ORIGINAL_ARTICLE
Cover vol. 14, no. 4, August 2017
http://ijfs.usb.ac.ir/article_3332_ce2c4b336fb4f06945a613ea89c56f1c.pdf
2017-08-01T11:23:20
2018-09-20T11:23:20
0
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
2017-08-30T11:23:20
2018-09-20T11:23:20
1
25
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,
14
38 (1990), 309-312.
15
[8] L. M. Campos and A. Gonzalez, A subjective approach for ranking fuzzy numbers, Fuzzy
16
Sets and Systems, 29 (1989), 145-153.
17
[9] I. Couso, D. Dubois, S. Montes and L. Sanchez, On various denitions of the variance of
18
a fuzzy random variable, 5th International Symposium on Imprecise Probabilities and Their
19
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.
22
[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.
24
[12] Y. Feng, L. Hu and H. Shu, The variance and covariance of fuzzy random variables and their
25
application, Fuzzy Sets and Systems, 120 (2001), 487-497.
26
[13] H. U. Gerber, Life Insurance Mathematics, Springer-Verlag, Berlin/Heidelberg, 1995.
27
[14] S. Heilpern, The expected value of a fuzzy number, Fuzzy Sets and Systems, 47(1) (1992),
28
[15] R. Korner, On the variance of fuzzy random variables, Fuzzy Sets and Systems, 92 (1997),
29
[16] V. Kratschmer, A unied approach to fuzzy random variables, Fuzzy Sets and Systems, 123
30
(2001), 1-9.
31
[17] H. Kwakernaak, Fuzzy random variables I: denitions and theorems, Information Sciences,
32
15 (1978), 1-29.
33
[18] J. Lemaire, Fuzzy insurance, Astin Bulletin, 20 (1990), 33-55.
34
[19] M. Li Calzi, Towards a general setting for the fuzzy mathematics of nance, Fuzzy Sets and
35
Systems, 35 (1990), 265-280.
36
[20] M. Lopez-Diaz and M. A. Gil, The -average value and the fuzzy expectation of a fuzzy
37
random variable, Fuzzy Sets and Systems, 99 (1998), 347-352.
38
[21] H. T. Nguyen, A note on the extension principle for fuzzy sets, Journal of Mathematical
39
Analysis and Applications, 64 (1978), 369-380.
40
[22] K. Ostaszewski, An Investigation Into Possible Applications of Fuzzy Sets Methods in Actu-
41
arial Science, Society of Actuaries, Schaumburg, 1993.
42
[23] E. Pitacco, Simulation in insurance, In: Goovaerts, M. De Vylder, F. Etienne and J. Haezendonck
43
(Eds.), Insurance and risk theory, Reidel, Dordretch, (1986), 37-77.
44
[24] M. L. Puri and D. A. Ralescu, Fuzzy random variables, Journal of Mathematical Analysis
45
and Applications, 114 (1986), 409-422.
46
[25] E. Roventa and T. Spircu, Averaging procedures in defuzzication processes, Fuzzy Sets and
47
Systems, 136 (2003), 375{385.
48
[26] A. Shapiro, Modeling future lifetime as a fuzzy random variable, Insurance: Mathematics
49
and Economics, 53 (2013), 864-870.
50
[27] R. Viertl and D. Hareter, Fuzzy information and stochastics, Iranian Journal of Fuzzy Systems,
51
1 (2004), 43-56.
52
[28] L. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
53
[29] C. Zhong and G. Zhou, The equivalence of two denitions of fuzzy random variables, Proceedings
54
of the 2nd IFSA Congress (1987), Tokyo, 59-62,
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
2017-08-30T11:23:20
2018-09-20T11:23:20
27
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
8
Computation, 12 (2016), 135-155.
9
[6] P. Bhattacharya, Some remarks on fuzzy graphs, Pattern Recognition Letter, 6 (1987), 297-
10
[7] J. Chen, S. G. Li, S. Ma and X. Wang, m-polar fuzzy sets, The Scientic World Journal,
11
Article ID 416530, 2014 (2014), 8 pages.
12
[8] A. Kauman, Introduction to la Theorie des Sous-emsembles Flous, Masson et Cie, 1 (1973).
13
[9] S. Mathew and M. S. Sunitha, Types of arcs in a fuzzy graph, Information Sciences, 179
14
(2009), 1760-1768.
15
[10] N. R. S. Maheswari and C. Sekar, On strongly edge irregular fuzzy graphs, Kragujevac J.
16
Math., 40 (2016), 125-135.
17
[11] J. N. Mordeson and P. S. Nair, Fuzzy graphs and fuzzy hypergraphs, Physica Verlag, Heidel-
18
berg, 2nd Edition, 2001.
