ORIGINAL_ARTICLE
Cover vol. 13, no. 5, October 2016
http://ijfs.usb.ac.ir/article_2735_12510c52a206e7cedd530ebf852f21aa.pdf
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10.22111/ijfs.2016.2735
ORIGINAL_ARTICLE
New Approach to Exponential Stability Analysis and Stabilization for Delayed T-S Fuzzy Markovian Jump Systems
This paper is concerned with delay-dependent exponential stability analysis and stabilization for continuous-time T-S fuzzy Markovian jump systems with mode-dependent time-varying delay. By constructing a novel Lyapunov-Krasovskii functional and utilizing some advanced techniques, less conservative conditions are presented to guarantee the closed-loop system is mean-square exponentially stable. Then, the stabilization conditions are derived and the fuzzy controller can be obtained by solving a set solutions of LMIs. The upper bound of time-delay that the system can be stabilized is given by using an optimal algorithm. Two examples are presented to illustrate the effectiveness and potential of our methods.
http://ijfs.usb.ac.ir/article_2730_096df7afb4edcb0d9b4337a5c7b03947.pdf
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19
10.22111/ijfs.2016.2730
Delay-dependent exponential stability and stabilization
Fuzzy systems
Lyapunov-Krasovskii functional
Markovian jump systems
Mode-dependent time delay
Liu
Cui
cuiliu8475@msn.com
true
1
School of Computer Science and Information Engineering, Shanghai Institute of Technology, No.100 Haiquan Road, Fengxian Distinct, 201418, Shanghai ,
China
School of Computer Science and Information Engineering, Shanghai Institute of Technology, No.100 Haiquan Road, Fengxian Distinct, 201418, Shanghai ,
China
School of Computer Science and Information Engineering, Shanghai Institute of Technology, No.100 Haiquan Road, Fengxian Distinct, 201418, Shanghai ,
China
LEAD_AUTHOR
Yanchai
Liu
true
2
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
AUTHOR
Yueying
Wang
68942275@163.com
true
3
School of Aeronautics and Astronautics, Shanghai Jiao Tong Uni-
versity, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
School of Aeronautics and Astronautics, Shanghai Jiao Tong Uni-
versity, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
School of Aeronautics and Astronautics, Shanghai Jiao Tong Uni-
versity, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
AUTHOR
Dengping
Duan
ddp@sjtu.edu.cn
true
4
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
School of Aeronautics and Astronautics, Shanghai Jiao Tong University, No.800 Dongchuan Road, Minhang Distinct, 200240, Shanghai, China
AUTHOR
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ing genetic regulatory networks with time-varying delays by delay decomposition approach,
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Comm. Nonlinear Science Numerical Simul., 16(2) (2011), 928–939.
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H∞ control for nonlinear uncertain stochastic fuzzy systems with mode-dependent time delays
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and Markovian jump parameters, Int. J. Syst. Sci.,(2012), 1–14.
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with time-varying delays by adopting the state-space Takagi-Sugeno fuzzy model, Int. J. Fuzzy
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Syst., 12(3) (2015), 1–16.
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time randomly switched fuzzy systems with known sojourn probabilities, Nonlinear Anal.
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:Hybrid Syst., 17 (2015), 128–143.
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jump linear systems with time-delay, Int. J. Control, 74(4) (2001), 329–340.
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time delays, Automatica, 45(10) (2010), 2300–2306.
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ian jump systems with mode-depdendent time-varying delays, IEEE Trans. Autom. Control,
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56(1) (2011), 223–229.
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of time-delay systems, International Journal of Control, 74(1) (2001), 737–744.
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[10] D. W. C. Ho and Y. G. Niu, Robust fuzzy design for nonlinear uncertain stochastic systems
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via sliding-mode control, IEEE Trans. Fuzzy Syst., 15(3) (2007), 350–358.
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[11] M. Liu, P. Shi, L. X. Zhang and X. D. Zhao, Fault-tolerant control for nonlinear Markovian
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jump systems via proportional and derivative sliding mode observer technique, IEEE Trans.
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Circuits. Syst. I. Regul., 58(5) (2011), 1109–1118.
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fuzzy systems with Markovian jumps: an LMI approach, In: American Control Conference,
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(2005), 1805–1810.
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approach, IEEE Trans. Fuzzy Syst., 15(6) (2007), 1251–1262.
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jump systems, IEEE Trans. Autom. Control, 51(1) (2006), 97–103.
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[15] Z. Shu, J. Lam and S. Y. Xu, Robust stabilization of Markovian jump delay systems with
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delay-dependent exponential estimates, Automatica, 42(11) (2006), 2001–2008.
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[16] E. G. Tian and C. Peng, Delay-dependent stability analysis and synthesis of uncertain T-S
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fuzzy systems with time-varying delay, Fuzzy Sets, Syst., 157 (2006), 544–559.
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[17] S. C. Tong, W. Wang and L. J. Qu, Decentralized robust control for uncertain T-S fuzzy
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large-scale systems with time-dela, Int. J.Innovative Comput., 3(3) (2007), 657–672.
