共查询到20条相似文献,搜索用时 31 毫秒
1.
《佛山科学技术学院》2014,6(4):505-522
In this paper, we discuss some properties of the self complement and self weak complement bipolar fuzzy graphs, and get a sufficient condition for a bipolar fuzzy graph to be the self weak complement bipolar fuzzy graph. Also we investigate relations between operations union, join, and complement on bipolar fuzzy graphs. 相似文献
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In the relational model of data, Rissanen's Theorem provides the basis for the usual normalization process based on decomposition of relations. However, many difficulties occur if information is incomplete in databases and nulls are required to represent missing or unknown data. We concentrate here on the notion of outer join and find some reasonable conditions to guarantee that outer join will also preserve the lossless join property for two relations. Next we provide a generalization of this result to several relations. 相似文献
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Fuzzy矩阵Schein秩的计算复杂性 总被引:1,自引:0,他引:1
本文讨论Fuzzy矩阵Schein秩的计算复杂性问题,证明了它是一个"NP-完全问题".首先,刻画了交可分解的Puzzy关系的交分解解集.然后,从Fuzzy关系的交分解与广义分解之间的关系出发,给出了Fuzzy关系广义分解的算法.最后,从Fuzzy关系广义分解的角度来讨论Fuzzy矩阵的Schein秩.指出它与色数问题之间的关系,即Fuzzy矩阵的Schein秩等于由它生成的简单图的色数,从而证明了计算Fuzzy矩阵的Schein秩是一个"NP-完全问题". 相似文献
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The concept of fuzzy sets of type 2 has been proposed by L.A. Zadeh as an extension of ordinary fuzzy sets. A fuzzy set of type 2 can be defined by a fuzzy membership function, the grade (or fuzzy grade) of which is taken to be a fuzzy set in the unit interval [0, 1] rather than a point in [0, 1].This paper investigates the algebraic properties of fuzzy grades (that is, fuzzy sets of type 2) under the operations of algebraic product and algebraic sum which can be defined by using the concept of the extension principle and shows that fuzzy grades under these operations do not form such algebraic structures as a lattice and a semiring. Moreover, the properties of fuzzy grades are also discussed in the case where algebraic product and algebraic sum are combined with the well-known operations of join and meet for fuzzy grades and it is shown that normal convex fuzzy grades form a lattice ordered semigroup under join, meet and algebraic product. 相似文献
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Henry B Potoczny 《Fuzzy Sets and Systems》1984,12(3):231-235
A characterization of a certain type of similarity relation is presented. This characterization is conceptually very easy and may be used to provide easier proofs of already established theorems.We use this characterization to show that if only a few similarity values of a similarity relation are known, then the others may be computed. This results in efficient storage of similarity relations associated with fuzzy relational databases.In addition, we use our characterization to show that there is only one type of similarity relation that provides a non-redundant decomposition of data in a fuzzy relational data base. 相似文献
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Optimization schemes for decomposition of fuzzy relations 总被引:3,自引:0,他引:3
Witold Pedrycz 《Fuzzy Sets and Systems》1998,100(1-3):301-325
The paper proposes an optimization environment for decomposing fuzzy relations. Two basic categories of approaches are developed: (i) based on direct gradient-oriented optimization methods, and (ii) exploiting the ideas of fuzzy neurocomputation. These two approaches are carefully analyzed and contrasted making use of illustrative numerical material. Some immediate applications to pattern classification and fuzzy interpolation are studied in detail. The study includes also some generalizations of the generic decomposition problem. 相似文献
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In this paper, we focus our attention on join‐covered graphs, that is, ±1‐weighted graphs, without negative circuits, in which every edge lies in a zero‐weight circuit. Join covered graphs are a natural generalization of matching‐covered graphs. Many important properties of matching covered graphs, such as the existence of a canonical partition, tight cut decomposition and ear decomposition, have been generalized to join covered graphs by A. Seb? [5]. In this paper we prove that any two edges of a join‐covered graph lie on a zero‐weight circuit (under an equivalent weighting), generalize this statement to an arbitrary number of edges, and characterize minimal bipartite join‐covered graphs. © 2009 Wiley Periodicals, Inc. J Graph Theory 62, 220–233, 2009 相似文献
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Decision makers (DMs)’ preferences on decision alternatives are often characterized by multiplicative or fuzzy preference relations. This paper proposes a chi-square method (CSM) for obtaining a priority vector from multiplicative and fuzzy preference relations. The proposed CSM can be used to obtain a priority vector from either a multiplicative preference relation (i.e. a pairwise comparison matrix) or a fuzzy preference relation or a group of multiplicative preference relations or a group of fuzzy preference relations or their mixtures. Theorems and algorithm about the CSM are developed. Three numerical examples are examined to illustrate the applications of the CSM and its advantages. 相似文献