19
[12] S. P. Nandhini and E. Nandhini, Strongly irregular fuzzy graphs, Internat. J. Math. Archive,
20
5 (2014), 110-114.
21
[13] A. Nagoorgani and K. Radha, Regular property of fuzzy graphs, Bull. Pure Appl. Sci., 27E
22
(2008), 411-419.
23
[14] K. Radha and N. Kumaravel, On edge regular fuzzy graphs, Internat. J. Math. Archive, 5(9)
24
(2014), 100-112.
25
[15] A. Rosenfeld, Fuzzy graphs, Fuzzy Sets and Their Applications, Academic Press, New York,
26
(1975), 77-95.
27
[16] P. K. Singh and Ch. A. Kumar, Bipolar fuzzy graph representation of concept lattice, Infor-
28
mation Sciences, 288 (2014), 437-448.
29
[17] H. L. Yang, S. G. Li, W. H. Yang and Y. Lu, Notes on bipolar fuzzy graphs, Information
30
Sciences, 242 (2013), 113-121.
31
[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-353.
32
[19] L. A. Zadeh, Similarity relations and fuzzy orderings, Information Sciences, 3 (1971), 177-
33
[20] W. R. Zhang, Bipolar fuzzy sets and relations: a computational framework forcognitive mod-
34
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
2017-08-30T11:23:20
2018-09-20T11:23:20
51
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
LEAD_AUTHOR
[1] S. Assilian, Articial intelligence in the control of real dynamical systems, Ph.D. Thesis,
1
London University, Great Britain, 1974.
2
[2] J. Dombi, Pliant arithmetics and pliant arithmetic operations, Acta Polytechnica Hungarica,
3
6(5) (2009), 19{49.
4
[3] D. Driankov, H. Hellendoorn and M. Reinfrank, An introduction to fuzzy control, Springer
5
Science & Business Media, Berlin, 2013.
6
[4] D. Dubois and H. Prade, Operations on fuzzy numbers, Int. J. Systems Science, 9 (1978),
7
[5] D. Dubois and H. Prade, Fuzzy members: An overview, Analysis of Fuzzy Information, Vol.
8
I., CRC Press, Boca Raton, FL, (1987), 3{39.
9
[6] D. Dubois and H. Prade, Special issue on fuzzy numbers, Fuzzy Sets and System, 24 (3),
10
[7] D. Filev and R.Yager, A generalized defuzzication method via BAD distributions, Internat.
11
J. Intell. Systems, 6 (1991), 689{697.
12
[8] R. Fuller and R. Mesiar, Special issue on fuzzy arithmetic, Fuzzy Sets and System, 91(2)
13
[9] R. Jain, Tolerance analysis using fuzzy sets, International Journal of Systems Science, 7(12)
14
(1976), 1393{1401.
15
[10] T. Jiang and Y. Li, Generalized defuzzication strategies and their parameter learning pro-
16
cedures, IEEE Trans. Fuzzy Systems, 4 (1996), 64{71.
17
[11] A. Kaufmann and M. M. Gupta, Introduction to fuzzy arithmetic: theory and applications,
18
Van Nostrand Reinhold, New York, 1985.
19
[12] A. Kaufmann and M. M. Gupta, Fuzzy mathematical models in engineering and management
20
science, North-Holland, Amsterdam, 1988.
21
[13] E. Mamdani, Application of fuzzy algorithms for control of simple dynamic plant, Proc. IEE,
22
121 (1974), 1585{1588, .
23
[14] M. Mares, Computation over fuzzy quantities, CRC Press, Boca Raton, FL, 1994.
24
[15] M. Mizumoto and K. Tanaka, The four operations of arithmetic on fuzzy numbers, Systems
25
Comput. Controls, 7(5) (1976), 73{81.
26
[16] M. Mizumoto and K. Tanaka, Algebraic properties of fuzzy numbers, Proc. Int. Conf. On
27
Cybernetics and Society, Washington, DC, (1976), 559{563.
28
[17] S. Nahmias, Fuzy variables, Fuzzy Sets and System, 1 (1978), 97{110.
29
[18] H. T. Nguyen, A note on the extension principle for fuzzy sets, J. Math. Anal. Appl., 64
30
(1978), 369{380.
31
[19] A. Patel and B. Mohan, Some numerical aspects of center of area defuzzication method,
32
Fuzzy Sets and Systems, 132 (2002), 401{409.
33
[20] S. Roychowdhury and B.-H.Wang, Cooperative neighbors in defuzzication, Fuzzy Sets and
34
Systems,78 (1996), 37{49.
35
[21] S. Roychowdhury and W. Pedrycz, A survey of defuzzication strategies, Internat. J. Intell.
36
Systems, 16 (2001), 679{695.
