ORIGINAL_ARTICLE
Cover vol. 15, no. 2, April 2018
http://ijfs.usb.ac.ir/article_3756_a827a8e2afdf2fe8eb4bb7c5a5bd0217.pdf
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10.22111/ijfs.2018.3756
ORIGINAL_ARTICLE
POINTWISE CONVERGENCE TOPOLOGY AND FUNCTION SPACES IN FUZZY ANALYSIS
We study the space of all continuous fuzzy-valued functions from a space $X$ into the space of fuzzy numbers $(\mathbb{E}\sp{1},d\sb{\infty})$ endowed with the pointwise convergence topology. Our results generalize the classical ones for continuous real-valued functions. The field of applications of this approach seems to be large, since the classical case allows many known devices to be fitted to general topology, functional analysis, coding theory, Boolean rings, etc.
http://ijfs.usb.ac.ir/article_3753_2b8058838050761d26d4f9d8d6a43cfd.pdf
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10.22111/ijfs.2018.3753
Fuzzy-number
Fuzzy analysis
Function space
Pointwise convergence
Dual map
Evaluation map
Fr'echet space
Grothendieck's theorem
Cardinal function
D. R.
Jardon
true
1
Academia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa s/n, Col. Lomas de Zaragoza 09620, Ciudad de Mexico ,
Mexico
Academia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa s/n, Col. Lomas de Zaragoza 09620, Ciudad de Mexico ,
Mexico
Academia de Matematicas, Universidad Autonoma de la Ciudad de Mexico, Calz. Ermita Iztapalapa s/n, Col. Lomas de Zaragoza 09620, Ciudad de Mexico ,
Mexico
AUTHOR
M.
Sanchis
true
2
Institut de Matematiques i Aplicacions de Castello (IMAC), Universitat
Jaume I, Campus Riu Sec, 12071-Castello, Spain
Institut de Matematiques i Aplicacions de Castello (IMAC), Universitat
Jaume I, Campus Riu Sec, 12071-Castello, Spain
Institut de Matematiques i Aplicacions de Castello (IMAC), Universitat
Jaume I, Campus Riu Sec, 12071-Castello, Spain
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57
ORIGINAL_ARTICLE
L-CONVEX SYSTEMS AND THE CATEGORICAL ISOMORPHISM TO SCOTT-HULL OPERATORS
The concepts of $L$-convex systems and Scott-hull spaces are proposed on frame-valued setting. Also, we establish the categorical isomorphism between $L$-convex systems and Scott-hull spaces. Moreover, it is proved that the category of $L$-convex structures is bireflective in the category of $L$-convex systems. Furthermore, the quotient systems of $L$-convex systems are studied.
http://ijfs.usb.ac.ir/article_3754_de43053a691df5ee38c5df21e874a1b9.pdf
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40
10.22111/ijfs.2018.3754
$L$-convex system
Scott-hull space
Induced $L$-convex structure
Quotient system
Chong
Shen
shenchong0520@163.com
true
1
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
AUTHOR
Fu-Gui
Shi
fuguishi@bit.edc.cn
true
2
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
School of Mathematics and statistics, Beijing Institute of Technology,
Beijing 100081, P.R. China
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of Technology, Beijing, China, (2015), 21{64.
42
ORIGINAL_ARTICLE
BASES AND CIRCUITS OF FUZZIFYING MATROIDS
In this paper, as an application of fuzzy matroids, the fuzzifying greedy algorithm is proposed and an achievableexample is given. Basis axioms and circuit axioms of fuzzifying matroids, which are the semantic extension for thebasis axioms and circuit axioms of crisp matroids respectively, are presented. It is proved that a fuzzifying matroidis equivalent to a mapping which satisfies the basis axioms or circuit axioms.
