On generalized inverses of Boolean Matrices

Rao, P.S.S.N.V.P.; Rao, K. P. S. Bhaskara

doi:10.1016/0024-3795(75)90054-3

Cited by 27 publications

(6 citation statements)

References 3 publications

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“…As shown in [46], if a Boolean matrix A has the Moore-Penrose inverse A † , then A † = A * . The same result has been also proved for matrices with entries in an arbitrary Boolean algebra [45], matrices with entries in the Gödel structure [34] and in a Brouwerian lattice [14], and matrices with entries in inclines [6]. Here we discuss certain conditions on involutive ordered semigroups and involutive quantales that imply a † = a * , and prove two theorems that generalize the aforementioned results.…”

Section: Some Conditions That Imply a † = A *supporting

confidence: 57%

“…Note that Cui-Kui [13,14], Wang [55], and Han, Li, and Wang [20] studied generalized inverses of fuzzy matrices with entries in Brouwerian lattices using some kind of residuals. Generalized inverses of fuzzy matrices with entries in a Boolean algebra and the Gödel structure have been investigated by Rao and Rao [45], Kim and Roush [34], and Hashimoto [21]. Here we have generalized the results from all these articles.…”

Section: Introductionmentioning

confidence: 88%

“…The previous proposition has already been proved in the context of real matrices (cf. [57]), Boolean matrices [45], fuzzy matrices with entries in the Gödel structure [7], and involutive rings [61]. Since the proof in the case of involutive semigroups is similar, it will be omitted.…”

Section: Corollary 35 (Schein [50]) a Relation α ∈ 2 A×a Has A {1}-mentioning

confidence: 99%

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Moore-Penrose equations in involutive residuated semigroups and involutive quantales

Ignjatović

Ćirić

2017

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In this paper we provide procedures for testing the existence of various types of generalized inverses in involutive residuated semigroups and involutive quantales defined by the Moore-Penrose equations, and for computing the extreme inverses whenever they exist. We also determine certain instances when a? = a*, whenever a? exists. The obtained results can be applied to a wide class of quantales of fuzzy relations and fuzzy matrices, as well as to Gelfand quantales.

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Section: Some Conditions That Imply a † = A *supporting

confidence: 57%

Section: Introductionmentioning

confidence: 88%

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Moore-Penrose equations in involutive residuated semigroups and involutive quantales

Ignjatović

Ćirić

2017

Filomat

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“…The equation (2.1) has been studied by several authors ( [5,6,7]). Plemmons ( [6]) published algorithms for computing generalized inverses of Boolean matrices under certain conditions.…”

Section: Properties Of Regularity and Singularity Of Boolean Matricesmentioning

confidence: 99%

“…Plemmons ( [6]) published algorithms for computing generalized inverses of Boolean matrices under certain conditions. Also Rao and Rao ( [7]) had characterizations of regular matrices in M m,n (B).…”

Section: Properties Of Regularity and Singularity Of Boolean Matricesmentioning

confidence: 99%