016-01-01201610.1155/2016/90572639057263Fuzzy Logic for Incidence GeometryAlex Tserkovny0Dassault Systemes, 175 Wyman Street, Waltham, MA 02451, USAThe paper presents a mathematical framework for approximate geometric reasoning with extended objects in the context of Geography, in which all entities and their relationships are described by human language. These entities could be labelled by commonly used names of landmarks, water areas, and so forth. Unlike single points that are given in Cartesian coordinates, these geographic entities are extended in space and often loosely defined, but people easily perform spatial reasoning with extended geographic objects “as if they were points.” Unfortunately, up to date, geographic information systems (GIS) miss the capability of geometric reasoning with extended objects. The aim of the paper is to present a mathematical apparatus for approximate geometric reasoning with extended objects that is usable in GIS. In the paper we discuss the fuzzy logic (Aliev and Tserkovny, 2011) as a reasoning system for geometry of extended objects, as well as a basis for fuzzification of the axioms of incidence geometry. The same fuzzy logic was used for fuzzification of Euclid’s first postulate. Fuzzy equivalence relation “extended lines sameness” is introduced. For its approximation we also utilize a fuzzy conditional inference, which is based on proposed fuzzy “degree of indiscernibility” and “discernibility measure” of extended points.http://dx.doi.org/10.1155/2016/9057263 |
| spellingShingle | Alex Tserkovny Fuzzy Logic for Incidence Geometry The Scientific World Journal |
| title | Fuzzy Logic for Incidence Geometry |
| title_full | Fuzzy Logic for Incidence Geometry |
| title_fullStr | Fuzzy Logic for Incidence Geometry |
| title_full_unstemmed | Fuzzy Logic for Incidence Geometry |
| title_short | Fuzzy Logic for Incidence Geometry |
| title_sort | fuzzy logic for incidence geometry |
| url | http://dx.doi.org/10.1155/2016/9057263 |
| work_keys_str_mv | AT alextserkovny fuzzylogicforincidencegeometry |