共查询到20条相似文献,搜索用时 15 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
2.
S. Pulmannová E. Vinceková 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2014,18(1):5-13
The notion of a state-morphism on pseudo-effect algebras is introduced, and pseudo-effect algebras with distinguished state-morphisms are studied under the name state-morphism pseudo-effect algebras (SMPEAs). It is shown that every SMPEA admits a representation as a (total) state-morphism algebra, and some results from the general theory of state-morphism algebras (that is, algebras endowed with a distinguished idempotent endomorphism called a state-morphism), recently developed by Botur and Dvure?enskij, can be applied. In particular, it is shown that under suitable conditions, a SMPEA can be embedded into a so-called diagonal one, realized by a direct product of the SMPEA with itself endowed with a suitable natural state-morphism. 相似文献
3.
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.
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
5.
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
6.
Pseudo-BCK algebras and PD-posets 总被引:1,自引:1,他引:0
Yong Lin Liu San Yang Liu Yang Xu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(1):91-101
The notion of pseudo-BCK algebras was introduced by Georgescu and Iorgulescu Proceedings of DMTCS′01: Combinatorics, Computability and Logic, Springer, London, pp 97–114, 2001. It is so general that fleas, pseudo-hoops, psMTL, psBL, pseudo-MV et al., and so hoops, MTL, BL, MV et al. can be seen its extensions. In this paper, we extend the ideal and congruence theory to pseudo-BCK algebras, and investigate the connections between pseudo-BCK algebras and PD(GPD)-posets. 相似文献
7.
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.
Yun Shang Ruqian Lu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2007,11(9):847-853
In this paper, we describe the relationships between pseudo MV algebras and semirings. We also give definitions of automata
on lattice ordered semirings, prove that the family of K-Languages is closed under union, and discuss the conditions for the closedness of families of K-languages under intersection, generalized intersection and reversal operations. 相似文献
10.
Liu Lianzhen Zhang Xiangyang 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2008,12(11):1099-1104
The aim of this paper is to introduce the notion of states on R
0 algebras and investigate some of their properties. We prove that every R
0 algebra possesses at least one state. Moreover, we investigate states on weak R
0 algebras and give some examples to show that, in contrast to R
0 algebras, there exist weak R
0 algebras which have no states. We also derive the condition under which finite linearly ordered weak R
0 algebras have a state.
This work is supported by NSFC (No.60605017). 相似文献
11.
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
12.
J. Jakubík 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2003,7(7):468-471
Torsion classes of MV-algebras are defined as radical classes which are closed with respect to homomorphisms; in this paper we investigate their
relations to radical classes of lattice ordered groups and to varieties of MV-algebras.
Supported by Grant VEGA 1/9056/02. 相似文献
13.
Pseudo-t-norms and pseudo-BL algebras 总被引:1,自引:0,他引:1
P. Flondor G. Georgescu A. Iorgulescu 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2001,5(5):355-371
BL algebras were introduced by Hájek as algebraic structures for his Basic Logic, starting from continuous t-norms on [0,1]. MV algebras, product algebras and Gödel algebras are particular cases of BL algebras. On the other hand, the pseudo-MV algebras extend the MV-algebras in the same way in which the arbitrary l-groups extend the abelian l-groups. We have generalized the BL algebras and pseudo-MV algebras, introducing the pseudo-BL algebras. In this paper we introduce weak-BL algebras and weak-pseudo-BL algebras. We also introduce non-commutative t-norms (we call them pseudo-t-norms) and use them in constructing pseudo-BL algebras and weak-pseudo-BL algebras. 相似文献
14.
In the late seventies, the concept of the estimation algebra of a filtering system was introduced. It was proven to be an invaluable tool in the study of non-linear filtering problems. In the early eighties, Brockett proposed to classify finite dimensional estimation algebras and Mitter conjectured that all functions in finite dimensional estimation algebras are necessarily polynomials of total degree at most one. Despite the massive effort in understanding the finite dimensional estimation algebras, the 20 year old problem of Brockett and Mitter conjecture remains open. In this paper, we give a classification of finite dimensional estimation algebras of maximal rank and solve the Mitter conjecture affirmatively for finite dimensional estimation algebras of maximal rank. In particular, for an estimation algebra E of maximal rank, we give a necessary and sufficient conditions for E to be finite dimensional in terms of the drift fi (x) and observation hj (x). As an important corollary, we show that the number of statistics needed to compute the conditional density of the state given the observation {y(s):0?≤?s?≤?t} by the algebraic method is n where n is the dimension of the state. 相似文献
15.
