共查询到20条相似文献,搜索用时 31 毫秒
1.
J. Rachůnek 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2003,7(7):482-485
In the paper we study MV-algebras and their non-commutative generalizations, GMV-algebras, in which every element is compact. Further, we characterize finite MV-algebras as archimedean GMV-algebras which are 0-meet compact.
Dedicated to Prof. Ján Jakubík on the occasion of his 80th birthday
Supported by the Council of Czech Government, J 14/98: 15100011. 相似文献
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Jiří Rachůnek Dana Šalounová 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(6):565-571
The class of bounded residuated lattice ordered monoids Rl-monoids) contains as proper subclasses the class of pseudo BL-algebras (and consequently those of pseudo MV-algebras, BL-algebras and MV-algebras) and of Heyting algebras. In the paper we introduce and investigate local bounded Rl-monoids which generalize local algebras from the above mentioned classes of fuzzy structures. Moreover, we study and characterize
perfect bounded Rl-monoids. 相似文献
4.
Antonio Di Nola Salvatore Sessa Francesc Esteva Lluis Godo Pere Garcia 《Annals of Mathematics and Artificial Intelligence》2002,35(1-4):197-214
BL-algebras are the Lindenbaum algebras of the propositional calculus coming from the continuous triangular norms and their residua in the real unit interval. Any BL-algebra is a subdirect product of local (linear) BL-algebras. A local BL-algebra is either locally finite (and hence an MV-algebra) or perfect or peculiar. Here we study extensively perfect BL-algebras characterizing, with a finite scheme of equations, the generated variety. We first establish some results for general BL-algebras, afterwards the variety is studied in detail. All the results are parallel to those ones already existing in the theory of perfect MV-algebras, but these results must be reformulated and reproved in a different way, because the axioms of BL-algebras are obviously weaker than those for MV-algebras. 相似文献
5.
A. D. Nola A. Lettieri 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2005,9(12):889-896
BL-algebras were introduced by P. Hájek as algebraic structures of Basic Logic. The aim of this paper is to survey known results
about the structure of finite BL-algebras and natural dualities for varieties of BL-algebras. Extending the notion of ordinal sum of BL-algebras , we characterize a class of finite BL-algebras, actually BL-comets, which can be seen as a generalization of finite BL-chains. Then, just using BL-comets, we can represent any finite BL-algebra A as a direct product of BL-comets. This result can be seen as a generalization of the representation of finite MV-algebras as a direct product of MV-chains. Then we consider the varieties generated by one finite non-trivial totally ordered BL-algebra. For each of these varieties, we show the existence of a strong duality. As an application of the dualities, the
injective and the weak injective members of these classes are described. 相似文献
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ABSTRACTIn this paper, congruences, ideals, and prime ideals of an EMV-semiring and of its associated EMV-algebra are studied. Then EMV-semirings are characterized and it is proved that each EMV-semiring can be embedded into a direct product of a family of MV-semirings as an EMV-semiring. Moreover, another representation of EMV-semirings are presented by EMV-semirings of continuous sections in a sheaf of commutative semirings whose stalks are localizations of EMV-semirings over prime ideals. Also, using the categorical equivalence between EMV-semirings and EMV-algebras, a representation of EMV-algebras are obtained. 相似文献
8.
J. Jakubík 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2000,4(1):27-32
For MV-algebras (algebras of multivalued Lukasiewicz logics) we apply the same terminology and notation as in [3] and [8]. Retracts and retract mappings of abelian lattice ordered groups were studied in [4], cf. also [6], [7]; for the case of multilattice groups and cyclically ordered groups cf. [1] and [5]. To each MV-algebra ? there corresponds an abelian lattice ordered group G with a strong unit u such that (under the notation as in [8]), ? = ?0(G,u) (cf. also Section 1 below). In [2], a different (but equivalent) system of axioms for defining the notion of MV-algebra was applied; instead of ?0(G,u), the notation Γ(G,u) was used. In the present paper we investigate the relations between retract mappings of a projectable MV-algebra ? and the retract mappings of the corresponding lattice ordered group G. 相似文献
9.
In this paper, we introduced the notion of n-fold obstinate filter in BL-algebras and we stated and proved some theorems, which determine the relationship between this notion and other types of
n-fold filters in a BL-algebra. We proved that if F is a 1-fold obstinate filter, then A/F is a Boolean algebra. Several characterizations of n-fold fantastic filters are given, and we show that A is a n-fold fantastic BL-algebra if A is a MV-algebra (n ≥ 1) and A is a 1-fold positive implicative BL-algebra if A is a Boolean algebra. Finally, we construct some algorithms for studying the structure of the finite BL-algebras and n-fold filters in finite BL-algebras. 相似文献
10.
Ji?�� Rach?nek Dana ?alounov�� 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2011,15(2):327-334
Flaminio and Montagna recently introduced state MVMV algebras as MVMV algebras with an internal state in the form of a unary operation. Di Nola and Dvurečenskij further presented a stronger variation
of state MVMV algebras called state-morphism MVMV algebras. In the paper we present state GMVGMV algebras and state-morphism GMVGMV algebras which are non-commutative generalizations of the mentioned algebras. 相似文献
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Grzegorz Dymek 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2008,12(4):365-372
The aim of this paper is to introduce the notion of fuzzy prime ideals of pseudo-MV algebras and investigate some of its properties.
相似文献
13.
