共查询到20条相似文献,搜索用时 31 毫秒
1.
Deng-Feng Li 《Fuzzy Optimization and Decision Making》2011,10(1):45-58
The Atanassov’s intuitionistic fuzzy (IF) set theory has become a popular topic of investigation in the fuzzy set community.
However, there is less investigation on the representation of level sets and extension principles for interval-valued intuitionistic
fuzzy (IVIF) sets as well as algebraic operations. In this paper, firstly the representation theorem of IVIF sets is proposed
by using the concept of level sets. Then, the extension principles of IVIF sets are developed based on the representation
theorem. Finally, the addition, subtraction, multiplication and division operations over IVIF sets are defined based on the
extension principle. The representation theorem and extension principles as well as algebraic operations form an important
part of Atanassov’s IF set theory. 相似文献
2.
Deng-Feng Li 《Fuzzy Optimization and Decision Making》2008,7(1):17-34
The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference
(LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov’s intuitionistic
fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent
in decision data and decision making processes. In this methodology, Atanassov’s IF sets are used to describe fuzziness in
decision information and decision making processes by means of an Atanassov’s IF decision matrix. A Euclidean distance is
proposed to measure the difference between Atanassov’s IF sets. Consistency and inconsistency indices are defined on the basis
of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance
to an Atanassov’s IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov’s IFPIS and the weights of attributes
are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally,
the distance of each alternative to the Atanassov’s IFPIS can be calculated to determine the ranking order of all alternatives.
A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that
the methodology proposed in this article can deal with MADM problems under not only Atanassov’s IF environments but also both
fuzzy and crisp environments. 相似文献
3.
Some similarity measures of intuitionistic fuzzy sets and their applications to multiple attribute decision making 总被引:1,自引:0,他引:1
Zeshui Xu 《Fuzzy Optimization and Decision Making》2007,6(2):109-121
Atanassov (1986) defined the notion of intuitionistic fuzzy set, which is a generalization of the notion of Zadeh’ fuzzy set.
In this paper, we first develop some similarity measures of intuitionistic fuzzy sets. Then, we define the notions of positive
ideal intuitionistic fuzzy set and negative ideal intuitionistic fuzzy set. Finally, we apply the similarity measures to multiple
attribute decision making under intuitionistic fuzzy environment. 相似文献
4.
Rough set theory has been combined with intuitionistic fuzzy sets in dealing with uncertainty decision making. This paper proposes a general decision-making framework based on the intuitionistic fuzzy rough set model over two universes. We first present the intuitionistic fuzzy rough set model over two universes with a constructive approach and discuss the basic properties of this model. We then give a new approach of decision making in uncertainty environment by using the intuitionistic fuzzy rough sets over two universes. Further, the principal steps of the decision method established in this paper are presented in detail. Finally, an example of handling medical diagnosis problem illustrates this approach. 相似文献
5.
Molodtsov initiated the concept of soft set theory, which can be used as a generic mathematical tool for dealing with uncertainty. There has been some progress concerning practical applications of soft set theory, especially the use of soft sets in decision making. In this paper we generalize the adjustable approach to fuzzy soft sets based decision making. Concretely, we present an adjustable approach to intuitionistic fuzzy soft sets based decision making by using level soft sets of intuitionistic fuzzy soft sets and give some illustrative examples. The properties of level soft sets are presented and discussed. Moreover, we also introduce the weighted intuitionistic fuzzy soft sets and investigate its application to decision making. 相似文献
6.
Molodtsov’s soft set theory was originally proposed as a general mathematical tool for dealing with uncertainty. By combining the multi-fuzzy set and soft set models, the purpose of this paper is to introduce the concept of multi-fuzzy soft sets. Some operations on a multi-fuzzy soft set are defined, such as complement operation, “AND” and “OR” operations, Union and Intersection operations. Then, the DeMorgan’s laws are proved. Finally, by means of level soft set, an algorithm is presented, and a decision problem is analyzed using multi-fuzzy soft set. 相似文献
7.
In this paper, a new class of intuitionistic fuzzy closed sets called intuitionistic fuzzy generalized preregular closed sets (briefly intuitionistic fuzzy gpr-closed sets) and intuitionistic fuzzy generalized preregular open sets (briefly intuitionistic fuzzy gpr-open sets) are introduced and their properties are studied. Further the notion of intuitionistic fuzzy preregular T 1/2-spaces and intuitionistic fuzzy generalized preregular continuity (briefly intuitionistic fuzzy gpr-continuity) are introduced and studied. 相似文献
8.
A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. The family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets. In particular, the fuzzy set intersections are pointwisely generated by Frank t-norms. The fuzzification schemes are applied to a variety of previously studied rational cardinality-based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process. 相似文献
9.
