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Fuzzy Algebraic Hyperstructures : An Introduction.

By: Contributor(s): Material type: TextTextSeries: Studies in Fuzziness and Soft Computing SeriesPublisher: Cham : Springer International Publishing AG, 2015Copyright date: ©2015Edition: 1st edDescription: 1 online resource (250 pages)Content type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783319147628
Subject(s): Genre/Form: Additional physical formats: Print version:: Fuzzy Algebraic HyperstructuresDDC classification:
  • 512.2
LOC classification:
  • Q342
Online resources:
Contents:
Intro -- Preface -- Contents -- Fundamentals of Algebraic (Hyper)Structures -- 1.1 Groups -- 1.2 Rings -- 1.3 Polygroups -- 1.4 Hypergroups -- 1.5 Hyperrings -- 1.6 Hv-Structures -- Fuzzy Polygroups -- 2.1 What Fuzzy Sets Are? -- 2.2 Groups and Fuzzy Subgroups -- 2.3 Polygroups and Fuzzy Subpolygroups -- 2.4 Generalized Fuzzy Subpolygroups -- 2.5 Roughness in Polygroups -- 2.6 F-Polygroups -- Fuzzy Hv-Subgroups of Hv-Groups -- 3.1 Fuzzy Hv-Subgroups and Fuzzy Homomorphisms -- 3.2 Generalized Fuzzy Hv-Subgroups -- 3.3 Intuitionistic Fuzzy Hv-Subgroups -- 3.4 T-Product of Fuzzy Hv-Subgroups -- 3.5 Probabilistic Fuzzy Semihypergroups -- 3.6 F-Hypergroups -- Hv-Rings (Hyperrings) and Hv-Ideals -- 4.1 Fuzzy Hv-Ideals -- 4.2 Generalized Fuzzy Hv-Ideals -- 4.3 Interval-Valued Fuzzy Hv-Ideals -- 4.4 Fuzzy Hyperrings -- Connections between Hypergroups and Fuzzy Sets -- 5.1 Join Spaces and Fuzzy Sets -- 5.1.1 Constructions Using Fuzzy Sets -- 5.1.2 Generalizations to L-Fuzzy Sets -- 5.2 L-Fuzzy Join Spaces -- 5.3 Fuzzy Grade of a Hypergroupoid -- 5.3.1 The Main Construction -- 5.3.2 Intuitionistic Fuzzy Grade of a Hypergroupoid -- 5.3.3 Some Examples: Complete Hypergroups and i.p.s. Hypergroups -- 5.3.4 Extensions to Hypergraphs -- 5.4 Hypergroupoids and Fuzzy Sets Endowed with Two Membership Functions -- Bibliography -- Index.
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Intro -- Preface -- Contents -- Fundamentals of Algebraic (Hyper)Structures -- 1.1 Groups -- 1.2 Rings -- 1.3 Polygroups -- 1.4 Hypergroups -- 1.5 Hyperrings -- 1.6 Hv-Structures -- Fuzzy Polygroups -- 2.1 What Fuzzy Sets Are? -- 2.2 Groups and Fuzzy Subgroups -- 2.3 Polygroups and Fuzzy Subpolygroups -- 2.4 Generalized Fuzzy Subpolygroups -- 2.5 Roughness in Polygroups -- 2.6 F-Polygroups -- Fuzzy Hv-Subgroups of Hv-Groups -- 3.1 Fuzzy Hv-Subgroups and Fuzzy Homomorphisms -- 3.2 Generalized Fuzzy Hv-Subgroups -- 3.3 Intuitionistic Fuzzy Hv-Subgroups -- 3.4 T-Product of Fuzzy Hv-Subgroups -- 3.5 Probabilistic Fuzzy Semihypergroups -- 3.6 F-Hypergroups -- Hv-Rings (Hyperrings) and Hv-Ideals -- 4.1 Fuzzy Hv-Ideals -- 4.2 Generalized Fuzzy Hv-Ideals -- 4.3 Interval-Valued Fuzzy Hv-Ideals -- 4.4 Fuzzy Hyperrings -- Connections between Hypergroups and Fuzzy Sets -- 5.1 Join Spaces and Fuzzy Sets -- 5.1.1 Constructions Using Fuzzy Sets -- 5.1.2 Generalizations to L-Fuzzy Sets -- 5.2 L-Fuzzy Join Spaces -- 5.3 Fuzzy Grade of a Hypergroupoid -- 5.3.1 The Main Construction -- 5.3.2 Intuitionistic Fuzzy Grade of a Hypergroupoid -- 5.3.3 Some Examples: Complete Hypergroups and i.p.s. Hypergroups -- 5.3.4 Extensions to Hypergraphs -- 5.4 Hypergroupoids and Fuzzy Sets Endowed with Two Membership Functions -- Bibliography -- Index.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2024. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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