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[18] Z. D. Wang, Y. R. Liu and X. H. Liu, Exponential stabilization of a class of stochastic sys-
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tem with Markovian jump parameters and mode-dependent mixed time-delays, IEEE Trans.
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Autom. Control, 55(7) (2010), 1656–1662.
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jump nonlinear systems via fuzzy control, IEEE Trans. Man, Cybern., 36(3) (2006), 509–
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jump singular systems, IEEE Trans. Autom. Control, 55(5) (2010), 1213–1219.
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systems, Automatica, 44(7) (2008), 1849–1858.
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of discrete-time T-S time-varying delay systems, IEEE Trans. Syst. Man, Cybern., 40(1)
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(2011), 273–286.
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systems with uncertain switching probabilities, Automatica, 41(5) (2005), 897–903.
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output feedback controllers, IEEE Trans. Fuzzy Syst., 13(1) (2005), 82–93.
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time-varying delay, nonlinearity, and Markovian switching, IEEE Trans. Autom. Control,
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50(2) (2005), 217–222.
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fuzzy Markovian jump systems, Int. J. Control, Autom., Syst., 7(4) (2009), 520–529.
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discrete-time fuzzy Markovian jump systems with time-varying delays, IEEE Trans. Fuzzy
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Syst., 17(2) (2009), 411–420.
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[31] Y. Zhao, H. J. Gao, J. Lam and B. Z. Du, Stability and stabilization of delayed T-S fuzzy
72
systems: a delay partitioning approach, IEEE Trans. Fuzzy Syst., 17(4) (2009), 750–762.
73
ORIGINAL_ARTICLE
Assessing process performance with incapability index based on fuzzy critical value
Process capability indices are considered as an important concept in statistical quality control. They have been widely used in the manufacturing industry to provide numerical measures on process performance. Moreover, some incapability indices have been introduced to account the process performance. In this paper, we focus on the one proposed by Chen ~\cite{Che:Stat}. In today's modern world, accurate and flexible information is needed. So, we apply fuzzy logic to measure the process incapability. Buckley's approach is used to fuzzify this index and to make a decision on process incapability, we utilize fuzzy critical value. Numerical examples are presented to demonstrate the performance and effectiveness of the proposed index.
http://ijfs.usb.ac.ir/article_2731_f0db44c340e36bc04526843832163809.pdf
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10.22111/ijfs.2016.2731
Process incapability index
Fuzzy sets
Hypothesis testing
Critical value
Zainab
Abbasi Ganji
abbasiganji@stu.um.ac.ir
true
1
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
AUTHOR
Bahram
Sadeghpour Gildeh
sa deg hpour@umz.ac.ir
true
2
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
LEAD_AUTHOR
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15(4) (2009b), 789–810.
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Valued Logic and Soft Computing, 18(5-6) (2012), 493–511.
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processes, Journal of Intelligent and Fuzzy Systems, 19(45) (2008), 259–272.
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pollution, Stochastic Environmental Research and Risk Assessment, 23(4) (2009a), 529–541.
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approach, Human and Ecological Risk Assessment: An International Journal, 15(4)
29
(2009b), 689–713.
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32
[19] I. Kaya and C. Kahraman, A new perspective on fuzzy process capability indices: Robustness,
33
Expert Systems with Applications, 37(6) (2010b), 4593–4600.
34
[20] I. Kaya and C. Kahraman, Fuzzy process capability analyses with fuzzy normal distribution,
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[21] I. Kaya and C. Kahraman, Process capability analyses with fuzzy parameters, Expert Systems
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with Applications, 38(9) (2011a), 11918–11927.
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[22] I. Kaya and C. Kahraman, Process capability analyses based on fuzzy measurements and
39
fuzzy control charts, Expert Systems with Applications, 38(4) (2011b), 3172–3184.
40
[23] I. Kaya and C. Kahraman, Fuzzy process capability indices with asymmetric tolerances, Expert
41
Systems with Applications, 38 (2011c), 14882–14890.
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capability, International Journal of Advanced Manufacturing Technology, 15 (1999), 655–659.
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Research, 129 (2001), 683–688.
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capability index, Journal of Intelligent and Fuzzy Systems, 17 (2006), 287–295.
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66
ORIGINAL_ARTICLE
Profit maximization solid transportation problem under budget constraint using fuzzy measures
Fixed charge solid transportation problems are formulated as profit maximization problems under a budget constraint at each destination. Here item is purchased in different depots at different prices. Accordingly the item is transported to different destinations from different depots using different vehicles. Unitsare sold from different destinations to the customers at different selling prices. Here selling prices, purchasing costs, unit transportation costs, fixed charges, sources at origins, demands at destinations, conveyances capacities are assumed to be crisp or fuzzy. Budget constraints at destinations are imposed. Itis also assumed that transported units are integer multiple of packets. So the problem is formulated as constraint optimization integer programming problem in crisp and fuzzy environments. Asoptimization of fuzzy objective as well as consideration of fuzzy constraint is not well defined, different measures possibility/necessity/credibility of fuzzy event are used to transform the problem into equivalent crisp problem. The reduced crisp problem is solved following generalized reduced gradient(GRG) method using lingo software. A dominance based genetic algorithm (DBGA) and a particle swarm optimization (PSO) technique using swap sequence are also developed for this purpose and are used to solve the model. The models are illustrated with numerical examples. The results obtained using DBGA and PSO are compared with those obtained from GRG.Moreover, a statistical analysis is presented to compare the algorithms.
