ORIGINAL_ARTICLE
Cover vol. 14, no. 4, August 2017
http://ijfs.usb.ac.ir/article_3332_ce2c4b336fb4f06945a613ea89c56f1c.pdf
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10.22111/ijfs.2017.3332
ORIGINAL_ARTICLE
SOME COMPUTATIONAL RESULTS FOR THE FUZZY RANDOM VALUE OF LIFE ACTUARIAL LIABILITIES
The concept of fuzzy random variable has been applied in several papers to model the present value of life insurance liabilities. It allows the fuzzy uncertainty of the interest rate and the probabilistic behaviour of mortality to be used throughout the valuation process without any loss of information. Using this framework, and considering a triangular interest rate, this paper develops closed expressions for the expected present value and its defuzzified value, the variance and the distribution function of several well-known actuarial liabilities structures, namely life insurances, endowments and life annuities.
http://ijfs.usb.ac.ir/article_3323_242708c1c04780a4e8a45660e0ca3d78.pdf
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10.22111/ijfs.2017.3323
Financial pricing
Life insurance
Endowment
Life annuity
Stochastic mortality
Fuzzy numbers
Fuzzy triangular interest rate
Fuzzy random variable
Fuzzy financial mathematics
Fuzzy life insurance mathematics
J.
de Andres-Sanchez
true
1
Social and Business Research Laboratory, Department of Business Management, Rovira i Virgili University, Spain
Social and Business Research Laboratory, Department of Business Management, Rovira i Virgili University, Spain
Social and Business Research Laboratory, Department of Business Management, Rovira i Virgili University, Spain
LEAD_AUTHOR
L. Gonzalez-Vila
Puchades
true
2
Department of Mathematics for Economics, Finance and Actuarial Science, University of Barcelona, Spain
Department of Mathematics for Economics, Finance and Actuarial Science, University of Barcelona, Spain
Department of Mathematics for Economics, Finance and Actuarial Science, University of Barcelona, Spain
AUTHOR
[1] A. Alegre and M. Claramunt, Allocation of solvency cost in group of annuities: Actuarial
1
principles and cooperative game theory, Insurance: Mathematics and Economics, 17 (1995),
2
[2] J. Andres-Sanchez and L. Gonzalez-Vila Puchades, Using fuzzy random variables in life
3
annuities pricing, Fuzzy sets and Systems, 188 (2012), 27-44.
4
[3] J. Andres-Sanchez and L. Gonzalez-Vila Puchades, A fuzzy random variable approach to life
5
insurance pricing, In A. Gil-Lafuente; J. Gil-Lafuente and J.M. Merigo (Eds.), Studies in
6
Fuzziness and Soft Computing; Soft Computing in Management and Business Economics,
7
Springer-Verlag, Berlin/Heidelberg, (2012), 111-125.
8
[4] J. Andres-Sanchez and L. Gonzalez-Vila Puchades, Pricing endowments with soft computing,
9
Economic Computation and economic cybernetics studies research, 1 (2014), 124-142.
10
[5] J. Andres-Sanchez and A. Terce~no, Applications of Fuzzy Regression in Actuarial Analysis,
11
Journal of Risk and Insurance, 70 (2003), 665-699.
12
[6] J. J. Buckley, The fuzzy mathematics of nance, Fuzzy Sets and Systems, 21 (1987), 257-273.
13
[7] J. J. Buckley and Y. Qu, On using -cuts to evaluate fuzzy equations, Fuzzy Sets and Systems,
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38 (1990), 309-312.
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Sets and Systems, 29 (1989), 145-153.
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a fuzzy random variable, 5th International Symposium on Imprecise Probabilities and Their
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Applications, Prague, (2007), 135-144.
20
[10] J. D. Cummins and R. A. Derrig, Fuzzy nancial pricing of property-liability insurance,
21
North American Actuarial Journal, 1 (1997), 21-44.
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[11] R. A. Derrig and K. Ostaszewski, Managing the tax liability of a property liability insurance
23
company, Journal of Risk and Insurance, 64 (1997), 695-711.
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[12] Y. Feng, L. Hu and H. Shu, The variance and covariance of fuzzy random variables and their
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application, Fuzzy Sets and Systems, 120 (2001), 487-497.
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arial Science, Society of Actuaries, Schaumburg, 1993.
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and Economics, 53 (2013), 864-870.
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1 (2004), 43-56.
