共查询到20条相似文献,搜索用时 31 毫秒
1.
In this paper, notions of fuzzy closure system and fuzzy closure L —system on L —ordered sets are introduced from the fuzzy point of view. We first explore the fundamental properties of fuzzy closure systems. Then the correspondence between fuzzy closure systems (fuzzy closure L —systems) and fuzzy closure operators is established. Finally, we study the connections between fuzzy closure systems and fuzzy Galois connections. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim 相似文献
2.
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
3.
Javier Gutiérrez García Iraide Mardones‐Pérez María Angeles de Prada Vicente Dexue Zhang 《Mathematical Logic Quarterly》2010,56(2):131-147
This paper presents a systematic investigation of fuzzy (non‐commutative) Galois connections in the sense of R. Bělohlávek [1], from the point of view of enriched category theory. The results obtained show that the theory of enriched categories makes it possible to present the theory of fuzzy Galois connections in a succinct way; and more importantly, it provides a useful method to express and to study the link and the difference between the commutative and the non‐commutative worlds (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
Inma P. Cabrera Pablo Cordero Emilio Muñoz-Velasco Manuel Ojeda-Aciego Bernard De Baets 《Mathematical Methods in the Applied Sciences》2020,43(9):5673-5680
Fuzzy-directed graphs are often chosen as the data structure to model and implement solutions to several problems in the applied sciences. Galois connections have also shown to be useful both in theoretical and in practical problems. In this paper, the notion of relational Galois connection is extended to be applied between transitive fuzzy directed graphs. In this framework, the components of the connection are crisp relations satisfying certain reasonable properties given in terms of the so-called full powering. 相似文献
5.
It is shown here how the Galois connections theory provides a canonical procedure to fuzzify a crisp closure space. Roughly speaking, if S is a space equipped with an ∩-closed set
of subsets (the closed subsets), the closed fuzzy subsets of S are the Galois connections between
and the valuation set. The closed crisp subsets are particular closed fuzzy subsets. 相似文献
6.
Formal concept analysis (FCA) associates a binary relation between a set of objects and a set of properties to a lattice of
formal concepts defined through a Galois connection. This relation is called a formal context, and a formal concept is then
defined by a pair made of a subset of objects and a subset of properties that are put in mutual correspondence by the connection.
Several fuzzy logic approaches have been proposed for inducing fuzzy formal concepts from L-contexts based on antitone L-Galois connections. Besides, a possibility-theoretic reading of FCA which has been recently proposed allows us to consider
four derivation powerset operators, namely sufficiency, possibility, necessity and dual sufficiency (rather than one in standard
FCA). Classically, fuzzy FCA uses a residuated algebra for maintaining the closure property of the composition of sufficiency
operators. In this paper, we enlarge this framework and provide sound minimal requirements of a fuzzy algebra w.r.t. the closure
and opening properties of antitone L-Galois connections as well as the closure and opening properties of isotone L-Galois connections. We apply these results to particular compositions of the four derivation operators. We also give some
noticeable properties which may be useful for building the corresponding associated lattices. 相似文献
7.
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
8.
Jue Wang San-Yang Liu Jie Zhang Shou-Yang Wang 《Fuzzy Optimization and Decision Making》2006,5(1):5-20
The family of Ordered Weighted Averaging (OWA) operators, as introduced by Yager, appears to be very useful in multi-criteria
decision-making (MCDM). In this paper, we extend a family of parameterized OWA operators to fuzzy MCDM based on vague set
theory, where the characteristics of the alternatives are presented by vague sets. These families are specified by a few parameters
to aggregate vague values instead of the intersection and union operators proposed by Chen. The proposed method provides a
“soft” and expansive way to help the decision maker to make his decisions. Examples are shown to illustrate the procedure
of the proposed method at the end of this paper. 相似文献
9.
构造出9类具有函数的泛逼近性能的模糊控制器,这些模糊控制器均由模糊蕴涵算子构造而成.利用倒车仿真说明采用具有函数的泛逼近性能的模糊控制器可以用于实际的模糊控制系统中. 相似文献
10.
在Pythagorean模糊集和Hamacher集结算子基础上,研究了Pythagorean三角模糊语言环境下的Hamacher集成算子问题。首先给出了Pythagorean三角模糊语言的定义、运算规则、得分函数、精确函数;其次,介绍了一系列关于Pythagorean三角模糊语言Hamacher集结算子,比如Pythagorean三角模糊语言Hamacher加权平均算子(PTrFLHWA)、Pythagorean三角模糊语言Hamacher加权几何平均算子(PTrFLHWG)等,并研究其具有的性质;之后,提出了两种决策方法来解决Pythagorean三角模糊语言信息环境下的多属性群决策问题;最后,用示例验证所给方法的有效性。 相似文献
11.
Hesitant fuzzy information aggregation in decision making 总被引:2,自引:0,他引:2
Meimei Xia Zeshui Xu 《International Journal of Approximate Reasoning》2011,52(3):395-407
As a generalization of fuzzy set, hesitant fuzzy set is a very useful tool in situations where there are some difficulties in determining the membership of an element to a set caused by a doubt between a few different values. The aim of this paper is to develop a series of aggregation operators for hesitant fuzzy information. We first discuss the relationship between intutionistic fuzzy set and hesitant fuzzy set, based on which we develop some operations and aggregation operators for hesitant fuzzy elements. The correlations among the aggregation operators are further discussed. Finally, we give their application in solving decision making problems. 相似文献
12.
The composition of two previously introduced Galois connections is used to provide a wider perspective on the Clementino–Tholen connectedness versus separation Galois connection. Moreover, a link between this and Castellini's connectedness–disconnectednes Galois connection is also presented. 相似文献
13.
