共查询到20条相似文献,搜索用时 15 毫秒
1.
Dan Butnariu Erich Peter Klement Radko Mesiar Mirko Navara 《Archive for Mathematical Logic》2005,44(7):829-849
In many-valued logics with the unit interval as the set of truth values, from the standard negation and the product (or, more
generally, from any strict Frank t-norm) all measurable logical functions can be derived, provided that also operations with
countable arity are allowed. The question remained open whether there are other t-norms with this property or whether all
strict t-norms possess this property. We give a full solution to this problem (in the case of strict t-norms), together with
convenient sufficient conditions. We list several families of strict t-norms having this property and provide also counterexamples
(the Hamacher product is one of them). Finally, we discuss the consequences of these results for the characterization of tribes
based on strict t-norms. 相似文献
2.
3.
IMTL logic was introduced in [12] as a generalization of the infinitely-valued logic of Lukasiewicz, and in [11] it was proved
to be the logic of left-continuous t-norms with an involutive negation and their residua. The structure of such t-norms is
still not known. Nevertheless, Jenei introduced in [20] a new way to obtain rotation-invariant semigroups and, in particular,
IMTL-algebras and left-continuous t-norm with an involutive negation, by means of the disconnected rotation method. In order
to give an algebraic interpretation to this construction, we generalize the concepts of perfect, bipartite and local algebra
used in the classification of MV-algebras to the wider variety of IMTL-algebras and we prove that perfect algebras are exactly
those algebras obtained from a prelinear semihoop by Jenei's disconnected rotation. We also prove that the variety generated
by all perfect IMTL-algebras is the variety of the IMTL-algebras that are bipartite by every maximal filter and we give equational
axiomatizations for it. 相似文献
4.
Benjamín Callejas Bedregal 《Journal of Algorithms in Cognition, Informatics and Logic》2007,62(3-4):135-147
Most of the normal forms for fuzzy logics are versions of conjunctive and disjunctive classical normal forms. Unfortunately, they do not always preserve tautologies and contradictions which is important, for example, for automated theorem provers based on refutation methods.De Morgan implicative systems are triples like the De Morgan systems, which consider fuzzy implications instead of t-conorms. These systems can be used to evaluate the formulas of a propositional language based on the logical connectives of negation, conjunction and implication. Therefore, they determine different fuzzy logics, called implicative De Morgan fuzzy logics.In this paper, we will introduce a normal form for implicative De Morgan systems and we will show that for implicative De Morgan fuzzy logics whose t-norms are strict, this normal form preserves contradictions as well as tautologies. 相似文献
5.
The problem of whether a non-trivial convex combination of two continuous t-norms with the same diagonal function can be a t-norm is studied. It is shown that in both cases–of two nilpotent and of two strict t-norms–a non-trivial convex combination of t-norms with common diagonal function is associative only if the two t-norms involved coincide. For general continuous t-norms a similar result follows. An example of a convex class of non-continuous t-norms is also included. 相似文献
6.
Propositional fuzzy logics given by a combination of a continuous SBL t‐norm with finitely many idempotents and of an involutive negation are investigated. A characterization of continuous t‐norms which, in combination with different involutive negations, yield either isomorphic algebras or algebras with distinct and incomparable sets of propositional tautologies is presented. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
7.
Regular left-continuous t-norms 总被引:1,自引:0,他引:1
Thomas Vetterlein 《Semigroup Forum》2008,77(3):339-379
A left-continuous (l.-c.) t-norm ⊙ is called regular if there is an n<ω such that the map x
↦
x⊙a has, for any a∈[0,1], at most n discontinuity points, and if the function mapping every a∈[0,1] to the set
behaves in a specifically simple way. The t-norm algebras based on regular l.-c. t-norms generate the variety of MTL-algebras.
With each regular l.-c. t-norm, we associate certain characteristic data, which in particular specifies a finite number of
constituents, each of which belongs to one out of six different types. The characteristic data determines the t-norm to a
high extent; we focus on those t-norms which are actually completely determined by it. Most of the commonly known l.-c. t-norms
are included in the discussion.
Our main tool of analysis is the translation semigroup of the totally ordered monoid ([0,1];≤,⊙,0,1), which consists of commuting
functions from the real unit interval to itself. 相似文献
8.
For crisp relations the concept of a semi-order can be stated in a number of equivalent ways. When trying to extend this concept to the fuzzy setting, we observe that the (generalized) definitions fail to be equivalent. In this contribution, we discuss which is the most natural definition of a fuzzy semi-order, and study the hierarchy among the alternative definitions, in particular when using a t-norm without zero divisors. 相似文献
9.
Resolution of composite fuzzy relation equations based on Archimedean triangular norms 总被引:1,自引:0,他引:1
Lately, the sup-t-norm composition of fuzzy relations has been used instead of the well-known max–min. Thus, there is a need for methods of studying and solving sup-t-norm fuzzy relation equations (t is any t-norm). In this paper, the solution existence problem is first studied and solvability criteria for composite fuzzy relation equations of any t-norm are given. Then, a methodology for solving fuzzy relation equations based on sup-t composition, where t is an Archimedean t-norm, is proposed. This resolution method is simpler and faster than those proposed for covering all the continuous t-norms. The result is important, since, as is shown in the paper, the only continuous t-norm that is not Archimedean is the “minimum”. 相似文献
10.
