共查询到20条相似文献,搜索用时 140 毫秒
1.
We introduce a new class of algebras called EQ-algebras. An EQ-algebra has three basic binary operations (meet, multiplication and a fuzzy equality) and a top element. These algebras are intended to become algebras of truth values for a higher-order fuzzy logic (a fuzzy type theory, FTT). The motivation stems from the fact that until now, the truth values in FTT were assumed to form either an IMTL-, BL-, or MV-algebra, all of them being special kinds of residuated lattices in which the basic operations are the monoidal operation (multiplication) and its residuum. The latter is a natural interpretation of implication in fuzzy logic; the equivalence is then interpreted by the biresiduum, a derived operation. The basic connective in FTT, however, is a fuzzy equality and, therefore, it is not natural to interpret it by a derived operation. This defect is expected to be removed by the class of EQ-algebras introduced and studied in this paper. From the algebraic point of view, the class of EQ-algebras generalizes, in a certain sense, the class of residuated lattices and so, they may become an interesting class of algebraic structures as such. 相似文献
2.
Daniel G. Schwartz 《Fuzzy Sets and Systems》1985,17(2):153-165
This paper develops an interval-based approach to the concept of linguistic truth. A special-purpose interval logic is defined, and it is argued that, for many applications, this logic provides a potentially useful alternative to the conventional fuzzy logic.The key idea is to interpret the numerical truth value v(p) of a proposition p as a degree of belief in the logical certainty of p, in which case p is regarded as true, for example, if v(p) falls within a certain range, say, the interval [0.7, 1]. This leads to a logic which, although being only a special case of fuzzy logic, appears to be no less linguistically correct and at the same time offers definite advantages in terms of mathematical simplicity and computational speed.It is also shown that this same interval logic can be generalized to a lattice-based logic having the capacity to accommodate propositions p which employ fuzzy predicates of type 2. 相似文献
3.
Radim Bêlohlvek 《Mathematical Logic Quarterly》1999,45(4):497-504
The concept of Galois connection between power sets is generalized from the point of view of fuzzy logic. Studied is the case where the structure of truth values forms a complete residuated lattice. It is proved that fuzzy Galois connections are in one-to-one correspondence with binary fuzzy relations. A representation of fuzzy Galois connections by (classical) Galois connections is provided. 相似文献
4.
The paper presents generalizations of results on so-called Horn logic, well-known in universal algebra, to the setting of
fuzzy logic. The theories we consider consist of formulas which are implications between identities (equations) with premises
weighted by truth degrees. We adopt Pavelka style: theories are fuzzy sets of formulas and we consider degrees of provability
of formulas from theories. Our basic structure of truth degrees is a complete residuated lattice. We derive a Pavelka-style
completeness theorem (degree of provability equals degree of truth) from which we get some particular cases by imposing restrictions
on the formulas under consideration. As a particular case, we obtain completeness of fuzzy equational logic. 相似文献
5.
In this paper, credibilistic logic is introduced as a new branch of uncertain logic system by explaining the truth value of
fuzzy formula as credibility value. First, credibilistic truth value is introduced on the basis of fuzzy proposition and fuzzy
formula, and the consistency between credibilistic logic and classical logic is proved on the basis of some important properties
about truth values. Furthermore, a credibilistic modus ponens and a credibilistic modus tollens are presented. Finally, a
comparison between credibilistic logic and possibilistic logic is given. 相似文献
6.
7.
Gemma Carotenuto Giangiacomo Gerla 《International Journal of Approximate Reasoning》2013,54(8):1066-1086
In this exploratory paper we propose a framework for the deduction apparatus of multi-valued logics based on the idea that a deduction apparatus has to be a tool to manage information on truth values and not directly truth values of the formulas. This is obtained by embedding the algebraic structure V defined by the set of truth values into a bilattice B. The intended interpretation is that the elements of B are pieces of information on the elements of V. The resulting formalisms are particularized in the framework of fuzzy logic programming. Since we see fuzzy control as a chapter of multi-valued logic programming, this suggests a new and powerful approach to fuzzy control based on positive and negative conditions. 相似文献
8.
Some Properties of Residuated Lattices 总被引:1,自引:0,他引:1
Radim Bělohlávek 《Czechoslovak Mathematical Journal》2003,53(1):161-171
We investigate some (universal algebraic) properties of residuated lattices--algebras which play the role of structures of truth values of various systems of fuzzy logic. 相似文献
9.
10.
Vilm Vychodil 《Mathematical Logic Quarterly》2006,52(2):171-186
The paper deals with fuzzy Horn logic (FHL) which is a fragment of predicate fuzzy logic with evaluated syntax. Formulas of FHL are of the form of simple implications between identities. We show that one can have Pavelka‐style completeness of FHL w.r.t. semantics over the unit interval [0, 1] with (residuated lattices given by) left‐continuous t‐norm and a residuated implication, provided that only certain fuzzy sets of formulas are considered. The model classes of fuzzy structures of FHL are characterized by closure properties. We also give comments on related topics proposed by N. Weaver. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
11.
