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In order to study uncertainty reasoning and automatic reasoning with linguistic terms, in this paper, the set of basic linguistic truth values and the set of modifiers are defined, according to common sense; partially orderings are defined on them. Based on it, a lattice implication algebra model L18 of linguistic terms is built; furthermore, its some basic properties are discussed. 相似文献
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郑玉美 《湖北大学学报(自然科学版)》1994,16(4):385-389
若半环S有忠实既约的S-半模M,叫S为本原半环.我们证明了本原半环具有稠密性,然后在此基础上证明了所谓的Kaplansky定理,即PI-本原半环是单的,在其中心上是有限维的. 相似文献
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Inclines are additively idempotent semirings, in which the partial order ≤ : x ≤ y if and only if x + y = y is defined and products are less than or equal to either factor. Boolean algebra, max-min fuzzy algebra, and distributive lattices are examples of inclines. In this article, standard bases of a finitely generated vector space over a linearly ordered commutative incline are studied. We obtain that if a standard basis exists, then it is unique. In particular, if the incline is solvable or multiplicatively-declined or multiplicatively-idempotent (i.e., a chain semiring), further results are obtained, respectively. For a chain semiring a checkable condition for distinguishing if a basis is standard is given. Based on the condition an algorithm for computing the standard basis is described. 相似文献
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Igor Dolinka 《Semigroup Forum》2009,78(2):368-373
We generalize a criterion from a previous paper which ensures that an additively idempotent semiring is not finitely based.
As a consequence, we prove the NFB property for the semiring generated by transformations on a finite set with more than one
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Supported by Grant No. 144011 of the Ministry of Science of the Republic of Serbia. 相似文献
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Algebras of fuzzy sets 总被引:2,自引:0,他引:2
In this paper we investigate two kinds of algebras of fuzzy sets, which are obtained by using Zadeh's extension principle. We give conditions under which a homomorphism between two algebras induces a homomorphism between corresponding algebras of fuzzy sets. We prove that if the structure of truth values is a complete residuated lattice, the induced algebra of a subalgebra of an algebra can be embedded into the induced algebra of fuzzy sets of . For direct products we give conditions under which the direct product of algebras of fuzzy sets could be embedded into the algebra of fuzzy sets of the direct product. In the case of homomorphisms and direct products, the two kinds of algebras of fuzzy sets behave in different ways. 相似文献
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BCH-代数的闭模糊理想 总被引:3,自引:0,他引:3
引入了BCH-代数的闭模糊理想、子代数及优BCH-代数的概念,讨论它们的性质,获得若干结果。 相似文献