37
[22] A. Sakly and M. Benrejeb, Activation of trapezoidal fuzzy subsets with dierent inference
38
methods, International Fuzzy Systems Association World Congress, Springer Berlin Heidel-
39
berg, (2003), 450{457.
40
[23] Q. Song and R. Leland, Adaptive learning defuzzication techniques and applications, Fuzzy
41
Sets and Systems, 81 (1996), 321{329.
42
[24] M. Sugeno, Industrial Applications of Fuzzy Control, Elsevier Science Publishers, New York,
43
[25] E. Van Broekhoven and B. De Baets, Fast and accurate centre of gravity defuzzication of
44
fuzzy system outputs dened on trapezoidal fuzzy partitions, Fuzzy Sets and Systems, 157
45
(2006), 904{918.
46
[26] W. Van Leekwijck and E. Kerre, Defuzzication: criteria and classication, Fuzzy Sets and
47
Systems, 108 (1999), 159{178.
48
[27] R. Yager and D. Filev, SLIDE: a simple adaptive defuzzication method, IEEE Trans. Fuzzy
49
Systems, 1 (1993), 69{78.
50
[28] R. C. Young, The algebra of many-valued quantities, Math. Ann., 104 (1931), 260{290.
51
[29] L. A. Zadeh, The concept of a linquistic variable and its application to approximate reasoning,
52
Information Sciences, 1(8) (1975), 199{249.
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
2017-08-30T11:23:20
2018-09-20T11:23:20
67
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
[1] F. Allouani, D. Boukhetala and F. Boudjema, Particle swarm optimization based fuzzy sliding
1
mode controller for the twin rotor mimo system, 16th IEEE Mediterranean Electrotechnical
2
Conference (MELECON), (2012), 1063{1066.
3
[2] P. P. Bonissone, V. Badami, K. Chaing, P. Khedkar, K. Marcelle and M. Schutten, Industrial
4
applications of fuzzy logic at general electric, Proceedings of the IEEE, 83(3) (1995), 450{
5
[3] A. Boubaki, F. Boudjema, C. Boubakir and S. Labiod, A fuzzy sliding mode controller using
6
nonlinear sliding surface applied to the coupled tanks system, International Journal of Fuzzy
7
Systems, 10(2) (2008), 112{118.
8
[4] W. Chang, J. B. Park, Y. H. Joob and G. Chen, Design of robust fuzzy-model- based controller
9
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.
16
[7] P. C. Chen, C. W. Chen and W. L. Chiang, GA-based fuzzy sliding mode controller for
17
nonlinear systems, Mathematical Problems in Engineering, 2008 (2008), 1{16.
18
[8] C. M. Dorling and A. S. I. Zinober, Two approaches to hyperplane design in multivariable
19
variable structure control systems, International Journal of Control, 44(1) (1986), 65{82.
20
[9] P. Durato, C. Abdallah and V. Cerone, Linear quadratic control: An introduction, Prentice
21
Hall, USA, 1995.
22
[10] S. El Beid and S. Doubabi, DSP-Based implementation of fuzzy output tracking control for
23
a boost converter, IEEE Transactions on Industrial Electronics, 61(1) (2014), 196{209.
24
[11] P. Guan, X. J. Liu and J. Z. Liu, Adaptive fuzzy sliding mode control for
25
exible satellite,
26
Engineering Applications of Articial Intelligence, 18(4) (2005), 451{459.
27
[12] S. Hong and R. Langari, Robust fuzzy control of a magnetic bearing system subject to har-
28
monic disturbances, IEEE Transactions on Control Systems Technology, 8 (2) (2000), 366{
29
[13] Z. Hongbing, P. Chengdong, K. Eguchi and G. Jinguang, Euclidean particle swarm opti-
30
mization, Second International Conference on Intelligent Networks and Intelligent Systems,
31
Tianjin (2009), 669{672.
32
[14] Y. J. Huang and H. K. Wei, Sliding mode control design for discrete multivariable systems
33
with time-delayed input signals, International Journal of Systems Science, 33(10) (2002),
34
[15] L. Hung, H. Lin and H. Chung, Design of self-tuning fuzzy sliding mode control for TORA
35
system, Expert Systems with Applications, 32 (1) (2007), 201{212.
36
[16] E. Iglesias, Y. Garcia, M. Sanjuan, O. Camacho and C. Smith, Fuzzy surface-based sliding
37
mode control, ISA Transactions, 43(1) (2007), 73{83.
38
[17] A. Isidoti, Nonlinear Control Systems, Springer, Berlin, 1989.
39
[18] K. Jafar, B. M. Mohammad and K. Mansour, Feedback-linearization and fuzzy controllers
40
for trajectory tracking of wheeled mobile robots, Kybernetes, 39(1) (2010), 83{106.
