Introducing Mass-based Rough Mereology in a Mereological Universe with Relations to Fuzzy Logics and a Generalization of the Łukasiewicz Logical Foundations of Probability*.
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| Title: | Introducing Mass-based Rough Mereology in a Mereological Universe with Relations to Fuzzy Logics and a Generalization of the Łukasiewicz Logical Foundations of Probability*. |
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| Authors: | Polkowski, Lech1 (AUTHOR) polkow@pjwstk.edu.pl |
| Source: | Fundamenta Informaticae. 2019, Vol. 166 Issue 3, p227-249. 23p. |
| Subjects: | Whole & parts (Philosophy), Fuzzy logic, Rough sets, Behavioral assessment, Universe, Boolean algebra, Generalization |
| Abstract: | 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 systems1. 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. [ABSTRACT FROM AUTHOR] |
| Copyright of Fundamenta Informaticae is the property of Polskie Towarzystwo Matematyczne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
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| Items | – Name: Title Label: Title Group: Ti Data: Introducing Mass-based Rough Mereology in a Mereological Universe with Relations to Fuzzy Logics and a Generalization of the Łukasiewicz Logical Foundations of Probability<superscript>*</superscript>. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Polkowski%2C+Lech%22">Polkowski, Lech</searchLink><relatesTo>1</relatesTo> (AUTHOR)<i> polkow@pjwstk.edu.pl</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Fundamenta+Informaticae%22">Fundamenta Informaticae</searchLink>. 2019, Vol. 166 Issue 3, p227-249. 23p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Whole+%26+parts+%28Philosophy%29%22">Whole & parts (Philosophy)</searchLink><br /><searchLink fieldCode="DE" term="%22Fuzzy+logic%22">Fuzzy logic</searchLink><br /><searchLink fieldCode="DE" term="%22Rough+sets%22">Rough sets</searchLink><br /><searchLink fieldCode="DE" term="%22Behavioral+assessment%22">Behavioral assessment</searchLink><br /><searchLink fieldCode="DE" term="%22Universe%22">Universe</searchLink><br /><searchLink fieldCode="DE" term="%22Boolean+algebra%22">Boolean algebra</searchLink><br /><searchLink fieldCode="DE" term="%22Generalization%22">Generalization</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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 systems1. 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. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Fundamenta Informaticae is the property of Polskie Towarzystwo Matematyczne and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.3233/FI-2019-1801 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 23 StartPage: 227 Subjects: – SubjectFull: Whole & parts (Philosophy) Type: general – SubjectFull: Fuzzy logic Type: general – SubjectFull: Rough sets Type: general – SubjectFull: Behavioral assessment Type: general – SubjectFull: Universe Type: general – SubjectFull: Boolean algebra Type: general – SubjectFull: Generalization Type: general Titles: – TitleFull: Introducing Mass-based Rough Mereology in a Mereological Universe with Relations to Fuzzy Logics and a Generalization of the Łukasiewicz Logical Foundations of Probability*. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Polkowski, Lech IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 03 Text: 2019 Type: published Y: 2019 Identifiers: – Type: issn-print Value: 01692968 Numbering: – Type: volume Value: 166 – Type: issue Value: 3 Titles: – TitleFull: Fundamenta Informaticae Type: main |
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