http://ijfs.usb.ac.ir/article_3755_3eb0a96d3cd8eee16ffe525dc4b0db85.pdf
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10.22111/ijfs.2018.3755
Fuzzifying matroid
Fuzzifying base-map
Fuzzifying basis axiom
Fuzzifying circuit-map
Fuzzifying circuit axiom
Shao-Jun
Yang
shaojunyang@outlook.com
true
1
The Fujian Provincial Key Laboratory of Network Security and
Cryptology, School of Mathematics and Computer Science, Fujian Normal University,
Fuzhou 350007, P.R. China
The Fujian Provincial Key Laboratory of Network Security and
Cryptology, School of Mathematics and Computer Science, Fujian Normal University,
Fuzhou 350007, P.R. China
The Fujian Provincial Key Laboratory of Network Security and
Cryptology, School of Mathematics and Computer Science, Fujian Normal University,
Fuzhou 350007, P.R. China
AUTHOR
Fu-Gui
Shi
fuguishi@bit.edc.cn
true
2
School of Mathematics and Statistics, Beijing Institute of Technology,
Beijing 102488, P.R. China; Beijing Key Laboratory on MCAACI, Beijing Institute of
Technology, Beijing 102488, P.R. China
School of Mathematics and Statistics, Beijing Institute of Technology,
Beijing 102488, P.R. China; Beijing Key Laboratory on MCAACI, Beijing Institute of
Technology, Beijing 102488, P.R. China
School of Mathematics and Statistics, Beijing Institute of Technology,
Beijing 102488, P.R. China; Beijing Key Laboratory on MCAACI, Beijing Institute of
Technology, Beijing 102488, P.R. China
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24
[18] F. G. Shi, (L,M)-fuzzy matroids, Fuzzy Sets and Systems, 160 (2009), 2387{2400.
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[19] F. G. Shi and L.Wang, Characterizations and applications of M-fuzzifying matroids, Journal
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of Intelligent and Fuzzy Systems, 25 (2013), 919{930.
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[20] L. Wang and F. G. Shi, Characterization of L-fuzzifying matroids by M-fuzzifying families
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of δ- flats, Advances of Fuzzy Sets and Systems, 2 (2009), 203{213.
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operators, Iranian Journal of Fuzzy Systems, 7 (2010), 47{58.
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Computing, 62 (2009), 547{554.
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[24] X. Xin, F. G. Shi and S. G. Li, M-fuzzifying derived operators and difference derived oper-
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ators, Iranian Journal of Fuzzy Systems, 7(2) (2010), 71{81.
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[25] Z. Y. Xiu and F. G. Shi, M-fuzzifying submodular functions, Journal of Intelligent and Fuzzy
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Systems, 27 (2014), 1243{1255.
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[26] W. Yao and F. G. Shi, Bases axioms and circuits axioms for fuzzifying matroids, Fuzzy Sets
39
and Systems, 161 (2010), 3155{3165.
40
ORIGINAL_ARTICLE
QUANTALE-VALUED SUP-ALGEBRAS
Based on the notion of $Q$-sup-lattices (a fuzzy counterpart of complete join-semilattices valuated in a commutative quantale), we present the concept of $Q$-sup-algebras -- $Q$-sup-lattices endowed with a collection of finitary operations compatible with the fuzzy joins. Similarly to the crisp case investigated in \cite{zhang-laan}, we characterize their subalgebras and quotients, and following \cite{solovyov-qa}, we show that the category of $Q$-sup-algebras is isomorphic to a certain subcategory of a category of $Q$-modules.
http://ijfs.usb.ac.ir/article_3759_15a2e675b28ad7601164f7c1adefa982.pdf
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73
10.22111/ijfs.2018.3759
$Q$-order
$Q$-sup-lattice
$Q$-ordered algebra
$Q$-sup-algebra
Quotient
subalgebra
Radek
Slesinger
true
1
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic
Department of Mathematics and Statistics, Faculty of Science, Masaryk University, Kotlarska 2, 611 37 Brno, Czech Republic
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[1] R. Belohlavek, Fuzzy Relational Systems: Foundations and Principles, volume 20 of IFSR
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International Series on Systems Science and Engineering, Springer US, New York, 2002.
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and Soft Computing, Springer-Verlag Berlin Heidelberg, 2005.
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pedia of Mathematics and its Applications, Cambridge University Press, 2008.
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[4] S. Burris and H. P. Sankappanavar, A Course in Universal Algebra, Springer Verlag, New
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York, 2012.
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puter Science, 45 (2001), 77{87.
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Mathematical Society, Providence, Rhodes Island, USA, 1984.
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Systems, 14(5) (2017), 65-81.
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[9] J. Paseka, Quantale Modules, Habilitation thesis, Masaryk University, 1999.
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[10] J. Paseka, A note on nuclei of quantale modules, Cahiers de Topologie et Geometrie
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Differentielle Categoriques, 43 (2002), 19{34.
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(2008), 308{317.
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[12] P. Resende, Tropological Systems and Observational Logic in Concurrency and Specification,
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PhD thesis, IST, Universidade Tecnica de Lisboa, 1998.