41
[19] K. Jafar and B. M. Mohammad, From Nonlinear to Fuzzy Approaches in Trajectory Tracking
42
Control of Wheeled Mobile Robots, Asian Journal of Control, 14 (4) ( 2012), 960{973.
43
[20] A. Khosla, S. Kumar and K. R. Ghosh, A comparison of computational eorts between
44
particle swarm optimization and genetic algorithm for identication of fuzzy models, Fuzzy
45
Information Processing Society, (2007), 245{250.
46
[21] R. J. Lian, Adaptive self-organizing fuzzy sliding-mode radial basis-function neural-network
47
controller for robotic systems, IEEE Transactions on Industrial Electronics, 61(3) (2014),
48
1493{1503.
49
[22] C. Liang and J. P. Su, A new approach to the design of a fuzzy sliding mode controller, Fuzzy
50
Sets and Systems, 139(1) (2003), 111{124.
51
[23] Z. Liang, Y. Yang and Y. Zeng, Eliciting compact T-S fuzzy models using subtractive clus-
52
tering and coevolutionary particle swarm optimization, Neuro-computing, 72(10-12) (2009),
53
2569{2575.
54
[24] M. Mohamed, M. Anis, L. Majda, S. N. Ahmed and B. A. Ridha, Fuzzy discontinuous term
55
for a second order asymptotic dsmc: An experimental validation on a chemical reactor, Asian
56
Journal of Control, 13(3) (2010), 369{381.
57
[25] R. M. Nagarale and B. M. Patre, Decoupled neural fuzzy sliding mode control of nonlinear
58
systems, IEEE International Conference on Fuzzy Systems, (2013), 1{8.
59
[26] T. Niknam and B. Amiri, An ecient hybrid approach based on PSO, ACO and k-means for
60
cluster analysis, Applied Soft Computing, 10(1) (2010), 183{197.
61
[27] V. Panchal, K. Harish and K. Jagdeep, Comparative study of particle swarm optimization
62
based unsupervised clustering techniques, International Journal of Computer Science and
63
Network Security, 9(10) (2009), 132{140.
64
[28] K. Saji and K. Sasi, Fuzzy sliding mode control for a PH process, IEEE International Conference
65
on Communication Control and Computing Technologies, (2010), 276{281.
66
[29] A. Shahraz and R. B. Boozarjomehry, A fuzzy sliding mode control approach for nonlinear
67
chemical processes, Control Engineering Practice, 17(5) (2009), 541{550.
68
[30] S. F. Shehu, D. Filev and R. Langari, Fuzzy Control: Synthesis and Analysis, John Wiley
69
and Sons LTD, USA, 1997.
70
[31] L. Shieh, Y. Tsay and R. Yates, Some properties of matrix sign function derived from contin-
71
ued fractions, IEEE Proceedings of Control Theory and Applications, 130 (1983), 111{118.
72
[32] M. Singla, L. S. Shieh, G. Song, L. Xie and Y. Zhang, A new optimal sliding mode controller
73
design using scalar sign function, ISA Transactions, 53(2) (2014), 267{279.
74
[33] M. Soltani and A. Chaari, A PSO-Based fuzzy c-regression model applied to nonlinear data
75
modeling, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems,
76
23(6) (2015), 881{892.
77
[34] M. Sugeno and G. Kang, Fuzzy modeling and control of multilayer incinerator, Fuzzy Sets
78
and Systems, 18 (3) (1986), 329{345.
79
[35] T. Takagi and M. Sugeno, Fuzzy identication of systems and its application to modeling
80
and control, IEEE Transactions on Systems, Man and Cybernetics, 15(1) (1985 ), 116{132.
81
[36] K. Tanaka and M. Sugeno, Stability analysis and design of fuzzy control systems, Fuzzy Sets
82
and Systems, 45(2)(1992), 135{156.
83
[37] V. I. Utkin, Variable structure systems with sliding mode, IEEE Transactions on Automatic
84
Control, 26(2) (1977), 212{222.
85
[38] S. Vishnu Teja, T. N. Shanavas and S. K. Patnaik, Modied PSO based sliding-mode controller
86
parameters for buck converter, Conference on Electrical, Electronics and Computer Science
87
(SCEECS), (2012), 1{4.
88
[39] R. Wai, C. Lin and C. Hsu, Adaptive fuzzy sliding-mode control for electrical servo drive,
89
Fuzzy Sets and Systems, 143(2) (2004), 295{310.
90
[40] H. O. Wang, K. Tanaka and M. F. Grin, An approach to fuzzy control of nonlinear systems:
91
Stability and design issues, IEEE Transactions on Fuzzy Systems, 4(1) (1996), 14{23.
