The Existence of Generalized Inverses of Fuzzy Matrices

Ćirić, Miroslav; Ignjatović, Jelena

doi:10.1007/978-3-030-01632-6_2

Cited by 3 publications

(1 citation statement)

References 22 publications

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“…After their introduction, an impressive number of papers dealt with (b, c)-inverses and inverses along an element. They have been most studied in the contexts of rings [4,5,16,36,[38][39][40]53,67,68,75,[80][81][82][83][84] and semigroups [2,14,16,[24][25][26][27][44][45][46]49], and they have been also studied in the context of Banach algebras [8,9,45], residuated semigroups and quantales [33], matrices over a field [6,15,61,70], matrices over a ring [37], tensors [59], and fuzzy matrices with entries in a complete residuated lattice [18]. Core and dual core inverses were studied in [1,43,57,69,76], in the contexts of matrices and rings, and inner and outer inverses with prescribed idempotents and ideals have been considered in [13,22,…”

Section: Introductionmentioning

confidence: 99%

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Ćirić,

Ignjatović,

Stanimirović

2023

Semigroup Forum

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We provide existence criteria and characterizations for outer inverses in a semigroup belonging to the prescribed Green's R-, L -and H -classes. These results generalize the well-known problem of finding outer inverses of a matrix over a field with the prescribed range or/and null space. Outer inverses belonging to the prescribed Green's R-and L -classes also represent extensions of Drazin's (b, c)-inverses and Mary's inverses along an element. We provide an overview of other such extensions that have emerged recently and compare them with the extensions introduced in this paper.

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Section: Introductionmentioning

confidence: 99%

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Ćirić,

Ignjatović,

Stanimirović

2023

Semigroup Forum

Self Cite

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Inverses of fuzzy relation matrices with addition-min composition

Guo,

Fu,

Shen

2024

Fuzzy Sets and Systems

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Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Ćirić

Ignjatović

Stanimirović

2022

Preprint

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We provide existence criteria and characterizations for outer inverses in a semigroup belonging to the prescribed Green’s ℛ-, ℒ- and ℋ-classes. These results generalize the well-known problem of finding outer inverses of a matrix over a field with the prescribed range or/and null space.We show that Mary’s inverse along an element, Drazin’s (b, c)-inverse, and Bott-Duffin (e,f)-inverse of a given element are just three different ways of representing the same notion – the outer inverse of this element belonging to the prescribed Green’s ℋ-class. Hence, outer inverses belonging to the prescribed Green’s ℛ- and ℒ-classes represent extensions of (b,c)-inverses and inverses along an element. We provide an overview of other such extensions that have emerged recently and compare them with the extensions introduced in this paper. Mathematics Subject Classification (2010). 20M99, 15A09, 15A24.

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The Existence of Generalized Inverses of Fuzzy Matrices

Cited by 3 publications

References 22 publications

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

Inverses of fuzzy relation matrices with addition-min composition

Outer inverses in semigroups belonging to the prescribed Green’s equivalence classes

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