ORIGINAL_ARTICLE
Cover Vol.14, No.2 April 2017
http://ijfs.usb.ac.ir/article_3139_c3a2df4da9e30ac79bd3234e691206a2.pdf
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10.22111/ijfs.2017.3139
ORIGINAL_ARTICLE
SOME RESULTS OF MOMENTS OF UNCERTAIN RANDOM VARIABLES
Chance theory is a mathematical methodology for dealing with indeterminatephenomena including uncertainty and randomness.Consequently, uncertain random variable is developed to describe the phenomena which involveuncertainty and randomness.Thus, uncertain random variable is a fundamental concept in chance theory.This paper provides some practical quantities to describe uncertain random variable.The typical one is the expected value, which is the uncertain version of thecenter of gravity of a physical body.Mathematically, expectations are integrals with respect to chance distributionsor chance measures.In fact, expected values measure the center of gravity of a distribution; they aremeasures of location. In order to describe a distribution in brief terms thereexist additional measures, such as the variance which measures the dispersionor spread, and moments.For calculating the moments of uncertain random variable, some formulas are provided through chance distribution and inverse chance distribution. The main results are explained by using several examples.
http://ijfs.usb.ac.ir/article_3131_182175d48ed3270d60a18b815e0a7196.pdf
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10.22111/ijfs.2017.3131
Chance theory
Uncertain random variable
Chance distribution
Moments
Hamed
Ahmadzade
ahmadzadeh.h.63@gmail.com
true
1
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
Department of Statistics, University of Sistan and Baluchestan,
Zahedan, Iran
AUTHOR
Yuhong
Sheng
shengyuhong@sina.com
true
2
College of Mathematical and System Sciences, Xinjiang University,
Urumqi 830046, China
College of Mathematical and System Sciences, Xinjiang University,
Urumqi 830046, China
College of Mathematical and System Sciences, Xinjiang University,
Urumqi 830046, China
LEAD_AUTHOR
Fatemeh
Hassantabar Darzi
true
3
Department of Statistics, University of Sistan and
Baluchestan, Zahedan, Iran
Department of Statistics, University of Sistan and
Baluchestan, Zahedan, Iran
Department of Statistics, University of Sistan and
Baluchestan, Zahedan, Iran
AUTHOR
[1] X. Chen and W. Dai, Maximum entropy principlefor uncertain variables, International Jour-
1
nal of Fuzzy Systems, 13(3) (2011), 232{236.
2
[2] X. Chen, S. Kar and D. Ralescu, Cross-entropy measure of uncertain variables, Information
3
Sciences, 201 (2012), 53{60.
4
[3] X. Chen and D. Ralescu, Liu process and uncertain calculus, Journal of Uncertainty Analysis
5
and Applications, 1(3) (2013), 1{ 12.
6
[4] W. Dai and X. Chen, Entropy of function of uncertain variables, Mathematics and Computer
7
Modelling, 55 (2012), 754{760.
8
[5] H. Y. Guo and X. S. Wang, Variance of uncertain random variables, Journal of Uncertainty
9
Analysis and Applications, 2(6) (2014), 1{7.
10
[6] Y. C. Hou, Subadditivity of chance measur, Journal of Uncertainty Analysis and Applications,
11
2(14) (2014), 1{8.
12
[7] A. N. Kolmogorov, Grundbegrie der Wahrscheinlichkeitsrechnung, Julius Springer, Berlin,
13
[8] R. Kruse and K. Meyer, Statistics with Vague Data, Reidel Publishing Company, Dordrecht,
14
[9] B. Liu, Uncertainty Theory, 5th ed., http://orsc.edu.cn/liu/ut.pdf. 2014.
15
[10] B. Liu, Uncertainty Theory, 2nd ed., Springer-Verlag, Berlin, 2007.
16
[11] B. Liu, Some research problems in uncertainty theory, Journal of Uncertain Systems, 31
17
(2009), 3{10.
18
[12] B. Liu, Uncertainty Theory: A Branch of Mathematics for Modeling Human Uncertainty,
19
Springer-Verlag, Berlin, 2010.
20
[13] B. Liu, Toward uncertain nance theory, Journal of Uncertainty Analysis and Applications,
21
1(1) (2013), 1{15.
22
[14] Y. H. Liu, Uncertain random variables: A mixture of uncertainty and randomness, Soft
23
Computing, 17(4) (2013), 625{634.
24
[15] Y. H. Liu, Uncertain random programming with applications, Fuzzy Optimization and Deci-
25
sion Making, 12(2) (2013), 153{169.
26
[16] Y. H. Liu and M. H. Ha, Expected value of function of uncertain variables, Journal of Un-
27
certain Systems, 4(3) (2010), 181{186.
28
[17] Y. K. Liu and B. Liu, Fuzzy random variables: a scalar expected value operator, Fuzzy
29
Optimization and Decision Making, 2(2) (2003), 143{160.
30
[18] Y. K. Liu and B. Liu, Fuzzy random programming with equilibrium chance constraints, In-
31
formtion Sciences 170 (2005), 363{395.
32
[19] Z. X. Peng and K. Iwamura, A sucient and necessary condition of uncertainty distribution,
33
Journal of Interdisciplinary Mathematics, 13(3) (2010), 277{285.
34
[20] M. Puri and D. Ralescu, Fuzzy random variables, Journal of Mathmatical Application, 114
35
(1986), 409{422.