92
[41] H. O. Wang, K. Tanaka and M. F. Grin, Parallel distributed compensation of nonlinear
93
systems by Takagi-Sugeno fuzzy model, Proceedings FUZZY- IEEE/IFES, (1995), 531{538.
94
[42] G. O. Wang, K. Tanaka and T. Ikeda, Fuzzy modeling and control of chaotic systems, IEEE
95
Symposium Circuits and Systems, Atlanta, USA 3 (1996), 209{212.
96
[43] T. Wang, W. Xie and Y. Zhang, Sliding mode fault tolerant control dealing with modeling
97
uncertainties and actuator faults, ISA Transactions, 51(3) (2012), 386{392.
98
[44] J. Wu, M. Singla, C. Olmi, L. Shieh and G. Song, Digital controller design for absolute value
99
function constrained nonlinear systems via scalar sign function approach, ISA Transactions,
100
49(3) (2010), 302{310.
101
[45] Y. Xinghuo, Z. Man and B. Wu, Design of fuzzy sliding-mode control systems, Fuzzy Sets
102
and Systems, 95 (3) (1998), 295{306.
103
[46] F. K. Yeh and C. M. Chen, J. J. Huang, Fuzzy sliding-mode control for a MINI-UAV, IEEE
104
International Symposium on Computational Intelligence in Scheduling, (2010), 3317{3323.
105
[47] K. Young, V. I. Utkin and U. Ozguner, A control engineer's guide to sliding mode control,
106
IEEE Transactions on Control Systems Technology, 7(3) (1999), 328{342.
107
[48] Y. Zhang, D. Huang, M. Ji and F. Xie, Image segmentation using PSO and PCM with
108
mahalanobis distance, Expert Systems with Applications, 38(7) (2011), 9036{9040.
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
2018-09-20T11:23:20
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
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets Syst., 20 (1986), 87{96.
1
[2] K. T. Atanassov, Operators over interval valued intuitionistic fuzzy sets, Fuzzy Sets Syst., 64
2
(1994), 159{174.
3
[3] K. T. Atanassov, Intuitionistic Fuzzy Sets. Theory and Applications, Physica-Verlag, Heidelberg/
4
New York, 1999.
5
[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.
7
[5] K. Bosteels and E. E. Kerre, On a re
8
exivity-preserving family of cardinality-based fuzzy
9
comparison measures, Inform. Sci., 179 (2009), 2342{2352.
10
[6] H. Bustince, J. Fernandez, R. Mesiar, J. Montero and R. Orduna, Overlap functions, Nonlinear
11
Anal.: Theory Methods Appl., 72 (2010), 1488{1499.
12
[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.
14
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.
17
[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-
19
Verlag, New York, Aggregation Operators. Studies in Fuzziness and Soft Computing, 97
20
(2002), 3-104.
21
[10] B. De Baets and R. Mesiar, Triangular norms on product lattices, Fuzzy Sets Syst., 104
22
(1999), 61{76.
23
[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.
25
[12] B. De Baets and H. De Meyer, Transitivity frameworks for reciprocal relations:cycle-
26
transitivity versus FG-transitivity, Fuzzy Sets Syst., 152 (2005), 249{270.
27
[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.
36
[17] B. Jayaram and R. Mesiar, I-Fuzzy equivalence relations and I-fuzzy partitions, Inf. Sci., 179
37
(2009), 1278{1297.
38
[18] D. F. Li, Toposis-based nonlinear-programming methodology for multiattribute decision mak-
39
ing with interval-valued intuitionistic fuzzy sets, IEEE Trans. Fuzzy Syst., 18 (2010), 299{311.
40
[19] X. D. Liu, S. H. Zheng and F. L. Xiong, Entropy and subsethood for general interval-valued
41
intuitionistic fuzzy sets, Lecture Notes Artif. Intell., 3613 (2005), 42{52.
42
[20] N. Madrid, A. Burusco, H. Bustince, J. Fernandez and I. Perlieva, Upper bounding overlaps
43
by groupings, Fuzzy Sets Syst., 264 (2015), 76{99.
44
[21] S. Ovchinnikov, Numerical representation of transitive fuzzy relations, Fuzzy Sets Syst., 126
45
(2002), 225{232.
46
[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.
49
[23] Z. Switalski, General transitivity conditions for fuzzy reciprocal preference matrices, Fuzzy
50
Sets Syst., 137 (2003), 85{100.
51
[24] L. A. Zadeh, Fuzzy sets, Information Contr., 8 (1965), 338 { 353.
52
[25] W. Y. Zeng and P. Guo, Normalized distance, similarity measure, inclusion measure and
53
entropy of interval-valued fuzzy sets and their relationship, Inf. Sci., 178 (2008), 1334{1342.
