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Interval arithmetic has been proved to be very subtle, reliable, and most fundamental in addressing uncertainty and imprecision. However, the theory of classical interval arithmetic and all its alternates suffer from algebraic anomalies, and all have difficulties with interval dependency. A theory of interval arithmetic that seems promising is the theory of parametric intervals. The theory of parametric intervals is presented in the literature with the zealous claim that it provides a radical solution to the long-standing dependency problem in the classical interval theory, along with the claim that parametric interval arithmetic, unlike Moore's classical interval arithmetic, has additive and multiplicative inverse elements, and satisfies the distributive law. So, does the theory of parametric intervals accomplish these very desirable objectives? Here it is argued that it does not.
", "languages": [ { "id": "eng", "title": { "en": "English" } } ], "publication_date": "2019-07-01", "publisher": "Zenodo", "related_identifiers": [ { "identifier": "10.5281/zenodo.3234184", "relation_type": { "id": "cites", "title": { "de": "Zitiert", "en": "Cites" } }, "resource_type": { "id": "publication-article", "title": { "de": "Zeitschriftenartikel", "en": "Journal article" } }, "scheme": "doi" }, { "identifier": "10.5281/zenodo.2656089", "relation_type": { "id": "cites", "title": { "de": "Zitiert", "en": "Cites" } }, "resource_type": { "id": "publication-article", "title": { "de": "Zeitschriftenartikel", "en": "Journal article" } }, "scheme": "doi" }, { "identifier": "10.5281/zenodo.2702404", "relation_type": { "id": "cites", "title": { "de": "Zitiert", "en": "Cites" } }, "resource_type": { "id": "software", "title": { "de": "Software", "en": "Software" } }, "scheme": "doi" }, { "identifier": "10.4018/978-1-4666-4991-0.ch001", "relation_type": { "id": "cites", "title": { "de": "Zitiert", "en": "Cites" } }, "resource_type": { "id": "publication-section", "title": { "de": "Buchkapitel", "en": "Book chapter" } }, "scheme": "doi" } ], "resource_type": { "id": "publication-article", "title": { "de": "Zeitschriftenartikel", "en": "Journal article" } }, "rights": [ { "description": { "en": "The Creative Commons Attribution license allows re-distribution and re-use of a licensed work on the condition that the creator is appropriately credited." }, "icon": "cc-by-icon", "id": "cc-by-4.0", "props": { "scheme": "spdx", "url": "https://creativecommons.org/licenses/by/4.0/legalcode" }, "title": { "en": "Creative Commons Attribution 4.0 International" } } ], "subjects": [ { "subject": "Interval mathematics" }, { "subject": "Classical interval arithmetic" }, { "subject": "Parametric interval arithmetic" }, { "subject": "Constrained interval arithmetic" }, { "subject": "Overestimation-free interval arithmetic" }, { "subject": "Interval dependency" }, { "subject": "Functional dependence" }, { "subject": "Dependency predicate" }, { "subject": "Interval enclosures" }, { "subject": "S-semiring" }, { "subject": "Uncertainty" }, { "subject": "Reliability" } ], "title": "Parametric Intervals: More Reliable or Foundationally Problematic?" }, "parent": { "access": { "owned_by": { "user": 66235 } }, "communities": { "entries": [ { "access": { "member_policy": "open", "members_visibility": "public", "record_policy": "open", "review_policy": "open", "visibility": "public" }, "children": { "allow": false }, "created": "2019-05-01T03:46:55.440707+00:00", "custom_fields": {}, "deletion_status": { "is_deleted": false, "status": "P" }, "id": "c809ceb8-de06-4082-9c0b-931397f6130d", "links": {}, "metadata": { "curation_policy": "Scientific resources by staff at the Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
\r\n\r\nA resource can be either:
\r\n\r\nCurator: Hend Dawood (https://scholar.cu.edu.eg/henddawood)
\r\n", "page": "Resources by staff at the Department of Mathematics, Faculty of Science, Cairo University, Giza, Egypt.
\r\n\r\nOpen-access articles published by Online Mathematics Journal (OMJ).
\r\n\r\nCurator: Hend Dawood (https://scholar.cu.edu.eg/henddawood)
\r\n\r\nEditors-in-Chief:
\r\n\r\nFounded in 2018, by a group of volunteered academicians from different universities around the world, Online Mathematics Journal (OMJ) is a non-governmental open-access international platform that provides an unbiased publication opportunity for any noteworthy research in the field of mathematics. We are dedicated to provide the very best of scientific publication services and our aim is to help academicians share and exchange their knowledge and promote their work. Moreover, as part of our mission, we hope to encourage graduate students and young academicians to get more involved in the research domain, by supporting and funding their bright ideas.
\r\n\r\nThe scope of our journal is rather general and we tend to publish research findings in most subfields of mathematics.
\r\n\r\nThe mission of Online Mathematics Journal is to enhance the dissemination of knowledge across the mathematics field. We aim to publish original and thought provoking papers that will contribute to the field. We also aim to establish an open access forum for dialogue and debate between researchers and academicians. Thereupon, all articles published by Online Mathematics Journal are immediately made available worldwide, under an open access license. This means:
\r\n\r\nFounded: 2018
\r\n\r\nISSN: 2672-7501
\r\n\r\nJournal Website: http://www.onlinemathematics.net/
\r\n\r\nEditors-in-Chief:
\r\n\r\n