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Probabilistic Multiset.

Λεπτομέρειες βιβλιογραφικής εγγραφής
Τίτλος: Probabilistic Multiset.
Συγγραφείς: Chatterjee, Debjyoti1 (AUTHOR) debjyoti.chatterjee@jgec.ac.in, Mukherjee, Shashi Bajaj2 (AUTHOR) shashiagarwala@gmail.com
Πηγή: New Mathematics & Natural Computation. Aug2026, p1-41. 41p.
Θεματικοί όροι: *Multiplicity (Mathematics), *Stochastic orders, *Word frequency, *Ordered algebraic structures
Περίληψη: Multisets allow repeated elements, but in many applications their multiplicities are uncertain. We study probabilistic multisets in which each element is assigned a probability mass function on ℕ0. We develop independent additive superposition, max-based union, min-based intersection, truncated difference, capacity relative complement, and scalar multiplication, and examine their algebraic properties. Pointwise probability mass envelopes are distinguished from genuine probabilistic operations and are placed in an ambient profile lattice. For bounded multiplicities, first-order stochastic order yields a complete bounded distributive lattice. We also investigate expected multiplicity, expected cardinality, total variation and Wasserstein geometries, operation stability properties, and overlap similarity. Applications to word frequency modeling, genomic k-mer counts, and uncertain graph neighborhood aggregation illustrate the framework. [ABSTRACT FROM AUTHOR]
Βάση Δεδομένων: Academic Search Index
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  Data: Multisets allow repeated elements, but in many applications their multiplicities are uncertain. We study probabilistic multisets in which each element is assigned a probability mass function on ℕ0. We develop independent additive superposition, max-based union, min-based intersection, truncated difference, capacity relative complement, and scalar multiplication, and examine their algebraic properties. Pointwise probability mass envelopes are distinguished from genuine probabilistic operations and are placed in an ambient profile lattice. For bounded multiplicities, first-order stochastic order yields a complete bounded distributive lattice. We also investigate expected multiplicity, expected cardinality, total variation and Wasserstein geometries, operation stability properties, and overlap similarity. Applications to word frequency modeling, genomic k-mer counts, and uncertain graph neighborhood aggregation illustrate the framework. [ABSTRACT FROM AUTHOR]
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=asx&AN=196592560
RecordInfo BibRecord:
  BibEntity:
    Identifiers:
      – Type: doi
        Value: 10.1142/s1793005729500075
    Languages:
      – Code: eng
        Text: English
    PhysicalDescription:
      Pagination:
        PageCount: 41
        StartPage: 1
    Subjects:
      – SubjectFull: Multiplicity (Mathematics)
        Type: general
      – SubjectFull: Stochastic orders
        Type: general
      – SubjectFull: Word frequency
        Type: general
      – SubjectFull: Ordered algebraic structures
        Type: general
    Titles:
      – TitleFull: Probabilistic Multiset.
        Type: main
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      – PersonEntity:
          Name:
            NameFull: Chatterjee, Debjyoti
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          Name:
            NameFull: Mukherjee, Shashi Bajaj
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          Dates:
            – D: 31
              M: 08
              Text: Aug2026
              Type: published
              Y: 2026
          Identifiers:
            – Type: issn-print
              Value: 17930057
          Titles:
            – TitleFull: New Mathematics & Natural Computation
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