Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and th...Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.展开更多
In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3)...In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.展开更多
We say a divisien (S = SA or SB, g) is equal if it divides set S into two subsets SA and SB satisfying f (SA) = f (SB), where f is som attribute function on these sets and SA or SB need not be empty. In the present pa...We say a divisien (S = SA or SB, g) is equal if it divides set S into two subsets SA and SB satisfying f (SA) = f (SB), where f is som attribute function on these sets and SA or SB need not be empty. In the present paper, we have obtained some equal divisions on set of ordered tree with n modes: two equal divisions on tree set; two equal divisions on node set; two divisions on leaf set, one is equal, another one is ''asymptotically'' equal. We conclude that, ordered tree set is on its good behavior in equal dividing.展开更多
In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure...In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.展开更多
Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implicat...Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.展开更多
Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results...By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results are intuitional and realizable for computer.展开更多
This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for...This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.展开更多
There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions...There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.展开更多
This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two ...This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.展开更多
The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational law...The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.展开更多
This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontin...This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.展开更多
A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk ax...A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk axioms for intuitionistic fuzzy entropy. And a sufficient and necessary condition of order property in the Szmidt-Kacprzyk axioms is discussed. Additionally, some numerical examples are given to illustrate the applications of the proposed knowledge measure and some conventional entropies and knowledge measures of IFSs. The experimental results show that the results of the parametric model proposed in this paper are more accurate than those of most of the classic models.展开更多
By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof...By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.展开更多
In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic fu...In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.展开更多
The purpose of this paper is to introduce and discuss the concept of topical functions on upward sets. We give characterizations of topical functions in terms of upward sets.
基金supported by the National Natural Science Foundation of China (70871117 70571086)
文摘Multiattribute decision making（MADM） problems, in which the weights and ratings of alternatives are expressed with intuitionistic fuzzy（IF） sets, are investigated.Firstly, the relative degrees of membership and the relative degrees of non-membership are formulated as IF sets, the weights and values of alternatives on both qualitative and quantitative attributes may be expressed as IF sets in a unified way.Then a MADM method based on generalized ordered weighted averaging operators is proposed.The proposed method is illustrated with a numerical example.
文摘In this paper, we discuss the counting prob lem of an order n-group of set (A 1,A 2,…,A n) which satisfies ∪ni=1A i=｛a 1,a 2,…,a m｝ and one of the following: (1) ∩ni=1A i=Φ; (2) ∩ni=1A i=｛b 1,b 2,…,b k｝;(3) ∩ni=1A 1｛b 1,b 2,…,b k｝; (4) A i≠Φ (i=1,2,…,k). We solve these problems by element analytical meth od.
基金Supported by China National Natural Science Foundation.
文摘We say a divisien (S = SA or SB, g) is equal if it divides set S into two subsets SA and SB satisfying f (SA) = f (SB), where f is som attribute function on these sets and SA or SB need not be empty. In the present paper, we have obtained some equal divisions on set of ordered tree with n modes: two equal divisions on tree set; two equal divisions on node set; two divisions on leaf set, one is equal, another one is ''asymptotically'' equal. We conclude that, ordered tree set is on its good behavior in equal dividing.
文摘In this paper we have found a general subordinator, X, whose range up to time 1, X([0,1)), has similar structure as random re orderings of the Cantor set K(ω).X([0,1)) and K(ω) have the same exact Hausdorff measure function and the integal test of packing measure.
基金Science & Technology Depart ment of Sichuan Province,China(No.03226125)the Education Foundation of Sichuan Province,China(No.2006A084)
文摘Some sufficient and necessary conditions that implication algebra on a partial ordered set is associated implication algebra are obtained, and the relation between lattice H implication algebra and associated implication algebra is discussed. Also, the concept of filter is proposed with some basic properties being studied.
文摘Let F be a meromorphic functions family on the unit disc Δ, If for every (the zeros of f is a multiplicity of at least k) and if then and ( ), then F is normal on Δ.