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Zeshui Xu 《Fuzzy Optimization and Decision Making》2010,9(3):333-357
Incomplete fuzzy preference relations, incomplete multiplicative preference relations, and incomplete linguistic preference
relations are very useful to express decision makers’ incomplete preferences over attributes or alternatives in the process
of decision making under fuzzy environments. The aim of this paper is to investigate fuzzy multiple attribute group decision
making problems where the attribute values are represented in intuitionistic fuzzy numbers and the information on attribute
weights is provided by decision makers by means of one or some of the different preference structures, including weak ranking,
strict ranking, difference ranking, multiple ranking, interval numbers, incomplete fuzzy preference relations, incomplete
multiplicative preference relations, and incomplete linguistic preference relations. We transform all individual intuitionistic
fuzzy decision matrices into the interval decision matrices and construct their expected decision matrices, and then aggregate
all these expected decision matrices into a collective one. We establish an integrated model by unifying the collective decision
matrix and all the given different structures of incomplete weight preference information, and develop an integrated model-based
approach to interacting with the decision makers so as to adjust all the inconsistent incomplete fuzzy preference relations,
inconsistent incomplete linguistic preference relations and inconsistent incomplete multiplicative preference relations into
the ones with acceptable consistency. The developed approach can derive the attribute weights and the ranking of the alternatives
directly from the integrated model, and thus it has the following prominent characteristics: (1) it does not need to construct
the complete fuzzy preference relations, complete linguistic preference relations and complete multiplicative preference relations
from the incomplete fuzzy preference relations, incomplete linguistic preference relations and incomplete multiplicative preference
relations, respectively; (2) it does not need to unify the different structures of incomplete preferences, and thus can simplify
the calculation and avoid distorting the given preference information; and (3) it can sufficiently reflect and adjust the
subjective desirability of decision makers in the process of interaction. A practical example is also provided to illustrate
the developed approach. 相似文献
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This paper investigates the aggregation of multiple fuzzy preference relations into a collective fuzzy preference relation in fuzzy group decision analysis and proposes an optimization based aggregation approach to assess the relative importance weights of the multiple fuzzy preference relations. The proposed approach that is analytical in nature assesses the weights by minimizing the sum of squared distances between any two weighted fuzzy preference relations. Relevant theorems are offered in support of the proposed approach. Multiplicative preference relations are also incorporated into the approach using an appropriate transformation technique. An eigenvector method is introduced to derive the priorities from the collective fuzzy preference relation. The proposed aggregation approach is tested using two numerical examples. A third example involving broadband internet service selection is offered to illustrate that the proposed aggregation approach provides a simple, effective and practical way of aggregating multiple fuzzy preference relations in real-life situations. 相似文献
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Armando Freitas da Rocha 《Fuzzy Sets and Systems》1981,5(2):127-140
Synaptic events in neural systems were described as generated by an apparatus @ possessing memory and encoding a fuzzy point process (the presynaptic discharge) into another N (the postsynaptic discharge). @ was considered to be a fuzzy automata, for which state membership is dependent on input membership and distribution as well as on a control exercised by other neural structures. In such a device, irregular input distributions favour a direct monotonic codification, whereas regular ones induce discontinuous and inverse relations between both fuzzy point processes. Both behaviors favour analogic and membership relations between the fuzzy input and output. However, there exist intermediate grades of irregularities which result in a context-free encoding, where similitude and equivalence relations predominate. The importance of such findings to neurophysiology is discussed. 相似文献