http://ijfs.usb.ac.ir/article_2732_cf202305823d950fc1d3a3c0438eefd2.pdf
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63
10.22111/ijfs.2016.2732
Solid transportation problem
Budget constraints
Possibility /Necessity/Credibility measure
Dominance based genetic algorithm
particle swarm optimization
Pravash
Kumar Giri
true
1
Department of Applied Mathematics with Oceanology and
Computer Programming, Vidyasagar University, Paschim-Medinipur, W.B. 721102, India
Department of Applied Mathematics with Oceanology and
Computer Programming, Vidyasagar University, Paschim-Medinipur, W.B. 721102, India
Department of Applied Mathematics with Oceanology and
Computer Programming, Vidyasagar University, Paschim-Medinipur, W.B. 721102, India
LEAD_AUTHOR
Manas
Kumar Maiti
true
2
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba-Medinipur, W.B.-721628, India
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba-Medinipur, W.B.-721628, India
Department of Mathematics, Mahishadal Raj College, Mahishadal,
Purba-Medinipur, W.B.-721628, India
AUTHOR
Manoranjan
Maiti
mmmaiti2005@yahoo.co.in
true
3
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur, W.B. 721102, India
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur, W.B. 721102, India
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Paschim-Medinipur, W.B. 721102, India
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ORIGINAL_ARTICLE
Derived fuzzy importance of attributes based on the weakest triangular norm-based fuzzy arithmetic and applications to the hotel services
The correlation between the performance of attributes and the overallsatisfaction such as they are perceived by the customers is often used tocalculate the importance of attributes in the crisp case. Recently, the methodwas extended, based on the standard Zadeh extension principle, to the fuzzycase, taking into account the specificity of the human thinking. Thedifficulties of calculation are important and only approximations of theanalytic results can be obtained. In the present paper we give a simplifiedand exact method to compute the derived importance of the attributes in thecase of input data given by triangular fuzzy numbers. The effectivecalculation is based on the $T_{W}$-extension principle and it uses reasonablecomputer resources even if a large number of attributes and customers isconsidered. The proposed derived method is later on compared with othermethods of calculation of the fuzzy importance of attributes. The results ofa survey with respect to the quality of hotel services in Oradea (Romania)are subject to the application of the proposed method.
http://ijfs.usb.ac.ir/article_2734_1f8a66ea43434caec0ea2e4287752b55.pdf
2016-10-30T11:23:20
2018-12-16T11:23:20
65
85
10.22111/ijfs.2016.2734
Triangular fuzzy number
Correlation coefficient
Importance of attributes
Performance of attributes
Hotel services
Adrian I.
Ban
true
1
Department of Mathematics and Informatics, University of Oradea,
Universitatii 1, Oradea , Romania
Department of Mathematics and Informatics, University of Oradea,
Universitatii 1, Oradea , Romania
Department of Mathematics and Informatics, University of Oradea,
Universitatii 1, Oradea , Romania
LEAD_AUTHOR
Olimpia I.
Ban
true
2
Department of Economics, University of Oradea, Universitatii 1,
Oradea , Romania
Department of Economics, University of Oradea, Universitatii 1,
Oradea , Romania
Department of Economics, University of Oradea, Universitatii 1,
Oradea , Romania
AUTHOR
Delia A.
Tuse
true
3
Department of Mathematics and Informatics, University of Oradea,
Universitatii 1, Oradea , Romania
Department of Mathematics and Informatics, University of Oradea,
Universitatii 1, Oradea , Romania
Department of Mathematics and Informatics, University of Oradea,
Universitatii 1, Oradea , Romania
AUTHOR
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A formula for spreading out values derived from preference rankings, Journal of Bussiness
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Journal of Marketing Research, 45 (2003), 55{71.
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[3] A. I. Ban and L. Coroianu, Simplifying the search for eective ranking of fuzzy numbers,
6
IEEE Transactions on Fuzzy Systems, 23 (2014), 327{339.
7
[4] A. I. Ban, O. I. Ban and D. A. Tuse, Calculation of the fuzzy importance of attributes based
8
on the correlation coecient, applied to the quality of hotel services, Journal of Intelligent
9
and Fuzzy Systems, 30 (2015), 583{596.
10
[5] A. Ban and O. Ban, Optimization and extensions of a fuzzy multicriteria decision making
11
method and applications to selection of touristic destinations, Expert Systems with Applica-
12
tions, 39 (2012), 7216{7225.
13
[6] A. I. Ban and L. Coroianu, Characterization of the ranking indices of triangular fuzzy num-
14
bers. In: A. Laurent, O. Strauss, B. Bouchon-Meunier and R.R. Yager (Eds.), Communi-
15
cations in Computer and Information Science, vol. 443, Springer-Verlag, Berlin, Heidelberg,
16
2014, pp. 254{263.
17
[7] O. Ban, Fuzzy multicriteria decision making method applied to selection of the best touristic
18
destinations, International Journal of Mathematical Models and Methods in Applied Science,
19
5 (2011), 264{271.