36
[21] Y. H. Sheng and S. Kar, Some results of moments of uncertain variable through inverse
37
uncertainty distribution, Fuzzy Optimization and Decision Making, 14 (2015), 57{76.
38
[22] Y. H. Sheng and K. Yao, Some formulas of variance of uncertain random variable, Journal
39
of Uncertainty Analysis and Applications, 2(12) (2014), 1{10.
40
[23] J. L. Teugels and B. Sundt, Encyclopedia of actuarial science, Wiley & Sons, 1 (2004).
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[24] M. Wen and R. Kang, Reliability analysis in uncertain random system, Fuzzy Optimization
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and Decision Making, doi:10.1007/s10700-016-9235-y, (2016).
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[25] K. Yao, A formula to calculate the variance of uncertain variable, Soft Computing, 19(10)
44
(2015), 2947{2953.
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ORIGINAL_ARTICLE
A JOINT DUTY CYCLE SCHEDULING AND ENERGY AWARE ROUTING APPROACH BASED ON EVOLUTIONARY GAME FOR WIRELESS SENSOR NETWORKS
Network throughput and energy conservation are two conflicting important performance metrics for wireless sensor networks. Since these two objectives are in conflict with each other, it is difficult to achieve them simultaneously. In this paper, a joint duty cycle scheduling and energy aware routing approach is proposed based on evolutionary game theory which is called DREG. Making a trade-off between energy conservation and network throughput, the proposed approach prolongs the network lifetime. The paper is divided into the following sections: Initially, the discussion is presented on how the sensor nodes can be scheduled to sleep or wake up in order to reduce energy consumption in idle listening. The sensor wakeup/sleep scheduling problem with multiple objectives is formulated as an evolutionary game theory. Then, the evolutionary game theory is applied to find an optimal wakeup/sleep scheduling policy, based on a trade-off between network throughput and energy efficiency for each sensor. The evolutionary equilibrium is proposed as a solution for this game. In addition, a routing approach is adopted to propose an energy aware fuzzy logic in order to prolong the network lifetime. The results show that the proposed routing approach balances energy consumption among the sensor nodes in the network, avoiding rapid energy depletion of sensors that have less energy. The proposed simulation study shows the more efficient performance of the proposed system than other methods in term of network lifetime and throughput.
http://ijfs.usb.ac.ir/article_3132_5ac5352b2337405f917464e60dddab55.pdf
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10.22111/ijfs.2017.3132
Wireless sensor network
Duty cycle scheduling
Energy aware routing
Evolutionary game theory
Distributed reinforcement learning
M. S.
Kordafshari
true
1
Department of Computer Engineering, Science and Research
Branch, Islamic Azad University, Tehran, Iran
Department of Computer Engineering, Science and Research
Branch, Islamic Azad University, Tehran, Iran
Department of Computer Engineering, Science and Research
Branch, Islamic Azad University, Tehran, Iran
AUTHOR
A.
Movaghar
true
2
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
Department of Computer Engineering, Sharif University of Technology, Tehran, Iran
LEAD_AUTHOR
M. R.
Meybodi
true
3
Computer Engineering and Information Technology Department,
Amirkabir University of Technology, Tehran, Iran
Computer Engineering and Information Technology Department,
Amirkabir University of Technology, Tehran, Iran
Computer Engineering and Information Technology Department,
Amirkabir University of Technology, Tehran, Iran
AUTHOR
[1] A. Abrardo, L. Balucanti and A. Mecocci, A game theory distributed approach for energy
1
optimization in WSNs, ACM Trans SensNetw, 9(4) (2013), 44.
2
[2] I. F. Akyildiz and W. Su, Y. Sankarasubramaniam and E. Cayirci, Wireless sensor networks:
3
a survey, Elsevier Computer Networks, 38 (2002b), 393-422.
4
[3] T. AlSkaif, M. G. Zapata and B. Bellalta, Game theory for energy eciency in Wireless
5
Sensor Networks: Latest trends, Journal of Network and Computer Applications, 54 (2015),
6
[4] S. Arafat, A. AziziMohd, N. CheeKyun, N. Nor Kamariah, S. Aduwati and Y. MohdHanif,
7
Review of energy conservation using duty cycling schemes for IEEE 802.15.4 wireless sensor
8
networks, Wireless Personal Communications, Springer, 77 (2014), 589-604.
9
[5] T. Arampatzis, J. Lygeros and S. Manesis, A survey of applications of wireless sensors
10
and wireless sensor networks, In 13th Mediterrean Conference on Control and Automation.
11
Limassol, Cyprus, (2005), 719-724.
12
[6] M. Ayers and L. Yao, Gureen Game, An energy-ecient QoS control scheme for wireless
13
sensor networks In Proceedings of 2011 International Green Computing Conference, Orlando,
14
FL, USA, (2011), 25-28.
15
[7] A. Behzadan and A. Anpalagan, Prolonging network life time via nodal energy balancing in
16
heterogeneous wireless sensor networks, In: 2011 IEEE international conference on commu-
17
nications, Kyoto, Japan (2011), 1-5.
18
[8] M. Buettner, G. V. Yee, E. Anderson and R. Han, X-MAC: a short preamble MAC protocol
19
for duty-cycled wireless sensor networks, In Proc. of the 4th International Conference on
20
Embedded Networked Sensor Systems , (2006), 307-320.
21
[9] S. S. Chiang and C. H. Huang, A minimum hop routing protocol for home security systems
22
using wireless sensor networks, IEEE Transactions on Consumer Electronics, 53(4) (2007).