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55
ORIGINAL_ARTICLE
CERTAIN TYPES OF EDGE m-POLAR FUZZY GRAPHS
In this research paper, we present a novel frame work for handling $m$-polar information by combining the theory of $m-$polar fuzzy sets with graphs. We introduce certain types of edge regular $m-$polar fuzzy graphs and edge irregular $m-$polar fuzzy graphs. We describe some useful properties of edge regular, strongly edge irregular and strongly edge totally irregular $m-$polar fuzzy graphs. We discuss the relationship between degree of a vertex and degree of an edge in an $m-$polar fuzzy graph. We investigate edge irregularity on a path on $2n$ vertices and barbell graph $B_{n,n}.$We also present an application of $m-$polar fuzzy graph to decision making.
http://ijfs.usb.ac.ir/article_3324_59b5d39f5876cd527802f701f8ecc284.pdf
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50
10.22111/ijfs.2017.3324
Barbell graph
$m-$polar fuzzy sets
$m-$polar fuzzy graphs
Strongly edge totally irregular $m-$polar fuzzy graphs
decision making
Muhammad
Akram
m.akram@pucit.edu.pk
true
1
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan
AUTHOR
Neha
Waseem
neha_waseem@yahoo.com
true
2
Department of Mathematics, University of the Punjab, New Campus,
Lahore, Pakistan
Department of Mathematics, University of the Punjab, New Campus,
Lahore, Pakistan
Department of Mathematics, University of the Punjab, New Campus,
Lahore, Pakistan
AUTHOR
Wieslaw A.
Dudek
(wieslaw.dudek@pwr.wroc.pl
true
3
Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland
Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland
Faculty of Pure and Applied Mathematics, Wroclaw University of Science and Technology, Wyb. Wyspianskiego 27, 50-370, Wroclaw, Poland
LEAD_AUTHOR
[1] M. Akram, Bipolar fuzzy graphs, Information Sciences, 181 (2011), 5548-5564.
1
[2] M. Akram and A. Adeel, m-polar fuzzy labeling graphs with application, Math. Computer
2
Sci., 10 (2016), 387-402.
3
[3] M. Akram and W. A. Dudek, Regular bipolar fuzzy graphs, Neural Computing & Applications,
4
21 (2012), 197-205.
5
[4] M. Akram and H. R. Younas, Certain types of irregular m-polar fuzzy graphs, J. Appl. Math.
6
Computing, 53(1) (2017), 365-382.
7
[5] M. Akram and N. Waseem, Certain metrics in m-polar fuzzy graphs, New Math. Natural
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Computation, 12 (2016), 135-155.
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[7] J. Chen, S. G. Li, S. Ma and X. Wang, m-polar fuzzy sets, The Scientic World Journal,
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Article ID 416530, 2014 (2014), 8 pages.
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(2009), 1760-1768.
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Math., 40 (2016), 125-135.
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berg, 2nd Edition, 2001.
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mation Sciences, 288 (2014), 437-448.
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eling and multiagent decision analysis, Proc. of IEEE conf., (1994), 305-309.
35
ORIGINAL_ARTICLE
ARITHMETIC-BASED FUZZY CONTROL
Fuzzy control is one of the most important parts of fuzzy theory for which several approaches exist. Mamdani uses $\alpha$-cuts and builds the union of the membership functions which is called the aggregated consequence function. The resulting function is the starting point of the defuzzification process. In this article, we define a more natural way to calculate the aggregated consequence function via arithmetical operators. Defuzzification is the optimum value of the resultant membership function. The left and right hand sides of the membership function will be handled separately. Here, we present a new ABFC (Arithmetic Based Fuzzy Control) algorithm based on arithmetic operations which use a new defuzzification approach. The solution is much smoother, more accurate, and much faster than the classical Mamdani controller.
http://ijfs.usb.ac.ir/article_3325_9b07cd96f753146bc25062151c7c05e8.pdf
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66
10.22111/ijfs.2017.3325
Fuzzy controller
Mamdani controller
Defuzzification
Fuzzy arithmetic
Jozsef
Dombi
dombi@@inf.u-szeged.hu
true
1
Institute of Informatics, University of Szeged, Szeged, Hungary
Institute of Informatics, University of Szeged, Szeged, Hungary
Institute of Informatics, University of Szeged, Szeged, Hungary
AUTHOR
Tamas
Szepe
true
2
Department of Technical Informatics, University of Szeged, Szeged,
Hungary
Department of Technical Informatics, University of Szeged, Szeged,
Hungary
Department of Technical Informatics, University of Szeged, Szeged,
Hungary
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[1] S. Assilian, Articial intelligence in the control of real dynamical systems, Ph.D. Thesis,
1
London University, Great Britain, 1974.