20
[8] O. I. Ban and I. T. Mester, Using Kano two dimensional service quality classication and
21
characteristic analysis from the perspective of hotels' clients of Oradea, Journal of Tourism-
22
Studies and Research in Tourism, 18 (2014), 30{36.
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dynamics for the customer-producer-employment model, International Journal of Systems
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critical service attributes, Expert Systems with Applications, 36 (2009), 3774{3784.
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tributes, International Journal of Service Industry Management, 19 (2008), 252{270.
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Scientic, Singapore, 1994.
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ical Publications, 6 (1994), 75{81.
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(2003), 112-129.
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[44] L.A. Zadeh, Fuzzy sets as a basis for a theory of possibility, Fuzzy Sets and Systems, 1 (1978),
96
ORIGINAL_ARTICLE
A Hyers-Ulam-Rassias stability result for functional equations in Intuitionistic Fuzzy Banach spaces
Hyers-Ulam-Rassias stability have been studied in the contexts of several areas of mathematics. The concept of fuzziness and its extensions have been introduced to almost all branches of mathematics in recent times.Here we define the cubic functional equation in 2-variables and establish that Hyers-Ulam-Rassias stability holds for such equations in intuitionistic fuzzy Banach spaces.
http://ijfs.usb.ac.ir/article_2755_16e148218ff4f6b4d7055c7278c8bea5.pdf
2016-10-30T11:23:20
2018-12-16T11:23:20
87
96
10.22111/ijfs.2016.2755
Cubic functional equations
t-norm
t-conorm
Intuitionistic fuzzy Banach space
Hyers-Ulam-Rassias stability
Nabin
Chandra Kayal
true
1
Department of Mathematics, Indian Institute Of Engineering
Science and Technology, Shibpur, Howrah - 711103, West Bengal, India
Department of Mathematics, Indian Institute Of Engineering
Science and Technology, Shibpur, Howrah - 711103, West Bengal, India
Department of Mathematics, Indian Institute Of Engineering
Science and Technology, Shibpur, Howrah - 711103, West Bengal, India
LEAD_AUTHOR
Tapas Kumar
Samanta
true
2
Department of Mathematics, Uluberia College, Uluberia,
Howrah - 711315, West Bengal, India
Department of Mathematics, Uluberia College, Uluberia,
Howrah - 711315, West Bengal, India
Department of Mathematics, Uluberia College, Uluberia,
Howrah - 711315, West Bengal, India
AUTHOR
Parbati
Saha
true
3
Department of Mathematics, Indian Institute Of Engineering Science
and Technology, Shibpur, Howrah - 711103, West Bengal, India
Department of Mathematics, Indian Institute Of Engineering Science
and Technology, Shibpur, Howrah - 711103, West Bengal, India
Department of Mathematics, Indian Institute Of Engineering Science
and Technology, Shibpur, Howrah - 711103, West Bengal, India
AUTHOR
Binayak S.
Choudhury
binayak12@yahoo.co.in
true
4
Department of Mathematics, Indian Institute Of Engineering
Science and Technology, Shibpur, Howrah - 711103, West Bengal, India
Department of Mathematics, Indian Institute Of Engineering
Science and Technology, Shibpur, Howrah - 711103, West Bengal, India
Department of Mathematics, Indian Institute Of Engineering
Science and Technology, Shibpur, Howrah - 711103, West Bengal, India
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1
[2] J. H. Bae and W. G. Park, A xed-point approach to the stability of a functional equation
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on quadratic forms, Journal of Inequalities and Applications, 82 (2011), 1{7.
3
[3] J. H. Bae, W. G. Park,On the Ulam stability of the Cauchy-Jensen equation and the additive-
4
quadratic equation, J. Nonlinear Sci. Appl. 8(5) (2015), 710{718.
5
[4] G. Deschrijver, C. Cornelis and E. E. Kerre, On the representation of intuitionistic fuzzy
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t-norms and t-conorms, IEEE Transaction on Fuzzy Systems, 12 (2004), 45{61.
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[5] G. Deschrijver and E. E. Kerre, On the relationship between some extensions of fuzzy set
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theory, Fuzzy Sets and Systems, 23 (2003), 227{235.
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[6] Y. Dong, On approximate isometries and application to stability of a function, J. Math.
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Anal. Appl., 426(2) (2015), 125{137.
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[7] A. Grabiec, The generalized Hyers-Ulam stability of a class of functional equations, Publ.
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Math. Debrecen, 48 (1996), 217{235.
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[8] D. H. Hyers, On the stability of the linear functional equation, Proc. Nat. Acad. Sci. U.S.A.,
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27 (1941), 222{224.
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[9] K. W. Jun and H. M. Kim The generalized Hyers-Ulam-Rassias stability of a cubic functional
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equation, J. Math. Anal. Appl., 274 (2002), 867{878.
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[10] S. M. Jung, Hyers-Ulam stability of linear dierential equations of rst order, II, App. Math.
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Lett., 19 (2006), 854{858.