23
[10] A. M. Colman, Cooperation, psychological game theory, and limitations of rationality in
24
social interaction, Behavioral and Brain Sciences, 26 (2003), 139-198.
25
[11] J. C. Dagher, M. W. Marcellin and M. A. Neifeld, A theory for maximizing the lifetime of
26
sensor networks, IEEE Transaction on Communications, 55(2) (2007), 323-332.
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[12] D. Fudenberg and D. K. Levine, The theory of learning in games. cambridge, MIT Press,
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Cambridge, MA, 1998.
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[13] T. He, J. A. Stankovic, C. Lu and T. Abdelzaher, SPEED: A stateless protocol for real-
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time communication in sensor networks, Proceedings of IEEE International Conference on
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Distributed Computing Systems, (2005), 46-55.
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[14] M. Javidi and L. Aliahmadipour, Application of game theory approaches in routing protocols
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for wireless networks, In proceedings of 2011 International Conference on Numerical Analysis
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and Applied Mathematics, Halkidiki, Greece, (2011), 19-25.
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[15] Z. Jia, M. Chundi and H. Jianbin, Game theoretic energy balance routing in wireless sensor
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networks, In Chinese control conference, (2007), 420-424.
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[16] R. Kannan and S. S. Iyengar, Game-theoretic models for reliable path-length and energy-
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constrained routing with data aggregation in wireless sensor networks, IEEE JSAC,
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22(6)(2004), 1141-1150.
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[17] K. Lin, T. Xu, M. M. Hassan and A. Alamri An energy-eciency node scheduling game based
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on task prediction in WSNs , Mobile NetwAppl, Springer Science and Business Media New
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York, 20 (2015), 583-592.
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[18] G. Lu, B. Krishnamachari and C. S. Raghavendra, An adaptive energy-ecient and low-
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latency MAC for tree-based data gathering in sensor networks, Wirel. Commun. Mob. Com-
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put, Published online in Wiley Inter Science., 7 (2007), 863-875.
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[19] R. Machado and S. Tekinay, A survey of game theoretic approaches in wireless senso rnet-
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works, ComputNetw, 52(16) (2008), 3047-3061.
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[20] D. Niyato and E. Hossain, wireless sensor networks with energy harvesting technologies: a
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game-theoretic approach to optimal energy management, IEEE Wireless Communications,
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[21] D. Niyato and E. Hossain, Dynamics of network selection in heterogeneous wireless networks:
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an evolutionary game approach, IEEE Transactions on vehicular technology, 58(4) (2009).
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[22] N. A. Pantazis, S. A. Nikolidakis and D. D. Vergados, Energy-ecient routing protocols
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in wireless sensor networks: a survey, IEEE Communications Surveys & Tutorials, 15(2)
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[23] J. Polastre, J. Hill, and D. Culler, Versatile low power media access for wireless sensor
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networks, In The Second ACM Conference on Embedded Networked Sensor Systems, (2004),
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[24] O. Powell and A. Jarry, Gradient based routing in wireless sensor networks: a mixed strategy,
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CoRR Distributed, Parallel and Cluster Computing, 2005.
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[25] R. Rajagopalan and P. K. Varshney, Data aggregation techniques in sensor networks: A
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survey, IEEE Commun. Surv. Tutor., 8 (2006).
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[26] T. Rault, A. Bouabdallah and Y. Challal, Energy-eciency in wireless sensor networks: a
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top-down review approach, ComputNetw, 67 (2014), 104-122.
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[27] H. Ren and M. Meng, Game-theoretic modeling of joint topology control and power scheduling
63
for wireless heterogeneous sensor networks, IEEE Trans. Autom. Sci. Eng., 6 (2009), 610-625.
64
[28] A. Schillings and K. Yang, VGTR A collaborative, energy and information aware routing
65
algorithm for wireless sensor networks through the use of game theory, In Proceedings of 3rd
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International Geosensor Networks Conference, Oxford, UK, (2009), 13-14.
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[29] H. Shpungin and Z. Li Throughput and energy eciency in wireless AdHoc networks with
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gaussian channels, IEEE Communications Society, (2010), 289-298.
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[30] J. M. Smith, Evolution and the Theory of Games: In situations characterized byconict of
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interest, the best strategy to adopt depends on what others are doing, American Scientist,
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[31] R. S. Sutton and A. G. Barto, Reinforcement learning: an introduction (adaptive computation
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and machine learning), MIT Press, Cambridge, MA, 1998.
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[32] D. Tudose, L. Gheorghe and N. T. Apus, Radio transceiver consumption modeling for multi-
74
hop wireless sensor networks, UPB Scientic Bulletin, Series C, 75(1) (2013), 17-26.
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[33] Y. Wu, Zh. Mao and S. Fahmy, Constructing maximum-lifetime data-gathering forests in
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sensor networks, IEEE/ACM Transactions on Networking, 18(5) (2010).
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[34] G. Yang and G. Zhang, A power control algorithm based on non-cooperative game for wireless
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sensor networks, In Proceedings of 2011 International Conference on Electronic & Mechanical
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[35] KLA. Yau, P. Komisarczuk and P. D. Teal, Reinforcement learning for context awareness
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and intelligence in wireless networks: review, new features and open issues, J Netw Comput
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Appl., 35(1) (2012), 253-267.
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sleeping for wireless sensor networks, ACM Transactions on Networking, 12(3) (2004).