针对属性间含有关联信息的三角犹豫模糊多属性决策问题,提出一种基于三角犹豫模糊Heronian平均算子的决策方法。首先,考虑已有Heronian平均算子仅适用输入变量为两参数的情形,进一步定义三参数加权Heronian平均(TPWHM)和三参数加权几何Heronian平均(TPWGHM)算子,证明所提算子具有还原性、幂等性、单调性和有界性等性质,并研究它们的几种特例。其次,将TPWHM和TPWGHM算子推广至三角犹豫模糊决策环境下,提出三角犹豫模糊三参数加权Heronian平均(HTFTPWHM)和三角犹豫模糊三参数加权几何Heronian平均(HTFTPWGHM)算子,并证明算子的优良性质。在此基础上,提出基于两种算子的决策分析方法,并用来解决三角犹豫模糊决策问题。最后,通过算例验证所提方法的可行性和合理性。 相似文献
14.
《Applied Mathematical Modelling》2014,38(9-10):2689-2694
Interval-valued intuitionistic fuzzy prioritized operators are widely used in group decision making under uncertain environment due to its flexibility to model uncertain information. However, there is a shortcoming in the existing aggregation operators (interval-valued intuitionistic fuzzy prioritized weighted average (IVIFPWA)) to deal with group decision making in some extreme situations. For example, when an expert gives an absolute negative evaluation, the operators could lead to irrational results, so that they are not effectively enough to handle group decision making. In this paper, several examples are illustrated to show the unreasonable results in some of these situations. Actually, these unreasonable cases are common for operators in dealing with product averaging, not only emerging in IVIFPWA operators. To overcome the shortcoming of these kinds of operators, an improvement of making slight adjustment on initial evaluations is provided. Numerical examples are used to show the efficiency of the improvement. 相似文献
15.
《Applied Mathematical Modelling》2014,38(7-8):2190-2205
In this paper, we introduce a new operator called the continuous interval-valued intuitionistic fuzzy ordered weighted averaging (C-IVIFOWA) operator for aggregating the interval-valued intuitionistic fuzzy values. It combines the intuitionistic fuzzy ordered weighted averaging (IFOWA) operator and the continuous ordered weighted averaging (C-OWA) operator by a controlling parameter, which can be employed to diminish fuzziness and improve the accuracy of decision making. We further apply the C-IVIFOWA operator to the aggregation of multiple interval-valued intuitionistic fuzzy values and obtain a wide range of aggregation operators including the weighted C-IVIFOWA (WC-IVIFOWA) operator, the ordered weighted (OWC-IVIFOWA) operator and the combined C-IVIFOWA (CC-IVIFOWA) operator. Some desirable properties of these operators are investigated. And finally, we give a numerical example to illustrate the applications of these operators to group decision making under interval-valued intuitionistic fuzzy environment. 相似文献
16.
不同直觉模糊数在信息集结过程中,其隶属度与非隶属度之间可能存在着相互影响.提出了直觉模糊数上的改进的乘法运算和幂运算,重新给出了直觉模糊加权几何平均算子和直觉模糊有序加权几何平均算子的表达式,并研究了他们的一些性质.最后通过实例说明了新的IFWGA集成算子在多属性决策中的应用是可行和有效的. 相似文献
17.
L. Valverde 《Fuzzy Sets and Systems》1985,17(3):313-328
Some properties concerning the structure of F-indistinguishability operators are analyzed. It is shown that any of such operators is generated by a family of fuzzy subsets. This result, since it gives the way to construct F-indistinguishabilities, facilitates new applications of fuzzy relations. The links between F-indistinguishability operators and a kind of generalized metrics in the unit interval - which are also explored - are used to define the canonical generators of an F-indistinguishability operator, that is, the fuzzy partition associated with the operator. 相似文献
18.
PEI Dao-wu 《高校应用数学学报(英文版)》2014,29(3):253-264
In rough set theory, crisp and/or fuzzy binary relations play an important role in both constructive and axiomatic considerations of various generalized rough sets. This paper considers the uniqueness problem of the (fuzzy) relation in some generalized rough set model. Our results show that by using the axiomatic approach, the (fuzzy) relation determined by (fuzzy) approximation operators is unique in some (fuzzy) double-universe model. 相似文献
19.
On characterization of generalized interval-valued fuzzy rough sets on two universes of discourse 总被引:2,自引:0,他引:2
This paper proposes a general study of (I,T)-interval-valued fuzzy rough sets on two universes of discourse integrating the rough set theory with the interval-valued fuzzy set theory by constructive and axiomatic approaches. Some primary properties of interval-valued fuzzy logical operators and the construction approaches of interval-valued fuzzy T-similarity relations are first introduced. Determined by an interval-valued fuzzy triangular norm and an interval-valued fuzzy implicator, a pair of lower and upper generalized interval-valued fuzzy rough approximation operators with respect to an arbitrary interval-valued fuzzy relation on two universes of discourse is then defined. Properties of I-lower and T-upper interval-valued fuzzy rough approximation operators are examined based on the properties of interval-valued fuzzy logical operators discussed above. Connections between interval-valued fuzzy relations and interval-valued fuzzy rough approximation operators are also established. Finally, an operator-oriented characterization of interval-valued fuzzy rough sets is proposed, that is, interval-valued fuzzy rough approximation operators are characterized by axioms. Different axiom sets of I-lower and T-upper interval-valued fuzzy set-theoretic operators guarantee the existence of different types of interval-valued fuzzy relations which produce the same operators. 相似文献
20.