We study sequentially continuous measures on semisimple M
V-algebras. Let A be a semisimple M
V-algebra and let I be the interval [0,1] carrying the usual Łukasiewicz M
V-algebra structure and the natural sequential convergence. Each separating set H of M
V-algebra homomorphisms of A into I induces on A an initial sequential convergence. Semisimple M
V-algebras carrying an initial sequential convergence induced by a separating set of M
V-algebra homomorphisms into I are called I-sequential and, together with sequentially continuous M
V-algebra homomorphisms, they form a category SM(I). We describe its epireflective subcategory ASM(I) consisting of absolutely sequentially closed objects and we prove that the epireflection sends A into its distinguished σ-completion σ
H
(A). The epireflection is the maximal object in SM(I) which contains A as a dense subobject and over which all sequentially continuous measures can be continuously extended. We discuss some properties
of σ
H
(A) depending on the choice of H. We show that the coproducts in the category of D-posets [9] of suitable families of I-sequential M
V-algebras yield a natural model of probability spaces having a quantum nature. The motivation comes from probability: H plays the role of elementary events, the embedding of A into σ
H
(A) generalizes the embedding of a field of events A into the generated σ-field σ(A), and it can be viewed as a fuzzyfication
of the corresponding results for Boolean algebras in [8, 11, 14]. Sequentially continuous homomorphisms are dual to generalized
measurable maps between the underlying sets of suitable bold algebras [13] and, unlike in the Loomis–Sikorski Theorem, objects
in ASM(I) correspond to the generated tribes (no quotient is needed, no information about the elementary events is lost). Finally,
D-poset coproducts lift fuzzy events, random functions and probability measures to events, random functions and probability
measures of a quantum nature.
Supported by VEGA Grant 2/7193/01 相似文献
14.
Esko Turunen Janne Mertanen 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2008,12(4):353-357
Given a residuated lattice L, we prove that the subset MV(L) of complement elements x
* of L generates an MV-algebra if, and only if L is semi-divisible. Riečan states on a semi-divisible residuated lattice L, and Riečan states on MV(L) are essentially the very same thing. The same holds for Bosbach states as far as L is divisible. There are semi-divisible residuated lattices that do not have Bosbach states.
These results were obtained when the authors visited Academy of Science, Czech Republic, Institute of Comp. Sciences in Autumn
2006. 相似文献
15.
Xueling Ma Jianming Zhan Yang Xu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(11):1079-1087
In this paper, we introduce the notions of interval valued -fuzzy filters and interval valued -fuzzy Boolean (implicative) filters in R
0-algebras and investigate some of their related properties. Some characterization theorems of these generalized fuzzy filters
are derived. In particular, we prove that an interval valued fuzzy set F in R
0-algebras is an interval valued -fuzzy Boolean filter if and only if it is an interval valued -fuzzy implicative filter. 相似文献
16.
We introduce the notion of a pseudo d-algebra as a generalization of the idea of a d-algebra. The class of pseudo d-algebras can be included in the class of coupled d-algebras. We show that the class of pseudo d-algebras behaves well with respect to standard mappings such as direct products and standard mappings such as homomorphisms. Indeed, we are able to prove a fundamental theorem of homomorphisms and we are able to identify kernel objects as d-ideals in this theory. We also discuss several large classes of examples of pseudo d-algebras which occur in different settings and we identify properties sufficient for or equivalent to membership in important subclasses of the class of pseudo d-algebras in these settings. 相似文献
17.
Adel Mehrpooya Mohammad Ebrahimi Bijan Davvaz 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2016,20(4):1263-1276
In this paper, the notion of a semi-independent dynamical system on a hyper MV-algebra is introduced. The concept of the entropy for a semi-independent hyper MV-algebra dynamical system is developed, and its characteristics are considered. The notion of equivalent semi-independent systems is defined, and it is proved the fact that two equivalent semi-independent hyper MV-algebra dynamical systems have the same entropy. Theorems to help calculate the entropy are given. Specifically, a new version of Kolmogorov–Sinai Theorem has been proved. 相似文献
18.
L. P. Belluce A. Lettieri 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2005,9(7):536-543
In this paper we study an obvious generalization of the hyperarchimedean MV-algebras: boolean dominated MV-algebras. Particularly we point out the wide difference between the class of the hyperarchimedean MV-algebras and the class of the boolean dominated MV-algebras. 相似文献
19.
Rescaling is possibly the most popular approach to cost‐sensitive learning. This approach works by rebalancing the classes according to their costs, and it can be realized in different ways, for example, re‐weighting or resampling the training examples in proportion to their costs, moving the decision boundaries of classifiers faraway from high‐cost classes in proportion to costs, etc. This approach is very effective in dealing with two‐class problems, yet some studies showed that it is often not so helpful on multi‐class problems. In this article, we try to explore why the rescaling approach is often helpless on multi‐class problems. Our analysis discloses that the rescaling approach works well when the costs are consistent, while directly applying it to multi‐class problems with inconsistent costs may not be a good choice. Based on this recognition, we advocate that before applying the rescaling approach, the consistency of the costs must be examined at first. If the costs are consistent, the rescaling approach can be conducted directly; otherwise it is better to apply rescaling after decomposing the multi‐class problem into a series of two‐class problems. An empirical study involving 20 multi‐class data sets and seven types of cost‐sensitive learners validates our proposal. Moreover, we show that the proposal is also helpful for class‐imbalance learning. 相似文献
20.
Jianming Zhan Wiesław A. Dudek Young Bae Jun 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2009,13(1):13-21
We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new
idea, we introduce the notions of interval valued -fuzzy filters of pseudo BL-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued
fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo BL-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of
pseudo BL-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed. 相似文献