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[37] L. Zhao, L. Guo, L. Cong and H. Zhang, An energy-ecient MAC protocol for WSNs: game-
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theoretic constraint optimization with multiple objectives, WirelSensNetw, (2009), 358-364.
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[38] M. Zheng, Game theory used for reliable routing modeling in wireless sensor networks, In
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International Conference on Parallel and Distributed Computing, Applications and Technolo-
89
gies, China, (2010), 280-284.
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ORIGINAL_ARTICLE
MULTI-OBJECTIVE ROUTING AND SCHEDULING IN FLEXIBLE MANUFACTURING SYSTEMS UNDER UNCERTAINTY
The efficiency of transportation system management plays an important role in the planning and operation efficiency of flexible manufacturing systems. Automated Guided Vehicles (AGV) are part of diversified and advanced techniques in the field of material transportation which have many applications today and act as an intermediary between operating and storage equipment and are routed and controlled by an intelligent computer system. In this study, a two-objective mathematical programming model is presented to integrate flow shop scheduling and routing AVGs in a flexible manufacturing system. In real-life problems parameters like demand, due dates and processing times are always uncertain. Therefore, in order to solve a realistic problem, foregoing parameters are considered as fuzzy in our proposed model. Subsequently, to solve fuzzy mathematical programming model, one of the most effective technique in the literature is used. To solve the problem studied, two meta-heuristic algorithms of Non-dominated Sorting Genetic Algorithm-II (NSGAII) and multi-objective particle swarm optimization (MOPSO) are offered that the accuracy of mathematical models and efficiency of algorithms provided are assessed through numerical examples.
http://ijfs.usb.ac.ir/article_3133_2e5c34907c1ac6e7aaf5d6e41d80dabd.pdf
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10.22111/ijfs.2017.3133
Scheduling
Routing
Automated guided vehicle
Meta-heuristic algorithm
Flexible manufacturing
Ahmad
Mehrabian
ahmad.mehrabian@outlook.com
true
1
Department of Industrial Engineering, South-Tehran Branch,
Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, South-Tehran Branch,
Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, South-Tehran Branch,
Islamic Azad University, Tehran, Iran
AUTHOR
Reza
Tavakkoli-Moghaddam
tavakoli@ut.ac.ir
true
2
Department of Industrial Engineering, South-Tehran
Branch, Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, South-Tehran
Branch, Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, South-Tehran
Branch, Islamic Azad University, Tehran, Iran
LEAD_AUTHOR
Kaveh
Khalili-Damaghani
true
3
Department of Industrial Engineering, South-Tehran Branch,
Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, South-Tehran Branch,
Islamic Azad University, Tehran, Iran
Department of Industrial Engineering, South-Tehran Branch,
Islamic Azad University, Tehran, Iran
AUTHOR
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trips in the design of a unidirectional loop
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ow path, Computers & Operations Research,
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35(5) (2008), 1546-1561.
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[2] W. X. Bing, The application of analytic process of resource in an AGV scheduling, Computers
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& industrial engineering, 35(1) (1998), 169-172.
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exible manufacturing systems, Mathematical and computer modelling, 20(2) (1994), 19-31.
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[4] I. A. Chaudhry, S. Mahmood and M. Shami, Simultaneous scheduling of machines and au-
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tomated guided vehicles in
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exible manufacturing systems using genetic algorithms, Journal
11
of Central South University of Technology, 18(5) (2011), 1473-1486.
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[5] C. A. C. Coello, G. T. Pulido and M. S. Lechuga, Handling multiple objectives with particle
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swarm optimization, Evolutionary Computation, IEEE Transactions on, 8(3) (2004), 256-
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[6] A. I. Correa, A. Langevin and L. M. Rousseau, Scheduling and routing of automated guided
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vehicles: A hybrid approach, Computers & operations research, 34(6) (2007), 1688-1707.
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[7] K. Deb, Multi-objective optimization using evolutionary algorithms, John Wiley & Sons, 16
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[8] M. Desrochers, J. Desrosiers and M. Solomon, A new optimization algorithm for the vehicle
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routing problem with time windows, Operations research, 40(2) (1992), 342-354.
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[9] G. Desaulniers, A. Langevin, D. Riopel and B. Villeneuve, Dispatching and con
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routing of automated guided vehicles: An exact approach, International Journal of Flexible
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Manufacturing Systems, 15(4) (2003), 309-331.
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[10] M. E. Dogan and I. E. Grossmann, A decomposition method for the simultaneous planning
23
and scheduling of single-stage continuous multiproduct plants, Industrial & engineering chemistry
24
research, 45(1) (2006), 299-315.
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[11] I. G. Drobouchevitch and V. A.Strusevich, Heuristics for the two-stage job shop scheduling
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problem with a bottleneck machine, European journal of operational research,123(2) (2000),
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[12] G. El Khayat, A. Langevin and D. Riopel, Integrated production and material handling
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scheduling using mathematical programming and constraint programming, European Journal
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of Operational Research, 175(3) (2006), 1818-1832.
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[13] H. Fazlollahtabar, B. Rezaie, and H. Kalantari, Mathematical programming approach to op-
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timize material
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ow in an AGV-based
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exible jobshop manufacturing system with perfor-
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mance analysis, The International Journal of Advanced Manufacturing Technology, 51(9-12)
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(2010), 1149-1158.
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[14] H. Fazlollahtabar and M. Saidi-Mehrabad, Methodologies to optimize automated guided ve-
37
hicle scheduling and routing problems: a review study, Journal of Intelligent & Robotic
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Systems,77(3-4) (2013), 525-545.