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[2] J. Dombi, Pliant arithmetics and pliant arithmetic operations, Acta Polytechnica Hungarica,
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6(5) (2009), 19{49.
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Science & Business Media, Berlin, 2013.
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I., CRC Press, Boca Raton, FL, (1987), 3{39.
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53
ORIGINAL_ARTICLE
AN OPTIMAL FUZZY SLIDING MODE CONTROLLER DESIGN BASED ON PARTICLE SWARM OPTIMIZATION AND USING SCALAR SIGN FUNCTION
This paper addresses the problems caused by an inappropriate selection of sliding surface parameters in fuzzy sliding mode controllers via an optimization approach. In particular, the proposed method employs the parallel distributed compensator scheme to design the state feedback based control law. The controller gains are determined in offline mode via a linear quadratic regular. The particle swarm optimization is incorporated into the linear quadratic regular technique for determining the optimal weight matrices. Consequently, an optimal sliding surface is obtained using the scalar $sign$ function. This latter is used to design the proposed control law. Finally, the effectiveness of the proposed fuzzy sliding mode controller based on parallel distributed compensator and using particle swarm optimization is evaluated by comparing the obtained results with other reported in literature.
http://ijfs.usb.ac.ir/article_3326_f3456838d80940d4d0d34d523ff7c0b3.pdf
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85
10.22111/ijfs.2017.3326
Sliding mode control
Takagi-Sugeno fuzzy model
Particle swarm optimization
Parallel distributed compensator
Linear quadratic regulator
Lotfi
Chaouech
true
1
Laboratoire d'Ingenierie des Systemes Industriels et des Energies
Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies
Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies
Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia
LEAD_AUTHOR
Mo^ez
Soltani
true
2
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP
56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP
56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP
56, 1008 Tunis, Tunisia
AUTHOR
Slim
Dhahri
true
3
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP
56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP
56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP
56, 1008 Tunis, Tunisia
AUTHOR
Abdelkader
Chaari
true
4
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia
Laboratoire d'Ingenierie des Systemes Industriels et des Energies Renouvelables (LISIER), The National Higher Engineering School of Tunis (ENSIT), BP 56, 1008 Tunis, Tunisia
AUTHOR
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1
mode controller for the twin rotor mimo system, 16th IEEE Mediterranean Electrotechnical
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Conference (MELECON), (2012), 1063{1066.
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applications of fuzzy logic at general electric, Proceedings of the IEEE, 83(3) (1995), 450{
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Systems, 10(2) (2008), 112{118.
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[4] W. Chang, J. B. Park, Y. H. Joob and G. Chen, Design of robust fuzzy-model- based controller
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with sliding mode control for siso nonlinear systems, Fuzzy Sets and Systems, 125(1) (2002),
10
[5] L. Chaouech and A. Chaari, Design of sliding mode control of nonlinear system based on
11
Takagi-Sugeno fuzzy model, World Congress on Computer and Information Technology (WCCIT),
12
(2013), 1{6.
13
[6] L. Chaouech, M. Soltani, S. Dhahri and A. Chaari, Design of new fuzzy sliding mode con-
14
troller based on parallel distributed compensation controller and using the scalar sign func-
15
tion, Mathematics and Computers in Simulation, 132 (2017), 277{288.
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[7] P. C. Chen, C. W. Chen and W. L. Chiang, GA-based fuzzy sliding mode controller for
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nonlinear systems, Mathematical Problems in Engineering, 2008 (2008), 1{16.
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Hall, USA, 1995.
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a boost converter, IEEE Transactions on Industrial Electronics, 61(1) (2014), 196{209.
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exible satellite,
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Engineering Applications of Articial Intelligence, 18(4) (2005), 451{459.
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monic disturbances, IEEE Transactions on Control Systems Technology, 8 (2) (2000), 366{
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mization, Second International Conference on Intelligent Networks and Intelligent Systems,
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Tianjin (2009), 669{672.
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[14] Y. J. Huang and H. K. Wei, Sliding mode control design for discrete multivariable systems
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with time-delayed input signals, International Journal of Systems Science, 33(10) (2002),
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[15] L. Hung, H. Lin and H. Chung, Design of self-tuning fuzzy sliding mode control for TORA
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system, Expert Systems with Applications, 32 (1) (2007), 201{212.
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mode control, ISA Transactions, 43(1) (2007), 73{83.
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[18] K. Jafar, B. M. Mohammad and K. Mansour, Feedback-linearization and fuzzy controllers
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Control of Wheeled Mobile Robots, Asian Journal of Control, 14 (4) ( 2012), 960{973.