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[11] N. C. Kayal, P. Mondal and T. K. Samanta, The generalized Hyers - Ulam - Rassias stability
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of a quadratic functional equation in fuzzy banach spaces, Journal of New Results in Science,
21
1(5) (2014), 83{95.
22
[12] N. C. Kayal, P. Mondal and T. K. Samanta, The fuzzy stability of a pexiderized functional
23
equation, Mathematica Moravica, 18(2) (2014), 1{14.
24
[13] N. C. Kayal, P. Mondal and T. K. Samanta, Intuitionistic fuzzy stability of a quadratic
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functional equation, Tbilisi Mathematical Journal, 8(2) (2015), 139{147.
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[14] S. O. Kim, A. Bodaghi and C. Park, Stability of functional inequalities associated with the
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Cauchy-Jensen additive functional equalities in non-Archimedean Banach spaces, J. Nonlin-
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ear Sci. Appl., 8(5) (2015), 776{786.
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[15] Y. Lan and Y. Shen, The general solution of a quadratic functional equation and Ulam
30
stability, J. Nonlinear Sci. Appl. 8(5) (2015), 640{649.
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[16] A. K. Mirmostafaee and M. S. Moslehian, Fuzzy versions of Hyers-Ulam-Rassias theorem,
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Fuzzy Sets and Systems, 159 (2008), 720{729.
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[17] P. Mondal, N. C. Kayal and T. K. Samanta, The stability of pexider type functional equation
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in intuitionistic fuzzy Banach spaces via xed point technique, Journal of Hyperstructures,
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4(1) (2015), 37{49.
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[18] A. Najati, The generalized Hyers-Ulam-Rassias stability of a cubic functional equation, Turk
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J Math, 31 (2007), 395{408.
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[19] C. Park, Fuzzy stability of a functional equation associated with inner product space, Fuzzy
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Sets and Systems, 160 (2009), 1632{1642.
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[20] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fractals, 22 (2004), 1039{
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[21] Th. M. Rassias, On the stability of the linear mapping in Banach space, Proc. Amer. Math-
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ematical Society, 72(2) (1978), 297{300.
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[22] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and
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Fractals, 27 (2006), 331{344.
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[23] T. K. Samanta and Iqbal H. Jebril, Finite dimentional intuitionistic fuzzy normed linear
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space, Int. J. Open Problems Compt. Math., 2(4) (2009), 574{591.
47
[24] T. K. Samanta, N. C.Kayal and P. Mondal, The Stability of a General Quadratic Functional
48
Equation in Fuzzy Banach Space, Journal of Hyperstructures, 1(2) (2012), 71{87.
49
[25] T. K. Samanta, P. Mondal and N. C. Kayal, The generalized Hyers-Ulam-Rassias stability of
50
a quadratic functional equation in fuzzy Banach spaces, Annals of Fuzzy Mathematics and
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Informatics, 6(2) (2013), 285{294.
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[26] S. Shakeri, Intutionistic fuzzy stability of Jenson type mapping, J. Non linear Sc. Appl., 2(2)
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(2009), 105{112.
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[27] S. M. Ulam, Problems in Modern Mathematics, Science Editions, Wiley, New York,
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1964(Chapter VI, Some Questions in Analysis: x1, Stability).
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[28] L. A. Zadeh, Fuzzy sets, Information and control, 8 (1965), 338{353.
57
ORIGINAL_ARTICLE
MULTI-ATTRIBUTE DECISION MAKING METHOD BASED ON BONFERRONI MEAN OPERATOR and possibility degree OF INTERVAL TYPE-2 TRAPEZOIDAL FUZZY SETS
This paper proposes a new approach based on Bonferroni mean operator and possibility degree to solve fuzzy multi-attribute decision making (FMADM) problems in which the attribute value takes the form of interval type-2 fuzzy numbers. We introduce the concepts of interval possibility mean value and present a new method for calculating the possibility degree of two interval trapezoidal type-2 fuzzy sets (IT2 TrFSs). Then, we develop two aggregation techniques, which are called the interval type-2 trapezoidal fuzzy Bonferroni mean (IT2TFBM) operator and the interval type-2 trapezoidal fuzzy weighted Bonferroni mean (IT2TFWBM) operator. We study their properties and discuss their special cases. Based on the IT2TFWBM operator and the possibility degree, a new method of multi-attribute decision making with interval type-2 trapezoidal fuzzy information is proposed. Finally, an illustrative example is given to verify the developed approaches and to demonstrate their practicality and effectiveness.
http://ijfs.usb.ac.ir/article_2756_92d3e04187dcfd6414ef9a25b326977a.pdf
2016-10-30T11:23:20
2018-12-16T11:23:20
97
115
10.22111/ijfs.2016.2756
Multi-attributes group decision making
Interval type-2 fuzzy sets
Bonferroni mean operator
IT2TFWBM operator
Yanbing
Gong
true
1
Department of Information Management, Hohai University,Changzhou,
Jiangsu Province, China
Department of Information Management, Hohai University,Changzhou,
Jiangsu Province, China
Department of Information Management, Hohai University,Changzhou,
Jiangsu Province, China
LEAD_AUTHOR
Liangliang
Dai
true
2
Department of Information Management, Hohai University,Changzhou,
Jiangsu Province, China
Department of Information Management, Hohai University,Changzhou,
Jiangsu Province, China
Department of Information Management, Hohai University,Changzhou,
Jiangsu Province, China
AUTHOR
Na
Hu
true
3
Department of Information Management, Hohai University,Changzhou, Jiangsu
Province, China
Department of Information Management, Hohai University,Changzhou, Jiangsu
Province, China
Department of Information Management, Hohai University,Changzhou, Jiangsu
Province, China
AUTHOR
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and Systems,15(1) (1985), 1-19.