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[15] H. Fazlollahtabar, M. Saidi-Mehrabad and J. Balakrishnan, Mathematical optimization for
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earliness/tardiness minimization in a multiple automated guided vehicle manufacturing sys-
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tem via integrated heuristic algorithms, Robotics and Autonomous Systems, 2015.
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[16] M. L. Fisher, K. O. ornsten and O. B. Madsen, Vehicle routing with time windows: Two
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optimization algorithms, Operations Research, 45(3) (1997), 488-492.
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and practical insights, Operations Research, 47(5) (1999), 675-692.
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and Optimization: Multiobjective Genetic Algorithm Approach, (2008), 297-417.
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tion planning by using logic cut algorithm, Memoirs of the Faculty of Engineering, Okayama
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University, 41(1) (2007), 31-43.
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algorithm for simultaneously determining
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ow path and the location of P/D stations in bidi-
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rectional path, Journal of Manufacturing Systems, 32(4) (2013), 648-654.
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terminals, Springer Berlin Heidelberg, (2005), 207-230.
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[24] C. F. Hsueh, A simulation study of a bi-directional load-exchangeable automated guided ve-
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hicle system, Computers & Industrial Engineering, 58(4) (2010), 594-601.
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[27] J. Jerald, P. Asokan, R. Saravanan and A. D. C. Rani, Simultaneous scheduling of parts and
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177 (2007), 1599-1609.
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vehicle routing problem with time windows, Transportation Science, 33(1) (1999), 101-116.
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evenements discrets, Congres ROADEF, (2000), 128-129.
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mated guided vehicles in a
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exible manufacturing system, International Journal of Flexible
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[32] T. E. Liang, Application of interactive possibilistic linear programming to aggregate pro-
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duction planning with multiple imprecise objectives, Production Planning & Control, 18(7)
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(2007), 548-560.
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bilistic, and mixed fuzzy/possibilistic optimization, Fuzzy Sets and Systems, 158(17) (2007),
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1861-1872.
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[34] F. Mahmoodi, C. T. Mosier and J. R. Morgan, The eects of scheduling rules and rout-
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exibility on the performance of a random
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exible manufacturing system, International
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exible manufacturing systems, 11(3) (1999), 271-289.
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(ESE)., 2002.
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in a multi-plant, Computers & Industrial Engineering,48(2) (2005), 311-325.
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ORIGINAL_ARTICLE
TAUBERIAN THEOREMS FOR THE EULER-NORLUND MEAN-CONVERGENT SEQUENCES OF FUZZY NUMBERS
Fuzzy set theory has entered into a large variety of disciplines of sciences,technology and humanities having established itself as an extremely versatileinterdisciplinary research area. Accordingly different notions of fuzzystructure have been developed such as fuzzy normed linear space, fuzzytopological vector space, fuzzy sequence space etc. While reviewing theliterature in fuzzy sequence space, we have seen that the notion of Tauberiantheorems for the Euler-N\"{o}rlund mean-convergent sequences of fuzzy numbershas not been developed. In the present paper, we introduce some new conceptsabout statistical convergence of sequences of fuzzy numbers. The main purposeof this paper is to study Tauberian theorems for the Euler-N\"{o}rlundmean-convergent sequences of fuzzy numbers and investigate some other kind ofconvergences named Euler-N\"{o}rlund mean-level convergence so as to fill upthe existing gaps in the literature. The results which we obtained in thisstudy are much more general than those obtained by others.
http://ijfs.usb.ac.ir/article_3134_893168af5ed1d98fec0e8f295f68f1ce.pdf
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2018-05-25T11:23:20
79
92
10.22111/ijfs.2017.3134
Statistical convergence
Tauberian theorems
Fuzzy numbers
Naim L.
Braha
true
1
Department of Mathematics and Computer Sciences, University of
Prishtina, Avenue Mother Teresa, No-4, Prishtine, 10000, Kosova
Department of Mathematics and Computer Sciences, University of
Prishtina, Avenue Mother Teresa, No-4, Prishtine, 10000, Kosova
Department of Mathematics and Computer Sciences, University of
Prishtina, Avenue Mother Teresa, No-4, Prishtine, 10000, Kosova
LEAD_AUTHOR
Mikail
Et
mikailet68@gmail.com;mikailet@yahoo.com
true
2
Department of Mathematics, Frat University, Elazig, 23119, Turkey
Department of Mathematics, Frat University, Elazig, 23119, Turkey
Department of Mathematics, Frat University, Elazig, 23119, Turkey
AUTHOR
[1] Y. Altin, M. Mursaleen and H. Altinok, Statistical summability (C; 1) for sequences of fuzzy
1
real numbers and a Tauberian theorem, Journal of Intelligent and Fuzzy Systems, 21 (2010),
2
[2] S. Aytar, M. A. Mammadov and S. Pehlivan, Statistical limit inferior and limit superior for
3
sequences of fuzzy numbers, Fuzzy Sets and Systems, 157(7) (2006), 976{985.
4
[3] B. Bede and S. G. Gal, Almost periodic fuzzy number valued functions, Fuzzy Sets and
5
Systems, 147 (2004), 385{403.
6
[4] N. L. Braha, Tauberian conditions under which statistical convergence follows from statistical
7
summability (V; ), Miskolc Math. Notes, 16(2) (2015), 695{703.