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particle swarm optimization and genetic algorithm for identication of fuzzy models, Fuzzy
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[21] R. J. Lian, Adaptive self-organizing fuzzy sliding-mode radial basis-function neural-network
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controller for robotic systems, IEEE Transactions on Industrial Electronics, 61(3) (2014),
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1493{1503.
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tering and coevolutionary particle swarm optimization, Neuro-computing, 72(10-12) (2009),
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2569{2575.
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systems, IEEE International Conference on Fuzzy Systems, (2013), 1{8.
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62
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109
ORIGINAL_ARTICLE
INTERVAL-VALUED INTUITIONISTIC FUZZY SETS AND SIMILARITY MEASURE
In this paper, the problem of measuring the degree of inclusion and similarity measure for two interval-valued intuitionistic fuzzy sets is considered. We propose inclusion and similarity measure by using order on interval-valued intuitionistic fuzzy sets connected with lexicographical order. Moreover, some properties of inclusion and similarity measure and some correlation, between them and aggregations are examined. Finally, we have included example of ranking problem in car showrooms.
http://ijfs.usb.ac.ir/article_3327_4ffa11fa38d3e5873252092cc9181d0a.pdf
2017-08-30T11:23:20
2018-05-25T11:23:20
87
98
10.22111/ijfs.2017.3327
Interval-valued intuitionistic fuzzy sets
Inclusion measure
Similarity measure
Barbara
Pekala
bpekalaur@gmail.com
true
1
Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland
Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland
Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland
LEAD_AUTHOR
Krzysztof
Balicki
kbalicki@ur.edu.pl
true
2
Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland
Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland
Interdisciplinary Centre for Computational Modelling, Faculty of Mathematics and Natural Sciences, University of Rzeszow, Pigonia 1, 35-310 Rzeszow, Poland
AUTHOR
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[2] K. T. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 64
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(1994), 159{174.
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New York, 1999.
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[4] U. Bodenhofer, B. De Baets and J. Fodor, A compendium of fuzzy weak orders: Representa-
6
tions and constructions, Fuzzy Sets Syst., 158 (2007), 811{829.
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[5] K. Bosteels and E. E. Kerre, On a re
8
exivity-preserving family of cardinality-based fuzzy
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comparison measures, Inform. Sci., 179 (2009), 2342{2352.
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[6] H. Bustince, J. Fernandez, R. Mesiar, J. Montero and R. Orduna, Overlap functions, Nonlinear
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Anal.: Theory Methods Appl., 72 (2010), 1488{1499.
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[7] H. Bustince, M. Pagola, R. Mesiar, E. Hullermeier and F. Herrera, Grouping, overlaps, and
13
generalized bientropic functions for fuzzy modeling of pairwise comparisons, IEEE Trans.
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Fuzzy Syst., 20(3) (2012), 405{415.
15
[8] H. Bustince, J. Fernandez, A. Kolesarova and R. Mesiar, Generation of linear orders for
16
intervals by means of aggregation functions, Fuzzy Sets Syst., 220 (2013), 69-77.
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[9] T. Calvo, A. Kolesarova, M. Komornikova and R. Mesiar, Aggregation operators: properties,
18
classes and construction methods, In T. Calvo, G. Mayor, and R. Mesiar (Eds.), Physica-
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Verlag, New York, Aggregation Operators. Studies in Fuzziness and Soft Computing, 97
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(2002), 3-104.
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[10] B. De Baets and R. Mesiar, Triangular norms on product lattices, Fuzzy Sets Syst., 104
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(1999), 61{76.
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[11] B. De Baets, H. De Meyer and H. Naessens, A class of rational cardinality-based similarity
24
measures, J. Comp. Appl. Math., 132 (2001), 51{69.
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[12] B. De Baets and H. De Meyer, Transitivity frameworks for reciprocal relations:cycle-
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transitivity versus FG-transitivity, Fuzzy Sets Syst., 152 (2005), 249{270.
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[13] B. De Baets, S. Janssens and H. De Meyer, On the transitivity of a parametric family of
28
cardinality-based similarity measures, Int. J. Appr. Reason., 50 (2009), 104{116.
29
[14] M. De Cock and E. E. Kerre, Why fuzzy T-equivalence relations do not resolve the Poincar'e
30
paradox, and related issues, Fuzzy Sets Syst., 133 (2003), 181{192.
31
[15] L. De Miguel, H. Bustince, J. Fernandez, E. Indurain, A. Kolesarova and R. Mesiar, Con-
32
struction of admissible linear orders for interval-valued Atanassov intuitionistic fuzzy sets
33
with an application to decision making, Information Fusion, 27 (2016), 189-197.