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[13] S. E. Rodabough, Powerset operator foundations for poslat fuzzy set theories and topologies,
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In Mathematics of Fuzzy Sets. The Handbooks of Fuzzy Sets Series, Springer, 3 (1999),
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Longman Scientific & Technical, New York, 1990.
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ematics for Applications, 5(1) (2016), 39{53.
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[17] R. Slesinger, Triads in Ordered Sets, PhD thesis, Masaryk University, 2016.
32
[18] S. A. Solovyov, A representation theorem for quantale algebras, In Proceedings of the Kla-
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genfurt Workshop 2007 on General Algebra, 18 (2008), 189{197.
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[19] S. A. Solovyov, A note on nuclei of quantale algebras, Bulletin of the Section of Logic,
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40(1/2) (2011), 91{112.
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gories, Theory and Applications of Categories, 16 (2006), 286{306.
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mal University, 2012, In Chinese.
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Normal University (Natural Science Edition), In Chinese, 41(3) (2013), 1{6.
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[24] W. Yao, Quantitative domains via fuzzy sets: Part I: Continuity of fuzzy directed complete
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posets, Fuzzy Sets and Systems, 161(7) (2010), 973{987.
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terly, 55(1) (2009), 105{112.
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[33] B. Zhao, S.Wu, and K.Wang, Quantale algebras as lattice-valued quantales, Soft Computing,
60
21(10) (2017), 2561{2574.
61
ORIGINAL_ARTICLE
BASE AXIOMS AND SUBBASE AXIOMS IN M-FUZZIFYING CONVEX SPACES
Based on a completely distributive lattice $M$, base axioms and subbase axioms are introduced in $M$-fuzzifying convex spaces. It is shown that a mapping $\mathscr{B}$ (resp. $\varphi$) with the base axioms (resp. subbase axioms) can induce a unique $M$-fuzzifying convex structure with $\mathscr{B}$ (resp. $\varphi$) as its base (resp. subbase). As applications, it is proved that bases and subbases can be used to characterize CP mappings and CC mappings between $M$-fuzzifying convex spaces.
http://ijfs.usb.ac.ir/article_3760_b615cc331d0d71e72929cb7e6d511ca6.pdf
2018-04-29T11:23:20
2019-03-23T11:23:20
75
87
10.22111/ijfs.2018.3760
$M$-fuzzifying convex structure
Base axiom
Subbase axiom
CP mapping
CC mapping
Zhen-Yu
Xiu
xyz198202@163.com
true
1
College of Applied Mathematics, Chengdu University of Information
Technology, Chengdu 610225, P.R.China
College of Applied Mathematics, Chengdu University of Information
Technology, Chengdu 610225, P.R.China
College of Applied Mathematics, Chengdu University of Information
Technology, Chengdu 610225, P.R.China
AUTHOR
Bin
Pang
pangbin1205@163.com
true
2
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
School of Mathematics and Statistics, Beijing Institute of Technology, Beijing 100081, P.R.China
LEAD_AUTHOR
[1] P. Dwinger, Characterizations of the complete homomorphic images of a completely distribu-
1
tive complete lattice I, Indagationes Mathematicae (Proceedings), 85 (1982), 403{414.
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31
ORIGINAL_ARTICLE
ON THE MATCHING NUMBER OF AN UNCERTAIN GRAPH
Uncertain graphs are employed to describe graph models with indeterministicinformation that produced by human beings. This paper aims to study themaximum matching problem in uncertain graphs.The number of edges of a maximum matching in a graph is called matching numberof the graph. Due to the existence of uncertain edges, the matching number of an uncertain graph is essentially an uncertain variable.Different from that in a deterministic graph, it is more meaningful to investigate the uncertain measure that an uncertain graph is $k$-edge matching (i.e., the matching number is greater than or equal to $k$).We first study the properties of the matching number of an uncertain graph, and then give a fundamental formula for calculating the uncertain measure. We further prove that the fundamental formula can be transformedinto a simplified form. What is more, a polynomial time algorithm to numerically calculate the uncertain measure is derived from the simplified form.Finally, some numerical examples are illustrated to show the application and efficiency of the algorithm.