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In this paper, we study the group decision-making problem in which the preference information given by experts takes the form of intuitionistic fuzzy preference relations, and the information about experts’ weights is completely unknown. We first utilize the intuitionistic fuzzy weighted averaging operator to aggregate all individual intuitionistic fuzzy preference relations into a collective intuitionistic fuzzy preference relation. Then, based on the degree of similarity between the individual intuitionistic fuzzy preference relations and the collective one, we develop an approach to determine the experts’ weights. Furthermore, based on intuitionistic fuzzy preference relations, a practical interactive procedure for group decision-making is proposed, in which the similarity measures between the collective preference relation and intuitionistic fuzzy ideal solution are used to rank the given alternatives. Finally, an illustrative numerical example is given to verify the developed approach. 相似文献
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In order to simulate the uncertainty associated with impression or vagueness, a decision maker may give her/his judgments by means of triangular fuzzy reciprocal preference relations in the process of decision making. The study of their consistency becomes a very important aspect to avoid a misleading solution. Based on the reciprocity property, this paper proposes a new definition of consistent triangular fuzzy reciprocal preference relations. The new definition is different from that reduced by consistent fuzzy reciprocal preference relations proposed by Buckley (1985). The properties of consistent triangular fuzzy reciprocal preference relations in the light of the new definition are studied in detail. In addition, the shortcomings of the proof procedure of the proposition given by Wang and Chen (2008) are pointed out. And the proposition is reproved by using the new definition of consistent triangular fuzzy reciprocal preference relations. Finally, using the (n − 1) restricted comparison ratios, a method for obtaining consistent triangular fuzzy reciprocal preference relations is proposed, and an algorithm is shown to make a consistent decision ranking. Numerical results are further calculated to illustrate the new definition and the obtained algorithm. 相似文献
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This paper addresses the problem of defining and analyzing relations between finite sets which are involved in personnel management.Personnel management criteria are imprecise due to the complex nature of the requirements and the difficulties to deal with personnel characteristics. Fuzzy set theory seems to be an efficient tool for considering these imprecisions. According to this idea the relations involved in personnel management can be seen as fuzzy relations.R.H. Atkin has formulated the abstract simplicial complex, achieving a structure which permits a deep knowledge of non fuzzy relations. In a sense this structure can be interpreted as a geometrical multidimensional one. Our purpose is to set up a multidimensional structure associated with the fuzzy relations which appear in personnel management.By means of an analysis of the above structure it is possible to study problems concerning the recruitment selection and promotion of personnel. 相似文献
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《European Journal of Operational Research》1998,107(3):575-589
In this paper, by considering the experts' vague or fuzzy understanding of the nature of the parameters in the problem formulation process, multiobjective linear fractional programming problems with block angular structure involving fuzzy numbers are formulated. Using the a-level sets of fuzzy numbers, the corresponding nonfuzzy a-multiobjective linear fractional programming problem is introduced. The fuzzy goals of the decision maker for the objective functions are quantified by eliciting the corresponding membership functions including nonlinear ones. Through the introduction of extended Pareto optimality concepts, if the decision maker specifies the degree a and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the minimax problems for which the Dantzig-Wolfe decomposition method and Ritter's partitioning procedure are applicable. Then a linear programming-based interactive fuzzy satisficing method with decomposition procedures for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented. An illustrative numerical example is provided to demonstrate the feasibility of the proposed method. 相似文献
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Derivation of intuitionistic fuzzy weights based on intuitionistic fuzzy preference relations 总被引:1,自引:0,他引:1
This paper proposes linear goal programming models for deriving intuitionistic fuzzy weights from intuitionistic fuzzy preference relations. Novel definitions are put forward to define additive consistency and weak transitivity for intuitionistic fuzzy preference relations, followed by a study of their corresponding properties. For any given normalized intuitionistic fuzzy weight vector, a transformation formula is furnished to convert the weights into a consistent intuitionistic fuzzy preference relation. For any intuitionistic fuzzy preference relation, a linear goal programming model is developed to obtain its intuitionistic fuzzy weights by minimizing its deviation from the converted consistent intuitionistic fuzzy preference relation. This approach is then extended to group decision-making situations. Three numerical examples are provided to illustrate the validity and applicability of the proposed models. 相似文献