34
[16] S. Freson, B. De Baets and H. De Meyer, Closing reciprocal relations w.r.t. stochastic tran-
35
sitivity, Fuzzy Sets Syst., 241 (2014), 2{26.
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[17] B. Jayaram and R. Mesiar, I-Fuzzy equivalence relations and I-fuzzy partitions, Inf. Sci., 179
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(2009), 1278{1297.
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[18] D. F. Li, Toposis-based nonlinear-programming methodology for multiattribute decision mak-
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ing with interval-valued intuitionistic fuzzy sets, IEEE Trans. Fuzzy Syst., 18 (2010), 299{311.
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[19] X. D. Liu, S. H. Zheng and F. L. Xiong, Entropy and subsethood for general interval-valued
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intuitionistic fuzzy sets, Lecture Notes Artif. Intell., 3613 (2005), 42{52.
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[20] N. Madrid, A. Burusco, H. Bustince, J. Fernandez and I. Perlieva, Upper bounding overlaps
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by groupings, Fuzzy Sets Syst., 264 (2015), 76{99.
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[21] S. Ovchinnikov, Numerical representation of transitive fuzzy relations, Fuzzy Sets Syst., 126
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(2002), 225{232.
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[22] D. G. Park, Y. C. Kwun, J. H. Park and I. Y. Park, Correlation coecient of interval-
47
valued intuitionistic fuzzy sets and its application to multiple attribute group decision making
48
problems, Math. Comput. Modell., 50 (2009), 1279{1293.
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[23] Z. Switalski, General transitivity conditions for fuzzy reciprocal preference matrices, Fuzzy
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Sets Syst., 137 (2003), 85{100.
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[25] W. Y. Zeng and P. Guo, Normalized distance, similarity measure, inclusion measure and
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entropy of interval-valued fuzzy sets and their relationship, Inf. Sci., 178 (2008), 1334{1342.
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[26] H. Y. Zhang and W. X. Zhang, Hybrid monotonic inclusion measure and its use in measuring
55
similarity and distance between fuzzy sets, Fuzzy Sets Syst., 160 (2009), 107{118.
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[27] Q. Zhang, H. Xing, F. Liu and J. Ye, P. Tang, Some new entropy measures for interval-
57
valued intuitionistic fuzzy sets based on distances and their relationships with similarity and
58
inclusion measures, Inf. Sci., 283 (2014), 55{69.
59
ORIGINAL_ARTICLE
TOPOLOGICAL SIMILARITY OF L-RELATIONS
$L$-fuzzy rough sets are extensions of the classical rough sets by relaxing theequivalence relations to $L$-relations. The topological structures induced by$L$-fuzzy rough sets have opened up the way for applications of topological factsand methods in granular computing. In this paper, we firstly prove thateach arbitrary $L$-relation can generate an Alexandrov $L$-topology.Based on this fact, we introduce the topological similarity of $L$-relations,denote it by T-similarity, and we give intuitive characterization ofT-similarity. Then we introduce the variations of a given $L$-relation andinvestigate the relationship among them. Moreover, we prove that each$L$-relation is uniquely topological similar to an $L$-preorder. Finally,we investigate the related algebraic structures of different sets of$L$-relations on the universe.
http://ijfs.usb.ac.ir/article_3328_9d91e0d6e83d4532a68b2d14d8756c97.pdf
2017-08-30T11:23:20
2018-05-25T11:23:20
99
115
10.22111/ijfs.2017.3328
$L$-fuzzy rough set
$L$-relation
Alexandrov $L$-topology
$L$-preorder
Topological similarity
Jing
Hao
haojingzy@gmail.com
true
1
College of Mathematics and Information Science, Henan University of
Economics and Law, Zhengzhou, 450000, China
College of Mathematics and Information Science, Henan University of
Economics and Law, Zhengzhou, 450000, China
College of Mathematics and Information Science, Henan University of
Economics and Law, Zhengzhou, 450000, China
LEAD_AUTHOR
Shasha
Huang
s_s_huang@163.com
true
2
College of Mathematics and Information, North China University of
Water Resources and Electric Power, Zhengzhou, 450045, China
College of Mathematics and Information, North China University of
Water Resources and Electric Power, Zhengzhou, 450045, China
College of Mathematics and Information, North China University of
Water Resources and Electric Power, Zhengzhou, 450045, China
AUTHOR
[1] K. Blount and C. Tsinakis, The structure of residuated lattices, International Journal of
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Algebra and Computation, 13(4) (2003), 437{461.