8
[5] M. Et, H. Altinok and R. Colak, On -statistical convergence of dierence sequences of fuzzy
9
numbers, Inform. Sci., 176(15) (2006), 2268{2278.
10
[6] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241{244.
11
[7] J. X. Fang and H. Huang, On the level convergence of a sequence of fuzzy numbers, Fuzzy
12
Sets and Systems, 147(3) (2004), 417{435.
13
[8] A. Gokhan, M. Et and M. Mursaleen, Almost lacunary statistical and strongly almost lacunary
14
convergence of sequences of fuzzy numbers, Math. Comput. Modelling, 49(3-4) (2009),
15
[9] J. S. Kwon, On statistical and p-Cesaro convergence of fuzzy numbers, The Korean Journal
16
of Computational and Applied Mathematics, 7 (2000), 195{203.
17
[10] L. Leindler, Uber die de la Vallee-Pousinsche summierbarkeit allgemeiner orthogonalreihen,
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Acta Math. Acad. Sci. Hungar., 16 (1965), 375{387.
19
[11] M. Matloka, Sequence of fuzzy numbers, BUSEFAL, 28 (1986), 28{37.
20
[12] F. Moricz, Tauberian conditions under which statistical convergence follows from statistical
21
summability (C, 1), J. Math. Anal. Appl., 275 (2002), 277{287.
22
[13] S. Nanda, On sequence of fuzzy numbers, Fuzzy Sets and Systems, 33 (1989), 123{126.
23
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Amer. Math. Monthly, 66 (1959), 361{375.
25
92 N. L. Braha and M. Et
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[15] H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2
27
(1951), 73{74.
28
[16] C. Wu and G. Wang, Convergence of sequences of fuzzy numbers and xed point theorems for
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increasing fuzzy mappings and application, Theme: Fuzzy intervals. Fuzzy Sets and Systems,
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130(3) (2002), 383{390.
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[18] A. Zygmund, Trigonometric Series, Cambridge University Press, Cambridge, London and
33
New York, 1979.
34
ORIGINAL_ARTICLE
ON THE SYSTEM OF LEVEL-ELEMENTS INDUCED BY AN L-SUBSET
This paper focuses on the relationship between an $L$-subset and the system of level-elements induced by it, where the underlying lattice $L$ is a complete residuated lattice and the domain set of $L$-subset is an $L$-partially ordered set $(X,P)$. Firstly, we obtain the sufficient and necessary condition that an $L$-subset is represented by its system of level-elements. Then, a new representation theorem of intersection-preserving $L$-subsets is shown by using union-preserving system of elements. At last, another representation theorem of compatible intersection-preserving $L$-subsets is obtained by means of compatible union-preserving system of elements.
http://ijfs.usb.ac.ir/article_3135_8463d3b272c307c070fd6fde0df0c457.pdf
2017-04-29T11:23:20
2018-05-25T11:23:20
93
105
10.22111/ijfs.2017.3135
Complete residuated lattice
$L$-partially ordered set
$L$-subset
System of level-elements
Union-preserving system of elements
Compatible union-preserving system of elements
Representation theorem
Jinming
Fang
jining-fang@163.com
true
1
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
AUTHOR
Youyan
Li
true
2
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
LEAD_AUTHOR
Wenyi
Chen
ouccwy@126.com
true
3
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
Department of Mathematics, Ocean University of China, Qing Dao
266071, PR China
AUTHOR
[1] R. Belohlavek, Fuzzy relational systems: foundation and principles, New York: Kluwer Aca-
1
demic Plenum Publishers, (2002), 75{176.
2
[2] J. M. Fang and Y. L. Han, A new representation theorem of L-sets, Perodical of Ocean
3
University of China(Natural Science), 38(6) (2008), 1025{1028.
4
[3] J. M. Fang, Relationships between L-ordered convergence structures and strong L-topologies,
5
Fuzzy Sets and Systems, 161 (2010), 2923{2944.
6
[4] J. M. Fang, Stratied L-ordered convergence structures, Fuzzy Sets and Systems, 161 (2010),
7
[5] J. A. Goguen, L-fuzzy sets, J. Math. Appl., 18 (1967), 145{174.
8
[6] H. Han and J. M. Fang, Representation theorems of L-subsets and L-families on complete
9
residuated lattice, Iranian Journal of Fuzzy Systems, 10(3) (2013), 125{136.
10
[7] H. Lai and D. Zhang, Fuzzy preorder and fuzzy topology, Fuzzy Sets and Systems, 157 (2006),
11
1865{1885.
12
[8] C. Z. Luo, Fuzzy sets and nested systems, Journal of Fuzzy Mathematics, 3(4) (1983), 113{
13
[9] L. X. Meng and X. Z. Wang, An improved representation theorem of L-fuzzy set, Fuzzy Sets
14
and Systems, 161 (2010), 3134{3147.
15
[10] F. G. Shi, Theory of L-nested sets and L-nested sets and applications, Fuzzy Systems
16
and Mathematics, 9(4) (1995), 65{72.
17
[11] B. Seselja and A. Tepavcevic, A note on a natural equivalence relation on fuzzy power set,
18
Fuzzy Sets and Systems, 148(2) (2004), 201{210.
19
[12] B. Seselja and A. Tepavcevic, Representing ordered structures by fuzzy sets: an overview,
20
Fuzzy Sets and Systems, 136(1) (2003), 21{39.
21
[13] B. Seselja and A. Tepavcevc, Completion of ordered structures by cuts of fuzzy sets: an
22
overview, Fuzzy Sets and Systems, 136(1) (2003), 1{19.