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[3] Q. W. Cao and J. Wu, The extended COWG operators and their application to multiple
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attributive group decision making problems with interval numbers, Applied Mathematical
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Modelling, 35(5) (2011), 2075-2086.
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[4] C. T. Chen, Extensions of the TOPSIS for group decision-making under fuzzy environment,
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Fuzzy Sets and Systems, 114(1) (2000), 1-9.
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[5] S. M. Chen, Fuzzy group decision making for evaluating the rate of aggregative risk in software
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development, Fuzzy Sets and Systems, 118(1) (2001), 75-88.
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[6] S. M. Chen and L. W. Lee,Fuzzy multiple attributes group decision-making based on the
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ranking values and the arithmetic operations of interval type-2 fuzzy sets, Expert Systems
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with Applications, 37(4) (2010), 824-833.
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[7] S. M. Chen and L. W. Lee,Fuzzy multiple attributes group decision-making based on the
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interval type-2 TOPSIS method, Expert Systems with Applications, 37(4) (2010), 2790-2798.
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interval type-2 fuzzy sets, Expert Systems with Applications, 39(5) (2012), 5295-5308.
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[9] T. Y. Chen and C. H. Chang, The extended QUALIFLEX method for multiple criteria
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decision analysis based on interval type-2 fuzzy sets and applications to medical decision
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making, European Journal of Operational Research, 226(3) (2013), 615-625.
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[10] S. M. Chen and L. W. Lee,Fuzzy multiple criteria hierarchical group decision making based
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on interval type-2 fuzzy sets, IEEE Transactions on Systems, Man and Cybernetics, Part A:
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Systems and Humans, 40(5) (2010) , 1120-1128.
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[11] C. Carlsson and R. Fuller,On possibilistic mean value and variance of fuzzy numbers, Fuzzy
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Sets and Systems, 122122(2) (2001), 315-326.
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[12] F.J. Cabrerizo, R. Heradio, I. J. Prez and E. Herrera-Viedma,A selection process based on
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additive consistency to deal with incomplete fuzzy linguistic information, Journal of Universal
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Computer Science, 16(1) (2010), 62-81.
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[13] Y. C. Dong, G. Q. Zhang, W. C. Hong and Y. F. Xu, Consensus models for AHP group
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decision making under row geometric mean prioritization method, Decision Support Systems,
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49(3) (2010), 281{289.
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[14] Z. P. Fan and Y. Liu, A method for group decision-making based on multigranularity uncer-
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tain linguistic information, Expert Systems with Applications,37(5) (2010), 4000-4008.
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[15] Y. B. Gong, N. Hu, J. G. Zhang, G. F. Liu and J. G. Deng, Multi-attribute group decision
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making method based on geometric Bonferroni mean operator of trapezoidal interval type-2
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fuzzy numbers, Computers and Industrial Engineering, 81(3) (2015), 167-176.
37
[16] J. H. Hu, Y. Zhang, X. H. Chen and Y. M. Liu, Multi-criteria decision making method
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based on possibility degree of interval type-2 fuzzy number, Knowledge-Based Systems, 43(5)
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(2013), 21-29.
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[17] P. D. Liu, A weighted aggregation operators multi-attribute group decision-making method
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based on interval-valued trapezoidal fuzzy numbers, Expert Systems with Applications, 38(1)
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(2011), 1053-1060.
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[18] D. F. Li, A fuzzy closeness approach to fuzzy multi-attribute decision making, Fuzzy Opti-
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mization and Decision Making,6(3) (2007), 237-254.
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[19] C. J. Lin and W. Wu, A causal analytical method for group decision-making under fuzzy
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environment, Expert Systems with Applications,34(1) (2008), 205-213.
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[20] D. F. Li, A new methodology for fuzzy multi-attribute group decision making with multi-
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granularity and non-homogeneous information, Fuzzy Optimization and Decision Making,
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9(1) (2010), 83-103.
50
[21] P. D. Liu and F. Jin,The trapezoid fuzzy linguistic Bonferroni mean operators and their
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application to multiple attribute decision making, Scientia Iranica, 19(6) (2012),1947-1959.
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and their application to multiple attribute decision making, Applied Mathematical Modelling,
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Upper Saddle River, Prentice-Hall, NJ, 2001.
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1, forward problems, IEEE Transactions on Fuzzy Systems,14(6) (2006), 781-792.
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Applications, 34(4) (2008), 2921-2936.
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formation and their application to multiple attribute group decision making , Expert Systems
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with Applications, 39(5) (2012),5881-5886.
