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Properties of fuzzy relations powers

Józef Drewniak, Barbara Pȩkala (2007)

Kybernetika

Properties of sup - * compositions of fuzzy relations were first examined in Goguen [8] and next discussed by many authors. Power sequence of fuzzy relations was mainly considered in the case of matrices of fuzzy relation on a finite set. We consider sup - * powers of fuzzy relations under diverse assumptions about * operation. At first, we remind fundamental properties of sup - * composition. Then, we introduce some manipulations on relation powers. Next, the closure and interior of fuzzy relations are examined....

Pseudocomplements in sum-ordered partial semirings

Jānis Cīrulis (2007)

Discussiones Mathematicae - General Algebra and Applications

We study a particular way of introducing pseudocomplementation in ordered semigroups with zero, and characterise the class of those pseudocomplemented semigroups, termed g-semigroups here, that admit a Glivenko type theorem (the pseudocomplements form a Boolean algebra). Some further results are obtained for g-semirings - those sum-ordered partially additive semirings whose multiplicative part is a g-semigroup. In particular, we introduce the notion of a partial Stone semiring and show that several...

Pseudoringe

Stanislav Židek (1972)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica-Physica-Chemica

Quasitrivial semimodules. IV.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

Almost quasitrivial and critical semimodules are studied.

Quasitrivial semimodules. V.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

Critical semimodules over congruence-simple semirings are studied.

Quasitrivial semimodules. VI.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

The paper continues the investigation of quasitrivial semimodules and related problems. In particular, endomorphisms of semilattices are investigated.

Quasitrivial semimodules. VII.

Tomáš Kepka, Petr Němec (2013)

Acta Universitatis Carolinae. Mathematica et Physica

The paper continues the investigation of quasitrivial semimodules and related problems. In particular, strong endomorphisms of semilattices are studied.

Rank and perimeter preserver of rank-1 matrices over max algebra

Seok-Zun Song, Kyung-Tae Kang (2003)

Discussiones Mathematicae - General Algebra and Applications

For a rank-1 matrix A = a ⊗ b t over max algebra, we define the perimeter of A as the number of nonzero entries in both a and b. We characterize the linear operators which preserve the rank and perimeter of rank-1 matrices over max algebra. That is, a linear operator T preserves the rank and perimeter of rank-1 matrices if and only if it has the form T(A) = U ⊗ A ⊗ V, or T ( A ) = U ⊗ A t ⊗ V with some monomial matrices U and V.

Rational semimodules over the max-plus semiring and geometric approach to discrete event systems

Stéphane Gaubert, Ricardo Katz (2004)

Kybernetika

We introduce rational semimodules over semirings whose addition is idempotent, like the max-plus semiring, in order to extend the geometric approach of linear control to discrete event systems. We say that a subsemimodule of the free semimodule 𝒮 n over a semiring 𝒮 is rational if it has a generating family that is a rational subset of 𝒮 n , 𝒮 n being thought of as a monoid under the entrywise product. We show that for various semirings of max-plus type whose elements are integers, rational semimodules...

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