设M是一个MV-代数,Ω是从MV-代数M到MV-单位区间的全体赋值之集,μ是Ω上的概率测度.本文基于μ在M中引入了元素的尺寸和元素对之间的相似度概念,并由此在M上建立了度量结构.给出了MV-代数上的度量结构在多值逻辑中的一些应用. 相似文献
12.
Product logic is an important t-norm based fuzzy logic with conjunction interpreted as multiplication on the real unit interval [0,1], while Cancellative hoop logic CHL is a related logic with connectives interpreted as for but on the real unit interval with 0 removed (0,1]. Here we present several analytic proof systems for and CHL, including hypersequent calculi, co-NP labelled calculi and sequent calculi. 相似文献
13.
This paper proposes a model for the parametric representation of linguistic hedges in Zadeh’s fuzzy logic. In this model each linguistic truth-value, which is generated from a primary term of the linguistic truth variable, is identified by a real number r depending on the primary term. It is shown that the model yields a method of efficiently computing linguistic truth expressions accompanied with a rich algebraic structure of the linguistic truth domain, namely De Morgan algebra. Also, a fuzzy logic based on the parametric representation of linguistic truth-values is introduced. 相似文献
14.
Petr Hájek 《Mathematical Logic Quarterly》2007,53(1):66-77
Witnessed models of fuzzy predicate logic are models in which each quantified formula is witnessed, i.e. the truth value of a universally quantified formula is the minimum of the values of its instances and similarly for existential quantification (maximum). Systematic theory of known fuzzy logics endowed with this semantics is developed with special attention paid to problems of arithmetical complexity of sets of tautologies and of satisfiable formulas. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
15.
Axiomatizations are presented for fuzzy logics characterized by uninorms continuous on the half-open real unit interval [0,1),
generalizing the continuous t-norm based approach of Hájek. Basic uninorm logic BUL is defined and completeness is established with respect to algebras with lattice reduct [0,1] whose monoid operations are
uninorms continuous on [0,1). Several extensions of BUL are also introduced. In particular, Cross ratio logic CRL, is shown to be complete with respect to one special uninorm. A Gentzen-style hypersequent calculus is provided for CRL and used to establish co-NP completeness results for these logics.
Research supported by Marie Curie Fellowship Grant HPMF-CT-2004-501043. 相似文献
16.
Abstract. An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such
convergences on a given MV-algebra A are exactly the restrictions of the bounded -convergences on the abelian -group in which A appears as the unit interval. Thus the theory of -convergence and Cauchy structures transfers to MV-algebras.?We outline the general theory, and then apply it to three particular
MV-convergences and their corresponding Cauchy completions. The Cauchy completion arising from order convergence coincides
with the Dedekind-MacNeille completion of an MV-algebra. The Cauchy completion arising from polar convergence allows a tidy
proof of the existence and uniqueness of the lateral completion of an MV-algebra. And the Cauchy completion arising from α-convergence
gives rise to the cut completion of an MV-algebra.
Received August 8, 2001; accepted in final form October 18, 2001. 相似文献
17.
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
18.
Alexej P. Pynko 《Mathematical Logic Quarterly》1995,41(4):442-454
The aim of this paper is technically to study Belnap's four-valued sentential logic (see [2]). First, we obtain a Gentzen-style axiomatization of this logic that contains no structural rules while all they are still admissible in the Gentzen system what is proved with using some algebraic tools. Further, the mentioned logic is proved to be the least closure operator on the set of {Λ, V, ?}-formulas satisfying Tarski's conditions for classical conjunction and disjunction together with De Morgan's laws for negation. It is also proved that Belnap's logic is the only sentential logic satisfying the above-mentioned conditions together with Anderson-Belnap's Variable-Sharing Property. Finally, we obtain a finite Hilbert-style axiomatization of this logic. As a consequence, we obtain a finite Hilbert-style axiomatization of Priest's logic of paradox (see [12]). 相似文献
19.
Heinz J. Skala 《Fuzzy Sets and Systems》1978,1(2):129-149
This paper gives a survey of some aspects of many-valued logics and the theory of fuzzy sets and fuzzy reasoning, as advocated in particular by Zadeh. It starts with a short discussion of the development of many-valued logics and its philosophical background. In particular, the systems of Lukasiewicz and their algebraic models are presented. In connection with the famous Arrow paradoxon, Boolean valued and fuzzy social orderings are discussed. After some remarks on inference, fuzzy sets are introduced and it is shown that their definition is sound if some acceptable rationality requirements are demanded. Deformable prototypes are suggested in order to obtain the numerical values of the membership function for some applications. Finally, a recent paper of Bellman and Zadeh on a fuzzy logic, where the truth values themselves are fuzzy, is reviewed. 相似文献