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[2] D. Boixader, J. Jacas and J. Recasens, Upper and lower approximations of fuzzy sets, International
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Journal of General System, 29(4) (2000), 555{568.
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[3] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications,
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24(1) (1968), 182{190.
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[4] X. Chen and Q. Li, Construction of rough approximations in fuzzy setting, Fuzzy sets and
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Systems, 158(23) (2007), 2641{2653.
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9
2004 IEEE International Conference on Fuzzy Systems, 1 (2004), 103{108.
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[6] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of
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General System, 17(2-3) (1990), 191{209.
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[7] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1) (1967),
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[8] J. Hao and Q. Li, The relationship between L-fuzzy rough set and L-topology, Fuzzy Sets and
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Systems, 178(1) (2011), 74{83.
15
[9] J. Jarvinen and J. Kortelainen, A unifying study between modal-like operators, topologies and
16
fuzzy sets, Fuzzy Sets and Systems, 158(11) (2007), 1217{1225.
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[10] H. Lai and D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems, 157(14)
18
(2006), 1865{1885.
19
[11] Z. Li and R. Cui, T-similarity of fuzzy relations and related algebraic structures, Fuzzy Sets
20
and Systems, 275 (2015), 130{143.
21
[12] G. Liu, Generalized rough sets over fuzzy lattices, Information Sciences, 178(6) (2008), 1651{
22
[13] G. Liu and W. Zhu, The algebraic structures of generalized rough set theory, Information
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Sciences, 178(21) (2008), 4105{4113.
24
[14] R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis
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and Applications, 56(3) (1976), 621{633.
26
[15] Z. M. Ma and B. Q. Hu, Topological and lattice structures of L-fuzzy rough sets determined
27
by lower and upper sets, Information Sciences, 218 (2013), 194{204.
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[16] N. N. Morsi and M. Yakout, Axiomatics for fuzzy rough sets, Fuzzy sets and Systems, 100(1)
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(1998), 327{342.
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[17] Z. Pawlak, Rough sets, International Journal of Computer & Information Sciences, 11(5)
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(1982), 341{356.
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[18] K. Qin and Z. Pei, On the topological properties of fuzzy rough sets, Fuzzy Sets and Systems,
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151(3) (2005), 601{613.
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[19] A. M. Radzikowska and E. E. Kerre, A comparative study of fuzzy rough sets, Fuzzy Sets and
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Systems, 126(2) (2002), 137{155.
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[20] A. M. Radzikowska and E. E. Kerre, Fuzzy rough sets based on residuated lattices, In: Transactions
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on Rough Sets II, LNCS 3135, (2004), 278{296.
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[21] A. M. Radzikowska and E. E. Kerre, Characterisation of main classes of fuzzy relations using
39
fuzzy modal operators, Fuzzy Sets and Systems, 152(2) (2005), 223{247.
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[22] Y. H. She and G. J. Wang, An axiomatic approach of fuzzy rough sets based on residuated
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lattices, Computers & Mathematics with Applications, 58(1) (2009), 189{201.
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27(2-3) (1996), 245{253.
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[24] H. Thiele, On axiomatic characterization of fuzzy approximation operators II, the rough fuzzy
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set based case, Proceedings of the 31st IEEE International Symposium on Multiple-Valued
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Logic, (2001), 330{335.
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[25] H. Thiele, On axiomatic characterization of fuzzy approximation operators III, the fuzzy dia-
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mond and fuzzy box based cases, The 10th IEEE International Conference on Fuzzy Systems,
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2 (2001), 1148{1151.
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[26] D. Vanderpooten, Similarity relation as a basis for rough approximations, Advances in Machine
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Intelligence and Soft Computing, 4 (1997), 17{33.
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[27] C. Y. Wang and B. Q. Hu, Fuzzy rough sets based on generalized residuated lattices, Information
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Sciences, 248 (2013), 31{49.
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[28] M.Ward and R. P. Dilworth, Residuated lattices, Transactions of the American Mathematical
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Society, 45(3) (1939), 335{354.
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[29] W. Z.Wu, Y. Leung and J. S. Mi, On characterizations of (I;T )-fuzzy rough approximation
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operators, Fuzzy Sets and Systems, 154(1) (2005), 76{102.
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[30] W. Z. Wu, J. S. Mi and W. X. Zhang, Generalized fuzzy rough sets, Information Sciences,
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151 (2003), 263{282.
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[31] Y. Yao, Constructive and algebraic methods of the theory of rough sets, Information Sciences,
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109(1) (1998), 21{47.