http://ijfs.usb.ac.ir/article_3761_843af24ca521b1d9f207a6a79751dcc4.pdf
2018-04-29T11:23:20
2019-03-23T11:23:20
89
108
10.22111/ijfs.2018.3761
Uncertainty theory
Uncertain measure
Maximum matching
Matching number
Uncertain graph
Hui
Li
ximuhuizi@163.com
true
1
School of Information and Engineering, Wuchang University of Technology,
Wuhan, 430223, China
School of Information and Engineering, Wuchang University of Technology,
Wuhan, 430223, China
School of Information and Engineering, Wuchang University of Technology,
Wuhan, 430223, China
AUTHOR
Bo
Zhang
bzhang3@masonlive.gmu.edu
true
2
School of Statistics and Mathematics, Zhongnan University of Economics
and Law, Wuhan, 430073, China
School of Statistics and Mathematics, Zhongnan University of Economics
and Law, Wuhan, 430073, China
School of Statistics and Mathematics, Zhongnan University of Economics
and Law, Wuhan, 430073, China
AUTHOR
Jin
Peng
pengjin01@tsinghua.org.cn)
true
3
Institute of Uncertain Systems, Huanggang Normal University, Huang-
gang, 438000, China
Institute of Uncertain Systems, Huanggang Normal University, Huang-
gang, 438000, China
Institute of Uncertain Systems, Huanggang Normal University, Huang-
gang, 438000, China
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graph, Information Sciences, 296 (2015), 61-74.
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on Fuzzy Systems, 24(4) (2015), 981-991.
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(2009), 3-10.
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Springer-Verlag, Berlin, 2010.
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(2012), 3-10.
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uncertain information, Knowledge-Based Systems, 59 (2014), 161-172.
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ket, Knowledge-Based Systems, 35 (2012), 259-263.
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and Computational Mathematics, 12(3) (2013), 381-391.
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73
ORIGINAL_ARTICLE
RESOLUTION OF NONLINEAR OPTIMIZATION PROBLEMS SUBJECT TO BIPOLAR MAX-MIN FUZZY RELATION EQUATION CONSTRAINTS USING GENETIC ALGORITHM
This paper studies the nonlinear optimization problems subject to bipolar max-min fuzzy relation equation constraints. The feasible solution set of the problems is non-convex, in a general case. Therefore, conventional nonlinear optimization methods cannot be ideal for resolution of such problems. Hence, a Genetic Algorithm (GA) is proposed to find their optimal solution. This algorithm uses the structure of the feasible domain of the problems and lower and upper bound of the feasible solution set to choose the initial population. The GA employs two different crossover operations: 1- N-points crossover and 2- Arithmetic crossover. We run the GA with two crossover operations for some test problems and compare their results and performance to each other. Also, their results are compared with the results of other authors' works.
http://ijfs.usb.ac.ir/article_3762_2154eb21dc0b0710dca0c101b1419ad8.pdf
2018-04-29T11:23:20
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109
131
10.22111/ijfs.2018.3762
Bipolar fuzzy relation equations
Max-min composition
Nonlinear optimization
Genetic Algorithm
Hassan Dana
Mazraeh
true
1
School of Mathematics and Computer Sciences, Damghan
University, Damghan, Iran
School of Mathematics and Computer Sciences, Damghan
University, Damghan, Iran
School of Mathematics and Computer Sciences, Damghan
University, Damghan, Iran
AUTHOR
Ali Abbasi
Molai
a abbasimolai@du.ac.ir
true
2
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
School of Mathematics and Computer Sciences, Damghan University, Damghan, Iran
LEAD_AUTHOR
[1] S. Abbasbandy, E. Babolian and M. Allame, Numerical solution of fuzzy max-min systems,
1
Applied Mathematics and Computation, 174 (2006), 1321-1328.
2
[2] M. Allame and B. Vatankhahan, Iteration algorithm for solving Ax=b in max-min algebra,
3
Applied Mathematics and Computation, 175 (2006), 269-276.
4
[3] B. De Baets, Analytical solution methods for fuzzy relational equations, in: D. Dubois, H.
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Prade (Eds.), Fundamentals of Fuzzy Sets, The Handbooks of Fuzzy Sets Series, Kluwer
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Academic Publishers, Dordrecht, (2000), 291-340.
7
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8
Sets and Systems, 103 (1999), 107-113.
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11
straints, Information Sciences, 234 (2013), 3-15.
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optimization problems with fuzzy relation constraints using max-product composition, Applied
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[12] E. Khorram, A. Ghodousian and A. A. Molai, Solving linear optimization problems with max-
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star composition equation constraints, Applied Mathematics and Computation, 178 (2006),
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27
relation equation constraints with max-average composition using a modified genetic algo-
28
rithm, Computers and Industrial Engineering, 55 (2008), 1-14.
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the lukasiewicz triangular norm, Soft Computing, 18 (2014), 1399-1404.