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mation and their application to multiple attribute group decision making , Fuzzy Sets and
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terval type-2 and type-1 fuzzy sets, Information Sciences, 178(2) (2008), 381-402.
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and uncertainty measures for interval type-2 fuzzy sets, Information Sciences, 179(8) (2009),
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1169-1192.
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[34] D. R. Wu and J. M. Mendel,Corrections to aggregation using the linguistic weighted average
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and interval type-2 fuzzy sets, IEEE Transactions on Fuzzy Systems, 15(6) (2008), 1145-1161.
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[35] W. Z. Wang and X. W. Liu,Multi-attribute group decision making models under interval
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type-2 fuzzy environment, Knowledge-Based Systems, 30(6) (2012), 121-128.
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[36] G. W. Wei, X. F. Zhao, R. Lin and H. J. Wang, Uncertain linguistic Bonferroni mean
87
operators and their application to multiple attribute decision making, Applied Mathematical
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Modelling, 37(7) (2013), 5277-5285.
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[37] Z. S. Xu, An interactive procedure for linguistic multiple attribute decision making with
90
incomplete weight information, Fuzzy Optimization and Decision Making,6(1) (2007), 17-
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[38] Z. S. Xu and R. R. Yager,Intuitionistic fuzzy Bonferroni means, IEEE Transactions on Sys-
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tems, Man, and Cybernetics - Part B, 41(2) (2011), 568-578.
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[39] M. M. Xia, Z.S. Xu and B. Zhu, Geometric Bonferroni means with their application in
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multi-criteria decision making, Technical Report, 2011.
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[40] M. M. Xia, Z. S. Xu and B. Zhu,Geometric Bonferroni means with their application in
96
multi-criteria decision making, Knowledge-Based Systems, 40(1) (2013), 88-100.
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[41] R. R. Yager, On generalized Bonferroni mean operators for multi-criteria aggregation, Inter-
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national Journal of Approximate Reasoning, 50(8) (2009), 1279-1286.
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[42] L. Zadeh, The concept of a linguistic variable and its application to approximate reasoning,
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Part 1, Information Sciences, 8(3) (1975), 199-249.
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[43] Z. M. Zhang and S. H. Zhang,A novel approach to multi attribute group decision making
102
based on trapezoidal interval type-2 fuzzy soft sets, Applied Mathematical Modeling, 37(7)
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(2013), 4948-4971.
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[44] B. Zhu, Z. S. Xu and M. M. Xia,Hesitant fuzzy geometric Bonferroni means, Information
105
Sciences, 205 205(1) (2012), 72-85.
106
ORIGINAL_ARTICLE
Triangular Intuitionistic Fuzzy Triple Bonferroni Harmonic Mean Operators and Application to Multi-attribute Group Decision Making
As an special intuitionistic fuzzy set defined on the real number set, triangular intuitionistic fuzzy number (TIFN) is a fundamental tool for quantifying an ill-known quantity. In order to model the decision maker's overall preference with mandatory requirements, it is necessary to develop some Bonferroni harmonic mean operators for TIFNs which can be used to effectively intergrate the information of attribute values for multi-attribute group decision making (MAGDM) with TIFNs. The purpose of this paper is to develop some Bonferroni harmonic operators of TIFNs and apply to the MAGDM problems with TIFNs. The weighted possibility means of TIFN are firstly defined. Hereby, a new lexicographic approach is presented to rank TIFNs sufficiently considering the risk preference of decision maker. The sensitivity analysis on the risk preference parameter is made. Then, three kinds of triangular intuitionistic fuzzy Bonferroni harmonic aggregation operators are defined, including a triangular intuitionistic fuzzy triple weighted Bonferroni harmonic mean operator (TIFTWBHM) operator, a triangular intuitionistic fuzzy triple ordered weighted Bonferroni harmonic mean (TIFTOWBHM) operator and a triangular intuitionistic fuzzy triple hybrid Bonferroni harmonic mean (TIFTHBHM) operator. Some desirable properties for these operators are discussed in detail. By using the TIFTWBHM operator, we can obtain the individual overall attribute values of alternatives, which are further integrated into the collective ones by the TIFTHBHM operator. The ranking order of alternatives is generated according to the collective overall attribute values of alternatives. A real investment selection case study verifies the validity and applicability of the proposed method.
http://ijfs.usb.ac.ir/article_2757_50ec49ed0918abddb9a00e2cdcd2708a.pdf
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117
145
10.22111/ijfs.2016.2757
Multi-attribute group decision making
Triangular intuitionistic fuzzy number
Possibility mean
Bonferroni mean
Harmonic mean
Shu-Ping
Wan
true
1
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
LEAD_AUTHOR
Yong-Jun
Zhu
true
2
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
College of Information Technology, Jiangxi University of Finance
and Economics, Nanchang 330013, China
AUTHOR
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1
[2] G. Beliakov, S. James, J. Mordelova, T. Ruckschlossova and R. Yager, Generalized Bon-
2
ferroni mean operators in multi-criteria aggregation, Fuzzy Sets and Systems, 161 (2010),
3
2227{2242.