In this paper a new definition of a lattice valued intuitionistic fuzzy set (LIFS) is introduced, in an attempt to overcome
the disadvantages of earlier definitions. Some properties of this kind of fuzzy sets and their basic operations are given.
The theorem of synthesis is proved: For every two families of subsets of a set satisfying certain conditions, there is an
lattice valued intuitionistic fuzzy set for which these are families of level sets.
The research supported by Serbian Ministry of Science and Technology, Grant No. 1227. 相似文献
10.
Liviu C. Florescu 《Central European Journal of Mathematics》2007,5(4):619-638
We introduce two notions of tightness for a set of measurable functions — the finite-tightness and the Jordan finite-tightness
with the aim to extend certain compactness results (as biting lemma or Saadoune-Valadier’s theorem of stable compactness)
to the unbounded case. These compactness conditions highlight their utility when we look for some alternatives to Rellich-Kondrachov
theorem or relaxed lower semicontinuity of multiple integrals. Finite-tightness locates the great growths of a set of measurable
mappings on a finite family of sets of small measure. In the Euclidean case, the Jordan finite-tight sets form a subclass
of finite-tight sets for which the finite family of sets of small measure is composed by d-dimensional intervals. The main result affirms that each tight set H ⊆ W
1,1 for which the set of the gradients ∇H is a Jordan finite-tight set is relatively compact in measure. This result offers very good conditions to use fiber product
lemma for obtaining a relaxed lower semicontinuity condition.
相似文献
11.
《International Journal of Approximate Reasoning》2014,55(6):1369-1382
Two basic inference models of fuzzy reasoning are fuzzy modus ponens (FMP) and fuzzy modus tollens (FMT). The Triple I method is a very important method to solve the problems of FMP and FMT. The aim of this paper is to extend the Triple I method of approximate reasoning on Atanassov's intuitionistic fuzzy sets. In the paper, we first investigate the algebra operators' properties on the lattice structure of intuitionistic fuzzy information and provide the unified form of residual implications which indicates the relationship between intuitionistic fuzzy implications and fuzzy implications. Then we present the intuitionistic fuzzy reasoning version of the Triple I principles based on the models of intuitionistic fuzzy modus ponens (IFMP) and intuitionistic fuzzy modus tollens (IFMT) and give the Triple I method of intuitionistic fuzzy reasoning for residual implications. Moreover, we discuss the reductivity of the Triple I methods for IFMP and IFMT. Finally, we propose α-Triple I method of intuitionistic fuzzy reasoning. 相似文献
12.
Guangquan Zhang Tharam Singh Dillon Kai-Yuan Cai Jun Ma Jie Lu 《International Journal of Approximate Reasoning》2009,50(8):1227
A complex fuzzy set is a fuzzy set whose membership function takes values in the unit circle in the complex plane. This paper investigates various operation properties and proposes a distance measure for complex fuzzy sets. The distance of two complex fuzzy sets measures the difference between the grades of two complex fuzzy sets as well as that between the phases of the two complex fuzzy sets. This distance measure is then used to define δ-equalities of complex fuzzy sets which coincide with those of fuzzy sets already defined in the literature if complex fuzzy sets reduce to real-valued fuzzy sets. Two complex fuzzy sets are said to be δ-equal if the distance between them is less than 1-δ. This paper shows how various operations between complex fuzzy sets affect given δ-equalities of complex fuzzy sets. An example application of signal detection demonstrates the utility of the concept of δ-equalities of complex fuzzy sets in practice. 相似文献
13.
Sadaaki Miyamoto 《Annals of Operations Research》2012,195(1):221-236
We consider four different generalizations of bags (alias multisets). We first discuss Yager’s fuzzy bags having different
sets of operations. It is shown that one is not a generalization of fuzzy sets but a mapping of them into fuzzy bags, since
operations are inconsistent between the two, while the other includes fuzzy sets as particular cases. Third type is called
real-valued bags which is simpler than the former two and is a kind of the reduction of fuzzy bags. Finally, the fourth generalization
called G-bags includes all three except the first type. It is a minimal extension of the second and the third generalizations. Bag
relations are defined for the third type of real-valued bags, which can further be generalized for G-bags. 相似文献
14.
Heinz Gröflin 《Combinatorica》1984,4(4):281-290
Given a digraphG = (V, E), call a node setT ⊆V path-closed ifv, v′ εT andw εV is on a path fromv tov′ impliesw εT. IfG is the comparability graph of a posetP, the path-closed sets ofG are the convex sets ofP. We characterize the convex hull of (the incidence vectors of) all path-closed sets ofG and its antiblocking polyhedron inR
v
, using lattice polyhedra, and give a minmax theorem on partitioning a given subset ofV into path-closed sets. We then derive good algorithms for the linear programs associated to the convex hull, solving the
problem of finding a path-closed set of maximum weight sum, and prove another min-max result closely resembling Dilworth’s
theorem. 相似文献
15.