23
[14] F. L. Xiong, The representation theorems on complete lattice and their application, Perodical
24
of Ocean University of Qingdao, 28(2) (1998), 339{344.
25
[15] W. Yao, Quantitative domain via fuzzy sets: part I: continuity of fuzzy completed directed
26
posets, Fuzzy Sets and Systems, 161 (2010), 973{987.
27
[16] W. Y. Zeng and Y. Shi, A kind of approach to new representation theorem, Journal of Beijing
28
Normal University (Natural Science), 39(1) (2003), 34{39.
29
[17] D. Zhang, An enriched category approach to many valued topology, Fuzzy Sets and Systems,
30
158 (2007), 349{366.
31
ORIGINAL_ARTICLE
FUZZY FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS IN PARTIALLY ORDERED METRIC SPACES
In this paper, we consider fuzzy fractional partial differential equations under Caputo generalized Hukuhara differentiability. Some new results on the existence and uniqueness of two types of fuzzy solutions are studied via weakly contractive mapping in the partially ordered metric space. Some application examples are presented to illustrate our main results.
http://ijfs.usb.ac.ir/article_3136_9bf822b348b21a6081aacf90b19a7ccc.pdf
2017-04-29T11:23:20
2018-05-25T11:23:20
107
126
10.22111/ijfs.2017.3136
Fractional PDEs
Caputo gH-derivatives
Fuzzy weak solutions
Weakly contractive mapping
Partially ordered space
Hoang Viet
Long
true
1
Division of Computational Mathematics and Engineering, Insti-
tute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh
City, Vietnam
Division of Computational Mathematics and Engineering, Insti-
tute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh
City, Vietnam
Division of Computational Mathematics and Engineering, Insti-
tute for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh
City, Vietnam
LEAD_AUTHOR
Nguyen Thi Kim
Son
true
2
Department of Mathematics, Hanoi University of Education,
Vietnam
Department of Mathematics, Hanoi University of Education,
Vietnam
Department of Mathematics, Hanoi University of Education,
Vietnam
AUTHOR
Ngo Van
Hoa
true
3
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
Division of Computational Mathematics and Engineering, Institute
for Computational Science, Ton Duc Thang University, Ho Chi Minh City, Vietnam; Faculty of Mathematics and Statistics, Ton Duc Thang University, Ho Chi Minh City, Vietnam
AUTHOR
[1] S. Abbas, M. Benchohra and G. M. N'Guerekata, Topics in fractional DEs, Springer, Berlin,
1
Heidelberg, New York, Hong Kong, London, Milan, Paris, Tokyo, 2012.
2
[2] R. Alikhani and F. Bahrami, Global solutions of fuzzy integro-dierential equations under
3
generalized dierentiability by the method of upper and lower solutions, Inf. Sci., 295 (2015),
4
[3] T. Allahviranloo, Z. Gouyandeh and A. Armand, Fuzzy fractional dierential equations under
5
generalized fuzzy Caputo derivative, J. Intell. Fuzzy Syst., 26 (2014), 1481-1490.
6
[4] T. Allahviranloo, Z. Gouyandeh, A. Armand and A. Hasanoglu, On fuzzy solutions for heat
7
equation based on generalized Hukuhara dierentiability, Fuzzy Sets Syst., 265 (2015), 1-23.
8
[5] B. Bede and L. Stefanini, Generalized dierentiability of fuzzy-valued functions, Fuzzy Sets
9
Syst., 230 (2013), 119-141.
10
[6] M. Caputo, Linear models of dissipation whose Q is almost frequency independent-II, Geo-
11
physical J. Int., 13 (1967), 529-539.
12
[7] J. Harjani and K. Sadarangani, Generalized contractions in partially ordered metric spaces
13
and applications to ordinary dierential equations, Nonlinear Anal. (TMA), 72 (2010), 1188-
14
[8] N. V. Hoa, Fuzzy fractional functional dierential equations under Caputo gH-
15
dierentiability, Commun. Nonlinear Sci. Numer. Simul., 22 (2015), 1134-1157.
16
[9] N. V. Hoa, Fuzzy fractional functional integral and dierential equations, Fuzzy Sets Syst.,
17
280 (2015), 58-90.
18
[10] A. Khastan, J. J. Nieto and R. Rodrguez-Lopez, Schauder xed-point theorem in semilinear
19
spaces and its application to fractional dierential equations with uncertainty, Fixed Point
20
Theory Appl., 2014 (2014): 21.
21
[11] A. A. Kilbas, H. M. Srivastava and J. J. Trujillo, Theory and applications of fractional
22
dierential equations, Elsevier Science B.V, Amsterdam, 2006.
23
[12] H. V. Long, N. T. K. Son, N. T. M. Ha and L. H. Son, The existence and uniqueness of fuzzy
24
solutions for hyperbolic partial dierential equations, Fuzzy Optim. Decis. Mak., 13 (2014),
25
[13] H. V. Long, N. T. K. Son and H. T. T. Tam, Global existence of solutions to fuzzy partial
26
hyperbolic functional dierential equations with generalized Hukuhara derivatives, J. Intell.
27
Fuzzy Syst., 29 (2015), 939-954.
28
[14] H. V. Long, N. T. K. Son and H. T. T. Tam, The solvability of fuzzy fractional partial
29
dierential equations under Caputo gH-dierentiability, Fuzzy Sets Syst., 309 (2017), 35-63.