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[32] W. Zhu, Topological approaches to covering rough sets, Information Sciences, 177(6) (2007),
63
1499{1508.
64
ORIGINAL_ARTICLE
FUZZY INCLUSION LINEAR SYSTEMS
In this manuscript, we introduce a new class of fuzzy problems, namely ``fuzzy inclusion linear systems" and propose a fuzzy solution set for it. Then, we present a theoretical discussion about the relationship between the fuzzy solution set of a fuzzy inclusion linear system and the algebraic solution of a fuzzy linear system. New necessary and sufficient conditions are derived for obtaining the unique algebraic solution for a fuzzy linear system. Also, all new concepts are illustrated by numerical examples.
http://ijfs.usb.ac.ir/article_3329_0c798ba6903291db932f68673982de92.pdf
2017-08-30T11:23:20
2018-05-25T11:23:20
117
137
10.22111/ijfs.2017.3329
Fuzzy linear system
Fuzzy inclusion linear system
Fuzzy solution set
Lower $r$-boundary
Upper $r$-boundary
Mojtaba
Ghanbari
ghanbari@aliabadiau.ac.ir
true
1
Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
Department of Mathematics, Aliabad Katoul Branch, Islamic Azad University, Aliabad Katoul, Iran
LEAD_AUTHOR
[1] T. Allahviranloo, Numerical methods for fuzzy system of linear equations, Applied Mathematics
1
and Computation, 155 (2004), 493–502.
2
[2] T. Allahviranloo and M. Ghanbari, On the algebraic solution of fuzzy linear systems based
3
on interval theory, Applied Mathematical Modelling, 36 (2012), 5360–5379.
4
[3] T. Allahviranloo and M. Ghanbari, Solving Fuzzy Linear Systems by Homotopy Perturbation
5
Method, International Journal of Computational Cognition, 8(2) (2010), 24–30.
6
[4] T.Allahviranloo, M. Ghanbari, A.A. Hosseinzadeh, E. Haghi and R. Nuraei, A note on “Fuzzy
7
linear systems”, Fuzzy Sets and Systems, 177 (2011), 87–92.
8
[5] T. Allahviranloo and M. Ghanbari, A new approach to obtain algebraic solution of interval
9
linear systems, Soft Computing, 16 (2012), 121–133.
10
[6] T. Allahviranloo, E. Haghi and M. Ghanbari, The nearest symmetric fuzzy solution for a
11
symmetric fuzzy linear system, An. St. Univ. Ovidius Constanta, 20(1) (2012), 151–172.
12
[7] T. Allahviranloo and S. Salahshour, Fuzzy symmetric solution of fuzzy linear systems, Journal
13
of Computational and Applied Mathematics, 235(16) (2011), 4545–4553.
14
[8] T. Allahviranloo, R. Nuraei, M. Ghanbari, E. Haghi and A. A. Hosseinzadeh, A new metric
15
for L-R fuzzy numbers and its application in fuzzy linear systems, Soft Computing, 16 (2012),
16
1743-1754.
17
[9] B. Bede and S. G. Gal, Generalizations of the differentiability of fuzzy-number-valued functions
18
with applications to fuzzy differential equations, Fuzzy Sets and Systems, 151 (2005),
19
581–599.
20
[10] R. Ezzati, Solving fuzzy linear systems, Soft Computing, 15(2010), 193-197.
21
[11] M. Friedman, M. Ming and A. Kandel, Fuzzy linear systems, Fuzzy Sets and Systems,
22
96(1998), 201–209.
23
[12] M. Ghanbari, T. Allahviranloo and E. Haghi, Estimation of algebraic solution by limiting the
24
solution set of an interval linear system, Soft Computing, 16(12) (2012), 2135–2142.
25
[13] M. Ghanbari and R. Nuraei, Convergence of a semi-analytical method on the fuzzy linear
26
systems, Iranian Journal of Fuzzy Systems, 11(4) (2014), 45–60.
27
[14] M. Ghanbari and R. Nuraei, Note on new solutions of LR fuzzy linear systems using ranking
28
functions and ABS algorithms, Fuzzy Inf. Eng., 5(3) (2013), 317–326.
29
[15] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems, 12 (1984),
30
215–229.
31
[16] R. Nuraei, T. Allahviranloo and M. Ghanbari, Finding an inner estimation of the solution
32
set of a fuzzy linear system, Applied Mathematical Modelling, 37 (2013), 5148–5161.
33
[17] C. Wu and M. Ming, On embedding problem of fuzzy number space: Part 1, Fuzzy Sets and
34
Systems, 44 (1991), 33–38.