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with max-product composition, IEEE Transactions on Fuzzy Systems, 7 (1999), 441-445.
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fuzzy relation equation constraints, Fuzzy Sets and Systems, 127 (2002), 141-164.
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t-norm composition, Fuzzy Optimization and Decision Making, 3 (2004), 271-278.
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equation constraint, Fuzzy Sets and Systems, 150 (2005), 147-162.
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tion equations with a linear objective function, IEEE Transactions on Fuzzy Systems, 10(4)
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77
ORIGINAL_ARTICLE
SOME PROPERTIES OF UNCERTAIN INTEGRAL
Uncertainty theory is a mathematical methodology for dealing withnon-determinate phenomena in nature. As we all know, uncertainprocess and uncertain integral are important contents of uncertaintytheory, so it is necessary to have deep research. This paperpresents the definition and discusses some properties of strongcomonotonic uncertain process. Besides, some useful formulas ofuncertain integral such as nonnegativity, monotonicity, intermediateresults are studied.
http://ijfs.usb.ac.ir/article_3764_a8b8715f896bcb2aeaba59a2dcf9c552.pdf
2018-04-29T11:23:20
2019-03-23T11:23:20
133
142
10.22111/ijfs.2018.3764
Uncertain variable
Uncertain process
Uncertain integral
Monotonicity
Cuilian
You
yycclian@163.com
true
1
College of Mathematics and Information Science, Hebei University,
Baoding 071002, China
College of Mathematics and Information Science, Hebei University,
Baoding 071002, China
College of Mathematics and Information Science, Hebei University,
Baoding 071002, China
LEAD_AUTHOR
Na
Xiang
xiangnahbu@126.com
true
2
College of Mathematics and Information Science, Hebei University, Baoding 071002, China
College of Mathematics and Information Science, Hebei University, Baoding 071002, China
College of Mathematics and Information Science, Hebei University, Baoding 071002, China
AUTHOR
[1] X. Chen and B. Liu, Existence and uniqueness theorem for uncertain differential equations,
1
Fuzzy Optimization and Decision Making, 9(1) (2010), 69{81.
2
[2] D. Dubois and H. Prade, Possibility Theory: An Approach to Computerized Processing of
3
Uncertainty, Plenum, New York, 1988.
4
[3] X. Gao, Some properties of continuous uncertain measure, International Journal of Uncer-
5
tainty, Fuzziness and Knowledge-Based System, 17(3) (2009), 419{426.
6
[4] M. Ha and X. Li, Choquet integral based on self-dual measure, Journal of Hebei University
7
(Natrual Science Edition), 28(2) (2008), 113{115.
8
[5] B. Liu and Y. K. Liu, Expected value of fuzzy variable and fuzzy expected value models, IEEE
9
Transactions on Fuzzy Systems, 10(4) (2002), 445{450.
10
[6] B. Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
11
[7] B. Liu, Fuzzy process, hybrid process and uncertain process, Journal of Uncertain Systems,
12
2(1) (2008),3{16.
13
[8] B. Liu, Theory and Practice of Uncertain Programming, 2nd edn, Springer-Verlag, Berlin,
14
[9] B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 3(1)
15
(2009), 3{10.
16
[10] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncer-
17
tainty, Springer-Verlag, Berlin, 2010.
18
[11] B. Liu, Uncertain risk analysis and uncertain reliablity analysis, Journal of Uncertain Sys-
19
tems, 4(3) (2010), 163{170.
20
[12] B. Liu and X. Chen, Uncertain multiobjective programming and uncertain goal programming,
21
Journal of Uncertainty Analysis and Applications, 3(Artical 10) (2015), 10 pages.
22
[13] B. Liu and K. Yao, Uncertain multilevel programming: Algorithm and applications, Com-
23
puters and Industrial Engineering, 89 (2015), 235{240.
24
[14] B. Liu, Uncertain distribution and independence of uncertain processes, Fuzzy Optimization
25
and Decision Making, 13(3) (2014), 259{271.
26
[15] B. Liu, Uncertainty Theory, 5th ed., http : ==orsc:edu:cn=liu=ut:pdf:
27
[16] E. J. Mcshane, Stochastic Calculus and Stochastic Models, Academic Press, New York, 1974.
28
[17] J. Peng, Risk metrics of loss function for uncertain system, Fuzzy Optimization and Decision
29
Making, 12(1) (2013), 53{64.
30
[18] M. Radko, Fuzzy measure and integral, Fuzzy Sets and Systems, 156(3) (2005), 365{370.