30
[15] V. Lupulescu, Fractional calculus for interval-valued functions, Fuzzy Sets Syst., 265 (2015),
31
[16] M. T. Malinowski, Random fuzzy fractional integral equations - Theoretical foundations,
32
Fuzzy Sets Syst., 265 (2015) 39-62.
33
[17] J. J. Nieto and R. Rodrguez-Lopez, Applications of contractive-like mapping principles to
34
fuzzy equations, Revista Matematica Complutense, 19 (2006), 361-383.
35
[18] E. J. Villamizar-Roa, V. Angulo-Castillo and Y. Chalco-Cano, Existence of solutions to fuzzy
36
dierential equations with generalized Hukuhara derivative via contractive-like mapping prin-
37
ciples, Fuzzy Sets Syst., 265 (2015), 24-38.
38
[19] H. Vu and N. V. Hoa, On impulsive fuzzy functional dierential equations, Iranian Journal
39
of Fuzzy Systems, 13(4) (2016), 79-94.
40
ORIGINAL_ARTICLE
S-APPROXIMATION SPACES: A FUZZY APPROACH
In this paper, we study the concept of S-approximation spaces in fuzzy set theory and investigate its properties. Along introducing three pairs of lower and upper approximation operators for fuzzy S-approximation spaces, their properties under different assumptions, e.g. monotonicity and weak complement compatibility are studied. By employing two thresholds for minimum acceptance accuracy and maximum rejection error, these spaces are interpreted in three-way decision systems by defining the corresponding positive, negative and boundary regions.
http://ijfs.usb.ac.ir/article_3137_8dee0e281bea00cc18c46e1132414df5.pdf
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127
154
10.22111/ijfs.2017.3137
Fuzzy S-approximation Spaces
Fuzzy sets
Three-way Decisions
Monotonicity
Weak Complement Compatibility
Rough Set Theory
Rough Mereology
Ali
Shakiba
ali.shakiba@vru.ac.ir
true
1
Department of Computer Science, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
Department of Computer Science, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
Department of Computer Science, Vali-e-Asr University of Rafsanjan,
Rafsanjan, Iran
AUTHOR
MohammadReza
Hooshmandasl
true
2
Department of Computer Science, Yazd University,
Yazd, Iran
Department of Computer Science, Yazd University,
Yazd, Iran
Department of Computer Science, Yazd University,
Yazd, Iran
LEAD_AUTHOR
Bijan
Davvaz
davvaz@yahoo.com
true
3
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
Department of Mathematics, Yazd University, Yazd, Iran
AUTHOR
Seyed Abolfazl
Shahzadeh Fazeli
true
4
Department of Computer Science, Yazd University, Yazd, Iran
Department of Computer Science, Yazd University, Yazd, Iran
Department of Computer Science, Yazd University, Yazd, Iran
AUTHOR
[1] M. Alamuri, B. R. Surampudi and A. Negi, A survey of distance/similarity measures for
1
categorical data, In 2014 International Joint Conference on Neural Networks, IJCNN (2014),
2
1907-1914.
3
[2] N. Azam and J. T. Yao, Analyzing uncertainties of probabilistic rough set regions with game-
4
theoretic rough sets, International Journal of Approximate Reasoning, 55(1) (2014), 142-155,
5
[3] C. Cornelis, M. De Cock and A. M. Radzikowska, Fuzzy rough sets: from theory into practice,
6
Handbook of Granular computing, (2008), 533-552.
7
[4] B. Davvaz, A short note on algebraic T-rough sets, Information Sciences, 178 (2008), 3247-
8
[5] B. Davvaz, Approximations in n-ary algebraic systems, Soft Computing, 12(4) (2008), 409-
9
[6] B. Davvaz, Approximations in a semigroup by using a neighbourhood system, International
10
Journal of Computer Mathematics, 88(4) (2011), 709-713.
11
[7] B. Davvaz and M. Mahdavipour, Rough approximations in a general approximation space
12
and their fundamental properties, International Journal of General Systems, 37(3) (2008),
13
[8] A. P. Dempster, Upper and lower probabilities induced by a multivalued mapping, The Annals
14
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ORIGINAL_ARTICLE
FORMAL BALLS IN FUZZY PARTIAL METRIC SPACES
In this paper, the poset $BX$ of formal balls is studied in fuzzy partial metric space $(X,p,*)$. We introduce the notion of layered complete fuzzy partial metric space and get that the poset $BX$ of formal balls is a dcpo if and only if $(X,p,*)$ is layered complete fuzzy partial metric space.
http://ijfs.usb.ac.ir/article_3138_1731186cacc42a3620bb17542aac67dc.pdf
2017-04-29T11:23:20
2018-05-25T11:23:20
155
164
10.22111/ijfs.2017.3138
Fuzzy partial metric
Formal ball
$mathcal{Q}$-category
Domain
Jiyu
Wu
wjytun@aliyun.com
true
1
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
LEAD_AUTHOR
Yueli
Yue
ylyue@ouc.edu.cn
true
2
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
Department of Mathematics, Ocean University of China, 238 Songling
Road, 266100, Qingdao, P.R.China
AUTHOR
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ORIGINAL_ARTICLE
Persian-translation vol. 14, no. 2, April 2017
http://ijfs.usb.ac.ir/article_3140_e6302889fbbd7b0eddc238bdc864a467.pdf
2017-04-29T11:23:20
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174
10.22111/ijfs.2017.3140