Claudilene Gomes da Costa Benjamín Callejas Bedregal 《International Journal of Approximate Reasoning》2011,52(4):473-487
In this paper the relation between De Morgan triples on the unit interval and Atanassov’s intuitionistic De Morgan triples is presented, showing how to obtain, in a canonical way, Atanassov’s intuitionistic De Morgan triples from De Morgan triples. Moreover, we also show that the automorphisms on the unit interval and on L∗ (the intuitionistic value lattice) are in one-to-one correspondence and how automorphisms on L∗ act on Atanassov’s intuitionistic De Morgan triples. It is also proved that the action of automorphisms and the canonical construction of De Morgan triples on L∗ commutes. 相似文献
16.
Agata Ciabattoni 《Archive for Mathematical Logic》2005,44(4):435-457
We perform a proof-theoretical investigation of two modal predicate logics: global intuitionistic logic GI and global intuitionistic fuzzy logic GIF. These logics were introduced by Takeuti and Titani to formulate an intuitionistic set theory and an intuitionistic fuzzy set theory together with their metatheories. Here we define analytic Gentzen style calculi for GI and GIF. Among other things, these calculi allows one to prove Herbrands theorem for suitable fragments of GI and GIF.Work Supported by C. Bühler-Habilitations-Stipendium H191-N04, from the Austrian Science Fund (FWF). 相似文献
17.
Let α be an admissible ordinal, and leta
* be the Σ1-projectum ofa. Call an α-r.e. setM maximal if α→M is unbounded and for every α→r.e. setA, eitherA∩(α-M) or (α-A)∩(α-M) is bounded. Call and α-r.e. setM amaximal subset of α* if α*−M is undounded and for any α-r.e. setA, eitherA∩(α*-M) or (⇌*-A)∩(α*-M) is unbounded in α*. Sufficient conditions are given both for the existence of maximal sets, and for the existence of maximal subset of α*. Necessary conditions for the existence of maximal sets are also given. In particular, if α ≧ ℵ
L
then it is shown that maximal sets do not exist.
Research partially supported by NSF Grant GP-34088 X.
Some of the results in this paper have been taken from the second author’s Ph. D. Thesis, written under the supervision of
Gerald Sacks. 相似文献
18.
Some aspects of intuitionistic fuzzy sets 总被引:1,自引:0,他引:1
Ronald R. Yager 《Fuzzy Optimization and Decision Making》2009,8(1):67-90
We first discuss the significant role that duality plays in many aggregation operations involving intuitionistic fuzzy subsets.
We then consider the extension to intuitionistic fuzzy subsets of a number of ideas from standard fuzzy subsets. In particular
we look at the measure of specificity. We also look at the problem of alternative selection when decision criteria satisfaction
is expressed using intuitionistic fuzzy subsets. We introduce a decision paradigm called the method of least commitment. We
briefly look at the problem of defuzzification of intuitionistic fuzzy subsets. 相似文献
19.
We analyze the concept of large set for a coalitional game v introduced by Martínez-de-Albéniz and Rafels (Int. J. Game Theory 33(1):107–114, 2004). We give some examples and identify some of these sets. The existence of such sets for any game is proved, and several properties
of largeness are provided. We focus on the minimality of such sets and prove its existence using Zorn’s lemma.
Institutional support from research grants (Generalitat de Catalunya) 2005SGR00984 and (Spanish Government and FEDER) SEJ2005-02443/ECON
is gratefully acknowledged, and the support of the Barcelona Economics Program of CREA. 相似文献
20.
In this paper, we deal with Aubin cores and bargaining sets in convex cooperative fuzzy games. We first give a simple and
direct proof to the well-known result (proved by Branzei et al. (Fuzzy Sets Syst 139:267–281, 2003)) that for a convex cooperative
fuzzy game v, its Aubin core C(v) coincides with its crisp core C
cr
(v). We then introduce the concept of bargaining sets for cooperative fuzzy games and prove that for a continuous convex cooperative
fuzzy game v, its bargaining set coincides with its Aubin core, which extends a well-known result by Maschler et al. for classical cooperative
games to cooperative fuzzy games. We also show that some results proved by Shapley (Int J Game Theory 1:11–26, 1971) for classical
decomposable convex cooperative games can be extended to convex cooperative fuzzy games. 相似文献