摘要 :
We characterize aperiodic relational morphisms as those that are injective on regular $\H$-classes. This result is applied to obtain simple proofs and generalizations of McAlister’s results on joins of aperiodic semigroups and gr...
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We characterize aperiodic relational morphisms as those that are injective on regular $\H$-classes. This result is applied to obtain simple proofs and generalizations of McAlister’s results on joins of aperiodic semigroups and groups. Also, we show that if $\pv H$ is a proper, non-trivial pseudovariety of groups, then \[\pv A\ast \pv H\subsetneq (\pv A\ast \pv G)\cap \ov {\pv H}.\] We provide coordinate-free formulations and proofs of Rhodes’s Presentation Lemma and generalizations. As an application, we give simpler proofs of Tilson’s theorem on the complexity of semigroups with at most $2$ non-zero $\J$-classes and Rhodes’s theorem that complexity is not local.
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A generic definition of fuzzy morphism between graphs (GFM) is introduced that includes classical graph related problem definitions as sub-cases (such as graph and subgraph isomorphism). The GFM uses a pair of fuzzy relations, one...
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A generic definition of fuzzy morphism between graphs (GFM) is introduced that includes classical graph related problem definitions as sub-cases (such as graph and subgraph isomorphism). The GFM uses a pair of fuzzy relations, one on the vertices and one on the edges. Each relation is a mapping between the elements of two graphs. These two fuzzy relations are linked with constraints derived from the graph structure and the notion of association graph. The theory extends the properties of fuzzy relation to the problem of generic graph correspondence.
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In this paper, some earlier results dealing with fuzzy relations on fuzzy sets by one of the present authors are recapitulated to clarify the motivational background of the present study. Then concepts like fuzzy homorelation, cor...
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In this paper, some earlier results dealing with fuzzy relations on fuzzy sets by one of the present authors are recapitulated to clarify the motivational background of the present study. Then concepts like fuzzy homorelation, correlation, cohomorelation, fuzzy function and fuzzy morphism are introduced and discussed. The presentation is uniform and integrated in the sense that every concept is developed on fuzzy set as base and is organized from the angle of foundational aspects of fuzzy set theory.
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Multimodeling represents a recent remarkable progress in modeling methodology. It includes new types of relationships between models, which cannot be formulated as usual homomorphisms. First this paper identifies the three types o...
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Multimodeling represents a recent remarkable progress in modeling methodology. It includes new types of relationships between models, which cannot be formulated as usual homomorphisms. First this paper identifies the three types of morphism for the modeling relations involved in multimodeling: homomorphism-type, refinement-type, and integration-type. The morphism that can deal with all the types is required to have the properties of partiality and behavior preservation as well as structure preservation. This paper develops a rigorous framework of general morphism for modeling theory so as to provide a formal device that fulfills such requirements and represents all the types of relationships between models including the relationships among experimental frame, real system, base model, lumped model in modeling theory, as well as those involved especially in multimodeling.
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We present here the theory of generalized morphisms and fuzzy relational inequalities and discuss some of these applications. Results presented in this paper extend the work of Bandler and Kohout (1986) ["On the general theory of ...
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We present here the theory of generalized morphisms and fuzzy relational inequalities and discuss some of these applications. Results presented in this paper extend the work of Bandler and Kohout (1986) ["On the general theory of relational morphisms", International Journal of General Systems, 13, pp. 47-66] published in this journal previously, to relational systems based on residuated t-norm fuzzy logics.
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摘要 :
We characterize aperiodic relational morphisms as those that are injective on regular \H-classes. This result is applied to obtain simple proofs and generalizations of McAlisters results on joins of aperiodic semigroups and groups...
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We characterize aperiodic relational morphisms as those that are injective on regular \H-classes. This result is applied to obtain simple proofs and generalizations of McAlisters results on joins of aperiodic semigroups and groups. Also, we show that if \pv H is a proper, non-trivial pseudovariety of groups, then \[\pv A\ast \pv H\subsetneq (\pv A\ast \pv G)\cap \ov {\pv H}.\] We provide coordinate-free formulations and proofs of Rhodess Presentation Lemma and generalizations. As an application, we give simpler proofs of Tilsons theorem on the complexity of semigroups with at most 2 non-zero \J-classes and Rhodess theorem that complexity is not local.
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For a finite semigroup S and pseudovariety V, (Y, T) is a V-stable pair of S iff Y ? S, T ≤ S and for any relational morphism R: S→V with V ∈ V there exists a v ∈ V such that Y ? R~(-1)(v) and T ≤ R~(-1)(Stab(v)). X ≤ S is s...
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For a finite semigroup S and pseudovariety V, (Y, T) is a V-stable pair of S iff Y ? S, T ≤ S and for any relational morphism R: S→V with V ∈ V there exists a v ∈ V such that Y ? R~(-1)(v) and T ≤ R~(-1)(Stab(v)). X ≤ S is stable if it is generated by an L-chain a_i with a_ia_j = a_i for j < i. Given a relation R: S A ∈ A (where A denotes the pseudovariety of aperiodic semigroups) that computes Pl_A(S), we construct a new relation R~∞: S→(A~((M)))~# that computes A-stable pairs. This proves the main result of this paper: (Y, T) is an A-stable pair of S iff T ≤ ∪ X for some stable X ≤ Pl_A(S) and Y ? Y' for some Y' ∈ Pl_A(S) with Y'x = Y' for all x ∈ X. As a corollary we get that if V is a local pseudovariety of semigroups, then V * A has decidable membership problem
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In this paper, we introduce the notion of universal fuzzy automaton with membership values in a complete residuated lattice, whose states are the factorizations of this fuzzy language and transition function is defined using the i...
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In this paper, we introduce the notion of universal fuzzy automaton with membership values in a complete residuated lattice, whose states are the factorizations of this fuzzy language and transition function is defined using the inclusion degree of related fuzzy languages. Next, we define the homomorphism of fuzzy automata, prove that every automaton accepting a fuzzy language can canonically map into the universal fuzzy automaton of this language, which is called the universal property. For a fuzzy language, the connections between the universal fuzzy automaton and fuzzy minimal automata of the given fuzzy language are exploited. Finally, we give a method to construct the universal fuzzy automaton by a deterministic fuzzy automaton accepting the given fuzzy language, which is effective in the case that this deterministic fuzzy automaton is finite.
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We formulate two open problems related to and, in a sense, suggested by the Reiterman-Tholen characterization of effective descent morphisms of topological spaces.
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We prove that if π is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are π-groups. In particular, when π is the empty set, we obtain Henckell's decidability of a...
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We prove that if π is a recursive set of primes, then pointlike sets are decidable for the pseudovariety of semigroups whose subgroups are π-groups. In particular, when π is the empty set, we obtain Henckell's decidability of aperiodic pointlikes. Our proof, restricted to the case of aperiodic semigroups, is simpler than the original proof
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