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[19] A. V. Skorokhod, On a generalization of a stochastic integral, Theory of Probability & Its
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Applications, 20(2) (1976), 219{233.
33
[20] M. Sugeno, Theorem of Fuzzy Integrals and Its Applications, Ph. D. Dissertation, Institute
34
of Technology, Tokyo, 1974.
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[21] R. R. Yager, A foundation for a theory of possibility, Journal of Cybernetics, 10 (1980),
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[22] K. Yao and X. Chen, A numerical method for solving uncertain differential equations, Journal
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of Intelligent and Fuzzy Systems, 25(3) (2013), 825{832.
38
[23] C. You, On the convergence of uncertain sequences, Mathematical and Computer Modelling,
39
49(3) (2009), 482{487.
40
[24] C. You and L. Yan, Relationships among convergence concepts of uncertain sequences, Com-
41
puter Modeling and New Technologies, 20(3) (2016), 12{16.
42
[25] C. You and W. Wang, Some properties of complex fuzzy integral, Mathematical Problems in
43
Engineering, 2015(Artical ID 290539) (2015), 7 pages.
44
[26] C. You, H. Ma and H. Huo, A new kind of generalized fuzzy integrals, Journal of Nonlinear
45
Science and Applications, 9(3) (2016), 1396{1401.
46
[27] C. You and L. Yan, The p-distance of uncertain variables, Journal of Intelligent and Fuzzy
47
Systems, 32(1) (2017), 999{1006.
48
[28] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
49
[29] L. A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1
50
(1978), 3{28.
51
ORIGINAL_ARTICLE
POWERSET OPERATORS OF EXTENSIONAL FUZZY SETS
Powerset structures of extensional fuzzy sets in sets with similarity relations are investigated. It is proved that extensional fuzzy sets have powerset structures which are powerset theories in the category of sets with similarity relations, and some of these powerset theories are defined also by algebraic theories (monads). Between Zadeh's fuzzy powerset theory and the classical powerset theory there exists a strong relation, which can be represented as a homomorphism. Analogical results are also proved for new powerset theories of extensional fuzzy sets.
http://ijfs.usb.ac.ir/article_3765_d621b021f19eac714bf7d16a69c7da75.pdf
2018-04-29T11:23:20
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143
163
10.22111/ijfs.2018.3765
Extensional fuzzy sets
Powerset operators
Monads in categories
J.
Mockor
true
1
University of Ostrava, Institute for Research and Applications of Fuzzy
Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Institute for Research and Applications of Fuzzy
Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Institute for Research and Applications of Fuzzy
Modeling, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
LEAD_AUTHOR
[1] C. De Mitri and C. Guido, Some remarks on fuzzy powerset operators, Fuzzy Sets and Systems
1
126 (2002), 241-251.
2
[2] G. File, and F. Ranzato, Improving Abstract Interpretations by Systematic Lifting to the
3
Powerset, Proceedings of the 1994 International Symposium on Logic programming, MIT
4
Press Cambridge, MA, USA (1994), 655{669.
5
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ORIGINAL_ARTICLE
GENERALIZED RESIDUATED LATTICES BASED F-TRANSFORM
The aim of the present work is to study the $F$-transform over a generalized residuated lattice. We discuss the properties that are common with the $F$-transform over a residuated lattice. We show that the $F^{\uparrow}$-transform can be used in establishing a fuzzy (pre)order on the set of fuzzy sets.
http://ijfs.usb.ac.ir/article_3766_2e1aae518019f70a853a251e8e71e464.pdf
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10.22111/ijfs.2018.3766
Generalized residuated lattice
Fuzzy partition
Direct $F$-transform
Inverse $F$-transform
S. P.
Tiwari
true
1
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
LEAD_AUTHOR
I.
Perfilieva
irina.perﬁlieva@osu.cz
true
2
University of Ostrava, Institute for Research and Applications of
Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Institute for Research and Applications of
Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
University of Ostrava, Institute for Research and Applications of
Fuzzy Modeling, NSC IT4Innovations, 30. dubna 22, 701 03 Ostrava 1, Czech Republic
AUTHOR
A. P.
Singh
true
3
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
Department of Applied Mathematics, Indian Institute of Technology
(ISM), Dhanbad-826004, Jharkhand, India
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ORIGINAL_ARTICLE
Persian-translation Vol.15, No.2 April 2018
http://ijfs.usb.ac.ir/article_3767_5165ec122a668e255726ff4271fa0e61.pdf
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10.22111/ijfs.2018.3767