Ji?�� Rach?nek Dana ?alounov�� 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2011,15(1):199-203
Bounded residuated lattice ordered monoids (RlR\ell-monoids) are a common generalization of pseudo-BLBL-algebras and Heyting algebras, i.e. algebras of the non-commutative basic fuzzy logic (and consequently of the basic fuzzy
logic, the Łukasiewicz logic and the non-commutative Łukasiewicz logic) and the intuitionistic logic, respectively. We investigate
bounded RlR\ell-monoids satisfying the general comparability condition in connection with their states (analogues of probability measures).
It is shown that if an extremal state on Boolean elements fulfils a simple condition, then it can be uniquely extended to
an extremal state on the RlR\ell-monoid, and that if every extremal state satisfies this condition, then the RlR\ell-monoid is a pseudo-BLBL-algebra. 相似文献
16.
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
17.
Lavinia Corina Ciungu Anatolij Dvurečenskij Marek Hyčko 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2010,15(4):619-634
The concept of a state MV-algebra was firstly introduced by Flaminio and Montagna (An algebraic approach to states on MV-algebras.
In: Novák V (ed) Fuzzy logic 2, proceedings of the 5th EUSFLAT conference, September 11–14, Ostrava, vol II, pp 201–206, 2007; Int J Approx Reason 50:138–152, 2009) as an MV-algebra with internal state as a unary operation. Di Nola and Dvurečenskij (Ann Pure Appl Logic 161:161–173, 2009a; Math Slovaca 59:517–534, 2009b) gave a stronger version of a state MV-algebra. In the present paper, we introduce the notion of a state BL-algebra, or more
precisely, a BL-algebra with internal state. We present different types of state BL-algebras, like strong state BL-algebras
and state-morphism BL-algebras, and we study some classes of state BL-algebras. In addition, we give a sample of important
examples of state BL-algebras and present some open problems. 相似文献
18.
Z. Riečanová 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2006,10(6):476-482
Generalized effect algebras as posets are unbounded versions of effect algebras having bounded effect-algebraic extensions.
We show that when the MacNeille completion MC(P) of a generalized effect algebra P cannot be organized into a complete effect algebra by extending the operation ⊕ onto MC(P) then still P may be densely embedded into a complete effect algebra. Namely, we show these facts for Archimedean GMV-effect algebras and
block-finite prelattice generalized effect algebras. Moreover, we show that extendable commutative BCK-algebras directed upwards
are equivalent to generalized MV-effect algebras. 相似文献
19.
Jan Paseka Zdenka Rie?anov�� 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2011,15(3):543-555
We study remarkable sub-lattice effect algebras of Archimedean atomic lattice effect algebras E, namely their blocks M, centers C(E), compatibility centers B(E) and sets of all sharp elements S(E) of E. We show that in every such effect algebra E, every atomic block M and the set S(E) are bifull sub-lattice effect algebras of E. Consequently, if E is moreover sharply dominating then every atomic block M is again sharply dominating and the basic decompositions of elements (BDE of x) in E and in M coincide. Thus in the compatibility center B(E) of E, nonzero elements are dominated by central elements and their basic decompositions coincide with those in all atomic blocks
and in E. Some further details which may be helpful under answers about the existence and properties of states are shown. Namely,
we prove the existence of an (o)-continuous state on every sharply dominating Archimedean atomic lattice effect algebra E with
B(E)\not = C(E).B(E)\not =C(E). Moreover, for compactly generated Archimedean lattice effect algebras the equivalence of (o)-continuity of states with their complete additivity is proved. Further, we prove “State smearing theorem” for these lattice
effect algebras. 相似文献
20.
Some types of filters in BL algebras 总被引:1,自引:0,他引:1
M. Haveshki A. Borumand Saeid E. Eslami 《Soft Computing - A Fusion of Foundations, Methodologies and Applications》2006,10(8):657-664
In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters
and quotient algebras that are constructed via these filters. 相似文献