54
[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.
56
[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
2018-09-20T11:23:20
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
1
Algebra and Computation, 13(4) (2003), 437{461.
2
[2] D. Boixader, J. Jacas and J. Recasens, Upper and lower approximations of fuzzy sets, International
3
Journal of General System, 29(4) (2000), 555{568.
4
[3] C. L. Chang, Fuzzy topological spaces, Journal of Mathematical Analysis and Applications,
5
24(1) (1968), 182{190.
6
[4] X. Chen and Q. Li, Construction of rough approximations in fuzzy setting, Fuzzy sets and
7
Systems, 158(23) (2007), 2641{2653.
8
[5] M. De Cock, C. Cornelis and E. Kerre, Fuzzy rough sets: beyond the obvious, Proceedings of
9
2004 IEEE International Conference on Fuzzy Systems, 1 (2004), 103{108.
10
[6] D. Dubois and H. Prade, Rough fuzzy sets and fuzzy rough sets, International Journal of
11
General System, 17(2-3) (1990), 191{209.
12
[7] J. A. Goguen, L-fuzzy sets, Journal of Mathematical Analysis and Applications, 18(1) (1967),
13
[8] J. Hao and Q. Li, The relationship between L-fuzzy rough set and L-topology, Fuzzy Sets and
14
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.
17
[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
23
Sciences, 178(21) (2008), 4105{4113.
24
[14] R. Lowen, Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis
25
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.
28
[16] N. N. Morsi and M. Yakout, Axiomatics for fuzzy rough sets, Fuzzy sets and Systems, 100(1)
29
(1998), 327{342.
30
[17] Z. Pawlak, Rough sets, International Journal of Computer & Information Sciences, 11(5)
31
(1982), 341{356.
32
[18] K. Qin and Z. Pei, On the topological properties of fuzzy rough sets, Fuzzy Sets and Systems,
33
151(3) (2005), 601{613.
34
[19] A. M. Radzikowska and E. E. Kerre, A comparative study of fuzzy rough sets, Fuzzy Sets and
35
Systems, 126(2) (2002), 137{155.
36
[20] A. M. Radzikowska and E. E. Kerre, Fuzzy rough sets based on residuated lattices, In: Transactions
37
on Rough Sets II, LNCS 3135, (2004), 278{296.
38
[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.
40
[22] Y. H. She and G. J. Wang, An axiomatic approach of fuzzy rough sets based on residuated
41
lattices, Computers & Mathematics with Applications, 58(1) (2009), 189{201.
42
[23] A. Skowron and J. Stepaniuk, Tolerance approximation spaces, Fundamenta Informaticae,
43
27(2-3) (1996), 245{253.
44
[24] H. Thiele, On axiomatic characterization of fuzzy approximation operators II, the rough fuzzy
45
set based case, Proceedings of the 31st IEEE International Symposium on Multiple-Valued
46
Logic, (2001), 330{335.
47
[25] H. Thiele, On axiomatic characterization of fuzzy approximation operators III, the fuzzy dia-
48
mond and fuzzy box based cases, The 10th IEEE International Conference on Fuzzy Systems,
49
2 (2001), 1148{1151.
50
[26] D. Vanderpooten, Similarity relation as a basis for rough approximations, Advances in Machine
51
Intelligence and Soft Computing, 4 (1997), 17{33.
52
[27] C. Y. Wang and B. Q. Hu, Fuzzy rough sets based on generalized residuated lattices, Information
53
Sciences, 248 (2013), 31{49.
54
[28] M.Ward and R. P. Dilworth, Residuated lattices, Transactions of the American Mathematical
55
Society, 45(3) (1939), 335{354.
56
[29] W. Z.Wu, Y. Leung and J. S. Mi, On characterizations of (I;T )-fuzzy rough approximation
57
operators, Fuzzy Sets and Systems, 154(1) (2005), 76{102.
58
[30] W. Z. Wu, J. S. Mi and W. X. Zhang, Generalized fuzzy rough sets, Information Sciences,
59
151 (2003), 263{282.
60
[31] Y. Yao, Constructive and algebraic methods of the theory of rough sets, Information Sciences,
61
109(1) (1998), 21{47.
62
[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
2018-09-20T11:23:20
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
2018-09-20T11:23:20
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.
2
[2] L. P. Belluce, Semisimple algebras of innite valued logic and bold fuzzy set theory, Can. J.
3
Math., 38 (1986), 1356{1379.
4
[3] W. Blok and D. Pigozzi, Algebraizable logics, Merm. Math. Soc., 77 (1989), 1-89.