35
ORIGINAL_ARTICLE
STONE DUALITY FOR R0-ALGEBRAS WITH INTERNAL STATES
$R\sb{0}$-algebras, which were proved to be equivalent to Esteva and Godo's NM-algebras modelled by Fodor's nilpotent minimum t-norm, are the equivalent algebraic semantics of the left-continuous t-norm based fuzzy logic firstly introduced by Guo-jun Wang in the mid 1990s.In this paper, we first establish a Stone duality for the category of MV-skeletons of $R\sb{0}$-algebras and the category of three-valued Stone spaces.Then we extend Flaminio-Montagna internal states to $R\sb{0}$-algebras.Such internal states must be idempotent MV-endomorphisms of $R\sb{0}$-algebras.Lastly we present a Stone duality for the category of MV-skeletons of $R\sb{0}$-algebras with Flaminio-Montagna internal states and the category of three-valued Stone spaces with Zadeh type idempotent continuous endofunctions.These dualities provide a topological viewpoint for better understanding of the algebraic structures of $R\sb{0}$-algebras.
http://ijfs.usb.ac.ir/article_3330_f12a0f74c6087b8efa1b0345bf21060c.pdf
2017-08-30T11:23:20
2018-05-25T11:23:20
139
161
10.22111/ijfs.2017.3330
$Rsb{0}$-algebra
Nilpotent minimum algebra
MV-skeleton
internal state
Stone duality
Hongjun
Zhou
true
1
School of Mathematics and Information Science, Shaanxi Normal
University, Xi'an, 710062, CHINA
School of Mathematics and Information Science, Shaanxi Normal
University, Xi'an, 710062, CHINA
School of Mathematics and Information Science, Shaanxi Normal
University, Xi'an, 710062, CHINA
AUTHOR
Hui-Xian
Shi
rubyshi@163.com
true
2
School of Mathematics and Information Science, Shaanxi Normal University
School of Mathematics and Information Science, Shaanxi Normal University
School of Mathematics and Information Science, Shaanxi Normal University
LEAD_AUTHOR
[1] S. Aguzzoli, M.Busaniche and V. Marra, Spectral duality for nitely generated nilpotent min-
1
imum algebras with applications, J. Logic Comput., 17 (2007), 749{765.
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Math., 38 (1986), 1356{1379.
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218 (2013), 90{102.
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[6] C. C. Chang, Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc., 88 (1958),
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[7] R. Cignoli and D. Mundici, Stone duality for Dedekind -complete `-groups with order unit,
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J. Algebra, 302 (2006), 848{861.
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[8] L. C. Ciungu, Non-commutative Multiple-Valued Logic Algebras, Springer, New York, 2014.
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[9] L. C. Ciungu, G. Georgescu and C. Muresan, Generalized Bosbach states: part I, Arch. Math.
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Logic, 52 (2013), 335{376.
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[10] L. C. Ciungu, G. Georgescu and C. Muresan, Generalized Bosbach states: part II, Arch.
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[11] A. Di Nola and A. Dvurecenskij, State-morphism MV-algebras, Ann. Pure Appl. Logic, 161
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(2009), 161{173.
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[12] A. Di Nola, A. Dvurecenskij and A. Lettieri, On varieties of MV-algebras with internal states,
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Inter. J. Approx. Reason., 51 (2010), 680{694.
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[13] A. Di Nola, A. Dvurecenskij and A. Lettieri, Stone duality type theorems for MV-algebras
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with internal states, Comm. Algebra, 40 (2012), 327{342.
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ORIGINAL_ARTICLE
REDUNDANCY OF MULTISET TOPOLOGICAL SPACES
In this paper, we show the redundancies of multiset topological spaces. It is proved that $(P^\star(U),\sqsubseteq)$ and $(Ds(\varphi(U)),\subseteq)$ are isomorphic. It follows that multiset topological spaces are superfluous and unnecessary in the theoretical view point.
http://ijfs.usb.ac.ir/article_3331_e60d0f147e0b8583bab007f0010335f2.pdf
2017-08-30T11:23:20
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10.22111/ijfs.2017.3331
Multiset
Multiset topology
Isomorphism
A.
Ghareeb
nasserfuzt@hotmail.com
true
1
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
Department of Mathematics, Faculty of Science, South Valley University, Qena 83523, Egypt
LEAD_AUTHOR
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ORIGINAL_ARTICLE
Persian-translation vol. 14, no. 4, August 2017
http://ijfs.usb.ac.ir/article_3333_1a06dcc38f465140c0747a83fca3fe11.pdf
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