Algebras of Lukasiewicz’s logic and their semiring reducts

Nola, Antonio Di; Gerla, Brunella

doi:10.1090/conm/377/06988

Cited by 47 publications

(32 citation statements)

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“…Theories of polynomials, formal series and automata have a natural interpretation by using of commutative lattice ordered semirings (Di Nola and Gerla 2004;Eilenberg 1974;Gerla 2003Gerla , 2004. In this section, we introduce automata theory over lattice ordered semirings, and discuss some algebraic operations of languages of automata.…”

Section: Application In Automata Theorymentioning

confidence: 99%

“…It is well known that semirings are powerful tools in the study of formal languages and automata theory. Many algebraic properties of formal languages and automata can be characterized by the semiring structures (Di Nola and Gerla 2004;Eilenberg 1974;Gerla 2003Gerla , 2004Krob 1998;Simon 1988).…”

Section: Introductionmentioning

confidence: 99%

“…These two algebraic structures constitute the main algebraic models for fuzzy logic. Starting from MV algebras, Di Nola and Gerla established the relationships between semirings and MV algebras (BL algebras), and showed some applications to automata theory (Di Nola and Gerla 2004;Gerla 2003Gerla , 2004.…”

Section: Introductionmentioning

confidence: 99%

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Semirings and pseudo MV algebras

Shang¹,

Lu²

2006

Soft Comput

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Section: Application In Automata Theorymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Semirings and pseudo MV algebras

Shang¹,

Lu²

2006

Soft Comput

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“…In this context it should be mentioned that connections between MV-algebras and semirings were investigated in [8].…”

Section: Pseudoringsmentioning

confidence: 99%

Ring-Like Structures Corresponding to MV-Algebras via Symmetric Difference

Chajda¹,

Länger²

2005

Sitz.ber. und Anz.

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“…There are several monographs [13,14,15,16] and collections of papers [18,19] on tropical mathematics and its applications. Let us also mention some connections between idempotent algebra and fuzzy sets theory [8,9].…”

Section: Introductionmentioning

confidence: 99%

Characterizing matrices with $\bf{X}$-simple image eigenspace in max-min semiring

Plávka¹,

Sergeev²

2016

Kybernetika

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A matrix A is said to have X-simple image eigenspace if any eigenvector x belonging to the interval X = {x : x ≤ x ≤ x} is the unique solution of the system A ⊗ y = x in X. The main result of this paper is a combinatorial characterization of such matrices in the linear algebra over max-min (fuzzy) semiring.The characterized property is related to and motivated by the general development of tropical linear algebra and interval analysis, as well as the notions of simple image set and weak robustness (or weak stability) that have been studied in max-min and max-plus algebras.

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Algebras of Lukasiewicz’s logic and their semiring reducts

Cited by 47 publications

References 0 publications

Semirings and pseudo MV algebras

Semirings and pseudo MV algebras

Ring-Like Structures Corresponding to MV-Algebras via Symmetric Difference

Characterizing matrices with $\bf{X}$-simple image eigenspace in max-min semiring

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