5
[4] M. Botur and A. Dvurecenskij, State-morphism algebras{general approach, Fuzzy Sets Syst.,
6
218 (2013), 90{102.
7
[5] M. Busaniche, Free nilpotent minimum algebras, Math. Logic Quart., 52 (2006), 219{236.
8
[6] C. C. Chang, Algebraic analysis of many-valued logics, Trans. Amer. Math. Soc., 88 (1958),
9
[7] R. Cignoli and D. Mundici, Stone duality for Dedekind -complete `-groups with order unit,
10
J. Algebra, 302 (2006), 848{861.
11
[8] L. C. Ciungu, Non-commutative Multiple-Valued Logic Algebras, Springer, New York, 2014.
12
[9] L. C. Ciungu, G. Georgescu and C. Muresan, Generalized Bosbach states: part I, Arch. Math.
13
Logic, 52 (2013), 335{376.
14
[10] L. C. Ciungu, G. Georgescu and C. Muresan, Generalized Bosbach states: part II, Arch.
15
Math. Logic, 52 (2013), 707{732.
16
[11] A. Di Nola and A. Dvurecenskij, State-morphism MV-algebras, Ann. Pure Appl. Logic, 161
17
(2009), 161{173.
18
[12] A. Di Nola, A. Dvurecenskij and A. Lettieri, On varieties of MV-algebras with internal states,
19
Inter. J. Approx. Reason., 51 (2010), 680{694.
20
[13] A. Di Nola, A. Dvurecenskij and A. Lettieri, Stone duality type theorems for MV-algebras
21
with internal states, Comm. Algebra, 40 (2012), 327{342.
22
[14] A. Dvurecenskij, J. Rachunek and D. Salounova, State operators on generalizations of fuzzy
23
structures, Fuzzy Sets Syst., 187 (2012), 58{76.
24
[15] C. Elkan, The paradoxical success of fuzzy logic, IEEE Expert, 9 (1994), 3{8.
25
[16] F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous
26
t-norms, Fuzzy Sets Syst., 124 (2001), 271{288.
27
[17] T. Flaminio and F. Montagna, MV-algebras with internal states and probabilistic fuzzy logic,
28
Inter. J. Approx. Reason., 50 (2009), 138{152.
29
[18] J. Fodor, Nilpotent minimum and related connectives for fuzzy logic, in: Proc. of the 4th
30
Inter. Conf. on Fuzzy Syst., March 20-24, Yokohama, (1995), 2077{2082.
31
[19] P. F. He, X. L. Xin and Y.W. Yang, On state residuated lattices, Soft Comput., 19 (2015),
32
2083{2094.
33
[20] A. Iorgulescu, Algebras of Logic as BCK-algebras, Editura ASE, Bucarest, 2008.
34
[21] H. W. Liu and G. J. Wang, Unied forms of fully implication restriction methods for fuzzy
35
reasoning, Inf. Sci., 177(3) (2007), 956{966.
36
[22] L. Liu and K. Li, Involutive monoidal t-norm based logic and R0-logic, Inter. J. Intelligent
37
Syst., 199 (2004), 491{497.
38
[23] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientic, Hong Kong, (1997), 15{68.
39
[24] D. Mundici, Advanced Lukasiewicz Calculus and MV-algebras, Springer, New York, (2011),
40
[25] D. Mundici, Averaging the truth-value in Lukasiewicz sentential logic, Stud. Logica, 55
41
(1995), 113{127.
42
[26] Z. M. Ma and Z. W. Fu, Algebraic study to generalized Bosbach states on residuated lattices,
43
Soft Comput., 19 (2015), 2541{2550.
44
[27] D. W. Pei, On equivalent forms of fuzzy logic systems NM and IMTL, Fuzzy Sets Syst., 138
45
(2003), 187{195.
46
[28] D. W. Pei, R0-implication: characteristics and applications, Fuzzy Sets Syst., 131 (2002),
47
[29] D. W. Pei and G. J. Wang, The completeness and applications of the formal system L, Sci.
48
China F, 45 (2002), 40{50.
49
[30] M. H. Stone, The theory of representation for Boolean algebras, Trans. Amer. Math. Soc.,
50
40 (1936), 37{111.
51
[31] G. J. Wang, A formal deductive system for fuzzy propositional calculus, Chin. Sci. Bull., 42
52
(1997), 1521{1526.
53
[32] G. J. Wang, Fuzzy logic and fuzzy reasoning, In: Proc. of the 7th National Many-Valued and
54
Fuzzy Logic Conf., November 10-13, Xi'an, (1996), 82{96.
55
[33] G. J. Wang, Implication lattices and their fuzzy implication space representation theorem,
56
Acta Math. Sin., (in Chinese), 42 (1999), 133{140.