文摘By means of Logic symmetric relation,the single neighboring Logic path for Ndimensions Boolean ordered set is solved.A new method of determining any logic neighboringsubset in limited dimension is proposed.Its results are intuitional and realizable for computer.
基金Supported by the National Natural Science Foundation of China（10871216） Supported by the Science and Technology Research Project of Chongqing Municipal Education Commission（KJ100419） Supported by the Natural Science Foundation Project of CQ CSTC（cstcjjA00019）
文摘This paper deals with higher-order optimality conditions for Henig effcient solutions of set-valued optimization problems.By virtue of the higher-order tangent sets, necessary and suffcient conditions are obtained for Henig effcient solutions of set-valued optimization problems whose constraint condition is determined by a fixed set.
基金Supported by the National Natural Science Foundation of China(11361001)Natural Science Foundation of Ningxia(NZ14101)
文摘There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.
文摘This paper mainly investigates the semicontinuity of solution mappings for set optimization problems under a partial order set relation instead of upper and lower set less order relations. To this end, we propose two types of monotonicity definition for the set-valued mapping introduced by two nonlinear scalarization functions which are presented by these partial order relations. Then, we give some sufficient conditions for the semicontinuity and closedness of solution mappings for parametric set optimization problems. The results presented in this paper are new and extend the main results given by some authors in the literature.
基金supported by the National Natural Science Foundation of China (70771025)the Fundamental Research Funds for the Central Universities of Hohai University (2009B04514)Humanities and Social Sciences Foundations of Ministry of Education of China(10YJA630067)
文摘The multiple attribute decision making problems are studied, in which the information about attribute weights is partly known and the attribute values take the form of intuitionistic fuzzy numbers. The operational laws of intuitionistic fuzzy numbers are introduced, and the score function and accuracy function are presented to compare the intuitionistic fuzzy numbers. The intuitionistic fuzzy ordered weighted averaging （IFOWA） operator which is an extension of the well-known ordered weighted averaging （OWA） operator is investigated to aggregate the intuitionistic fuzzy information. In order to determine the weights of intuitionistic fuzzy ordered weighted averaging operator, a linear goal programming procedure is proposed for learning the weights from data. Finally, an example is illustrated to verify the effectiveness and practicability of the developed method.
基金the National Natural Sciences Foundation of China
文摘This paper deals with the monotone iterative method for set -- valued operator equation in ordered normed space. Some results for the case of single valued operator are generalized here, as an application, a discontinuous nonlinear differential equation problem is discussed.
文摘A new knowledge measure with parameter of intuitionistic fuzzy sets (IFSs) is presented based on the membership degree and the non-membership degree of IFSs, which complies with the extended form of Szmidt-Kacprzyk axioms for intuitionistic fuzzy entropy. And a sufficient and necessary condition of order property in the Szmidt-Kacprzyk axioms is discussed. Additionally, some numerical examples are given to illustrate the applications of the proposed knowledge measure and some conventional entropies and knowledge measures of IFSs. The experimental results show that the results of the parametric model proposed in this paper are more accurate than those of most of the classic models.
文摘By using the partial ordering method,a more general type,of Ekeland’s ariational principle and a set-valued Caristi’s coincidence theorem in probabilistic metric spaces are obtained.In addition,a direct simple proof of the equivalence between these two theorems in probabilistic metric spaces is given.
基金Supported by the NNSFC (10671109)the NSFFC(2008J0190)+1 种基金the Research Fund for Talent Introduction of Ningde Teachers College (2009Y019)the Scitific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry
文摘In this article, we deal with the uniqueness problems on meromorphic functions sharing two finite sets in an angular domain instead of the whole plane C. In particular, we investigate the uniqueness for meromorphic functions of infinite order in an angular domain and obtain some results. Moreover, examples show that the conditions in theorems are necessary.
文摘The purpose of this paper is to introduce and discuss the concept of topical functions on upward sets. We give characterizations of topical functions in terms of upward sets.