In this paper it is investigated when some kinds of fuzzy implication functions derived from uninorms satisfy the Modus Ponens with respect to a continuous t-norm T, or equivalently, when they are T-conditionals. The study is done for RU-implications and -implications with N a continuous fuzzy negation leading to a lot of solutions in both cases. For RU-implications T-conditionality only depends on the underlying t-norm of the uninorm used to derive the residual implication. On the contrary, for -implications the underlying t-norm is never relevant and only the region out of the t-norm is so. Even the t-conorm can be not relevant also in some cases. 相似文献
11.
研究函数方程组I(x,T(y,z))=T(I(x,y),I(x,z)),I(x,y)=I(N(y),N(x))的解,其中T:[0,1]2→[0,1]是一个严格三角模,I:[0,1]2→[0,1]是一个模糊蕴涵算子和N:[0,1]→[0,1]是一个强否定.在I除了在点(0,0),(1,1)不连续的假设下,获得了满足这个函数方程组解的完全刻画. 相似文献
12.
In this paper we deal with the open problem of convex combinations of continuous triangular norms stated by Alsina, Frank, and Schweizer [C. Alsina, M.J. Frank, B. Schweizer, Problems on associative functions, Aequationes Math. 66 (2003) 128-140, Problems 5 and 6]. They pose a question whether a non-trivial convex combination of triangular norms can ever be a triangular norm. The main result of this paper gives a negative answer to the question for any pair of continuous Archimedean triangular norms with different supports. With the help of this result we show that a non-trivial convex combination of nilpotent t-norms is never a t-norm. The main result also gives an alternative proof to the result presented by Ouyang and Fang [Y. Ouyang, J. Fang, Some observations about the convex combination of continuous triangular norms, Nonlinear Anal., 68 (11) (2008) 3382-3387, Theorem 3.1]. In proof of the main theorem we utilize the Reidmeister condition known from the web geometry. 相似文献
13.
Disturbing Fuzzy Propositional Logic and its Operators 总被引:1,自引:0,他引:1
Xin Liu 《Fuzzy Optimization and Decision Making》2006,5(2):163-175
In this paper, the concept of disturbing fuzzy propositional logic is introduced, and the operators of disturbing fuzzy propositions
is defined. Then the 1-dimensional truth value of fuzzy logic operators is extended to be two-dimensional operators, which
include disturbing fuzzy negation operators, implication operators, “and” and “or” operators and continuous operators. The
properties of these logic operators are studied. 相似文献
14.
Petr Cintula Erich Peter Klement Radko Mesiar Mirko Navara 《Mathematical Logic Quarterly》2006,52(3):269-282
In general, there is only one fuzzy logic in which the standard interpretation of the strong conjunction is a strict triangular norm, namely, the product logic. We study several equations which are satisfied by some strict t‐norms and their dual t‐conorms. Adding an involutive negation, these equations allow us to generate countably many logics based on strict t‐norms which are different from the product logic. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Yaroslav Petrukhin 《Logica Universalis》2018,12(1-2):83-100
In this paper, we introduce the notion of dual Post’s negation and an infinite class of Dual Post’s finitely-valued logics which differ from Post’s ones with respect to the definitions of negation and the sets of designated truth values. We present adequate natural deduction systems for all Post’s k-valued (\(k\geqslant 3\)) logics as well as for all Dual Post’s k-valued logics. 相似文献
16.
The aim of this work is to study the functional equations of Frank and Alsina for two classes of commutative, associative and increasing binary operators. The first one is the class of uninorms introduced by Yager and Rybalov. The second one is the class of nullnorms arising from our study of the Frank equation for uninorms. Both classes contain t-norms and t-conorms as special cases. Moreover, the structure of the other uninorms and nullnorms is closely related to t-norms and t-conorms. These observations are the motivation for studying some generalizations of the Frank and Alsina equations. However, it is shown that all considerations lead back to the already known t-norm and t-conorm solutions. Important consequences in fuzzy preference modelling are pointed out. 相似文献
17.
《Fuzzy Sets and Systems》2004,145(2):253-266
By introducing a new family of partitions into the n-cube [0,1]n, the problem of characterizing truth tables of formulas in the nilpotent minimum logic is solved and their normal forms are presented. So far, only this kind of fuzzy truth functions have normal forms among all fuzzy propositional calculi which are based on left-continuous but discontinuous t-norm. 相似文献
18.
I. S. Krasil’shchik 《Acta Appl Math》1997,49(3):257-269
Three definitions for characteristics of linear differential operators in the category of modules over a commutative unitary algebra are given. These definitions are compared with each other and some basic fact concerning their properties are proved. It is shown that for algebras without zero divisors the characteristic ideal is involutive and is the support of the symbolic module. 相似文献
19.
Choice functions based on t-norms of valued binary relations are introduced. Strict preference is also specified with the use of a t-norm. Properties of the choice functions are investigated and rationality conditions are studied. Some classical particular cases are presented. 相似文献
20.
Songsong Dai Daowu Pei Donghui Guo 《International Journal of Approximate Reasoning》2013,54(5):653-666
This paper investigates the robustness of the full implication inference method and fully implicational restriction method for fuzzy reasoning based on two basic inference models: fuzzy modus ponens and fuzzy modus tollens. Some robustness results are proved based on general left continuous t-norms and induced residuated implications, and some important fuzzy implications. 相似文献