57
[34] G. J. Wang, L-Fuzzy Topological Spaces, Shaanxi Normal Univ. Press, Xi'an, (in Chinese),
58
(1988), 18{56.
59
[35] G. J. Wang, X. J. Hui and J. S. Song, The R0-type fuzzy logic metric space and an algorithm
60
for solving fuzzy modus ponens, Comput. Math. Appl., 55(9) (2008), 1974{1987.
61
[36] G. J. Wang and H. J. Zhou, Introduction to Mathematical Logic and Resolution Principle,
62
Science Press, Beijing, (2009), 156{298.
63
[37] S. M. Wang, B. S. Wang and X. Y. Wang, A characterization of truth-functions in the
64
nilpotent minimum logic, Fuzzy Sets Syst., 145 (2004), 253{266.
65
[38] D. X. Zhang and Y. M. Liu, L-fuzzy version of Stone's representation theorem for distributive
66
lattices, Fuzzy Sets Syst., 76 (1995), 259{270.
67
[39] H. J. Zhou, Probabilistically Quantitative Logic and its Applications, Science Press, Beijing,
68
(in Chinese), 2015.
69
[40] H. J. Zhou, G. J. Wang and W. Zhou, Consistency degrees of theories and methods of graded
70
reasoning in n-valued R0-logic (NM-logic), Inter. J. Approx. Reason., 43 (2006), 117{132.
71
[41] H. J. Zhou and B. Zhao, Characterizations of maximal consistent theories in the formal
72
deductive system L (NM-logic) and Cantor space, Fuzzy Set Syst., 158 (2007), 2591{2604.
73
[42] H. J. Zhou and B. Zhao, Generalized Bosbach and Riecan states based on relative negations
74
in residuated lattices, Fuzzy Sets Syst., 187 (2012) 33-57.
75
[43] H. J. Zhou and B. Zhao, Stone-like representation theorems and three-valued lters in R0-
76
algebras (nilpotent minimum algebras), Fuzzy Sets Syst., 162 (2011), 1{26.
77
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
2018-09-20T11:23:20
163
168
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
[1] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87{96.
1
[2] W. D. Blizard, Multiset theory, Notre Dame J. Formal Logic, 30(1) (1988), 36{66.
2
[3] S. A. El-Sheikh, R. A. K. Omar and M. Raafat,
3
-operation in m-topological space, Gen.
4
Math. Notes, 7(1) (2015), 40{54.
5
[4] S. A. El-Sheikh, R. A. K. Omar and M. Raafat, Separation axioms on multiset topological
6
space, Journal of New Theory, 7 (2015), 11{21.
7
[5] K. P. Girish and J. S. Jacob, On multiset topologies, Theory and Applications of Mathematics
8
and Computer Science, 2(1) (2012), 37{52.
9
[6] K. P. Girish and S. J. John, Transactions on rough sets XIV, Springer Berlin Heidelberg,
10
Berlin, Heidelberg, (2011), Ch. Rough Multiset and Its Multiset Topology, 62{80.
11
[7] K. P. Girish and S. J. John, Multiset topologies induced by multiset relations, Information
12
Sciences, 188 (2012), 298{313.
13
[8] A. Kandil, O. Tantawy, S. El-Sheikh and A. Zakaria, Multiset proximity spaces, Journal of
14
Egyptian Mathematical Society, 24(4) (2016), 562-567.
15
[9] P. M. Mahalakshmi and P. Thangavelu, m-connectedness in m-topology, International Journal
16
of Pure and Applied Mathematics, 106(8) (2016), 21-25.
17
[10] J. Mahanta and D. Das, Boundary and exterior of a multiset topology, ArXiv e-prints,
18
arXiv:1501.07193.
19
[11] D. Molodtsov, Soft set theory-rst results, Computers and Mathematics with Applications,
20
37 (45) (1999), 19{31.
21
[12] F. G. Shi and B. Pang, Redundancy of fuzzy soft topological spaces, Journal of Intelligent and
22
Fuzzy Systems, 27 (4) (2014), 1757{1760.
23
[13] F. G. Shi and B. Pang, A note on soft topological spaces, Iranian Journal of Fuzzy Systems,
24
12 (5) (2015), 149{155.
25
[14] R. R. Yager, On the theory of bags, International Journal of General Systems, 13 (1986),
26
[15] L. A. Zadeh, Fuzzy sets, Inform. Control, 8 (1965), 338{353.
27
ORIGINAL_ARTICLE
Persian-translation vol. 14, no. 4, August 2017
http://ijfs.usb.ac.ir/article_3333_1a06dcc38f465140c0747a83fca3fe11.pdf
2017-08-01T11:23:20
2018-09-20T11:23:20
171
179
10.22111/ijfs.2017.3333