4
[3] C. Bonferroni, Sulle medie multiple di potenze, Bolletino Matematica Italiana, 5 (1950),
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[4] C. Carlsson and R. Fuller, On possibilistic mean value and deviation of fuzzy numbers,
6
Fuzzy Sets and Systems, 122 (2001), 315-326.
7
[5] H. Y. Chen, C. L. Liu and Z. H. Sheng, Induced ordered weighted harmonic averaging
8
(IOWHA) operator and its application to combination forecasting method, Chinese Journal
9
of Management Science, 12(5) (2004), 35-40.
10
[6] J. Y. Dong and S. P. Wan, A new method for multi-attribute group decision making with
11
triangular intuitionistic fuzzy numbers, Kybernetes, 45(1) (2016), 158-180.
12
[7] J. Y. Dong and S. P.Wan, A new method for prioritized multi-criteria group decision mak-
13
ing with triangular intuitionistic fuzzy numbers, Journal of intelligent and Fuzzy systems,
14
30 (2016), 1719-1733.
15
[8] B. Dutta and D. Guha, Trapezoidal intuitionistic fuzzy Bonferroni means and its applia-
16
tion in multi-attribute decision making, Fuzzy Systems (FUZZ), (2013) IEEE International
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Conference on. IEEE, (2013), 1-8.
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and Systems, 94 (2) (1998), 157-169.
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[10] R. Fuller and P. Majlender, On weighted possibilistic mean and variance of fuzzy numbers,
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Fuzzy Sets and Systems, 136 (2003), 363-374.
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[11] D. F. Li, A note on "using intuitionistic fuzzy sets for fault-tree analysis on printed circuit
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board assembly", Microelectronics Reliability, 48(10) (2008), 1741.
24
[12] D. F. Li, A ratio ranking method of triangular intuitionistic fuzzy numbers and its appli-
25
cation to MADM problems, Computers and Mathematics with Applications, 60 (2010),
26
1557-1570.
27
[13] D. F. Li, J. X. Nan and M. J. Zhang, A ranking method of triangular intuitionistic fuzzy
28
numbers and application to decision making, International Journal of Computational Intelligence
29
Systems, 3(5) (2010), 522-530.
30
[14] J. X. Nan, D. F. Li and M. J. Zhang, A lexicographic method for matrix games with
31
payos of triangular intuitionistic fuzzy numbers, International Journal of Computational
32
Intelligence Systems, 3(3) (2010), 280-289.
33
[15] J. H. Park and E. J. Park, Generalized fuzzy Bonferroni harmonic mean operators
34
and their applications in group decision making, Journal of Applied Mathematics(2013),
35
http://dx.doi.org/10.1155/2013/604029.
36
[16] M. H. Shu, C. H. Cheng and J. R. Chang, Using intuitionistic fuzzy sets for fault tree
37
analysis on printed circuit board assembly, Microelectronics Reliability, 46(12) (2006),
38
2139-2148.
39
[17] H. Sun and M. Sun, Generalized Bonferroni harmonic mean operators and their applica-
40
tion to multiple attribute decision making, Journal of Computational Information Systems,
41
8 (2012), 5717-5724.
42
[18] S. P. Wan, G. L. Xu, F. Wang and J. Y. Dong, A new method for Atanassov's interval-
43
valued intuitionistic fuzzy MAGDM with incomplete attribute weight information, Information
44
Sciences, 316 (2015), 329-347.
45
[19] S. P. Wan and D. F. Li, Fuzzy mathematical programming approach to heterogeneous
46
multiattribute decision-making with interval-valued intuitionistic fuzzy truth degrees, Information
47
Sciences, 325 (2015), 484-503.
48
[20] S. P. Wan and J. Y. Dong, Interval-valued intuitionistic fuzzy mathematical programming
49
method for hybrid multi-criteria group decision making with interval-valued intuitionistic
50
fuzzy truth degrees, Information Fusion, 26 (2015), 49-65.
51
[21] S. P. Wan and J. Y. Dong, Power geometric operators of trapezoidal intuitionistic fuzzy
52
numbers and application to multi-attribute group decision making, Applied Soft Computing,
53
29 (2015), 153-168.
54
[22] S. P. Wan, F. Wang and J. Y. Dong,A novel group decision making method with intuition-
55
istic fuzzy preference relations for RFID technology selection, Applied Soft Computing,
56
38 (2016), 405-422.
57
[23] S. P. Wan, F. Wang, L. L. Lin and J. Y. Dong,An intuitionistic fuzzy linear programming
58
method for logistics outsourcing provider selection, Knowledge-Based Systems, 82 (2015),
59
[24] S. P. Wan, F. Wang and J. Y. Dong,A novel risk attitudinal ranking method for intu-
60
itionistic fuzzy values and application to MADM, Applied Soft Computing, 40 (2016),
61
[25] S. P. Wan, Multi-attribute decision making method based on possibility variance coecient
62
of triangular intuitionistic fuzzy numbers, International Journal of Uncertainty, Fuzziness
63
and Knowledge-Based Systems, 21(2) (2013), 223-243.
64
[26] S. P. Wan, Q. Y. Wang and J. Y. Dong, The extended VIKOR method for multi-attribute
65
group decision making with triangular intuitionistic fuzzy numbers, Knowledge-Based Systems,
66
52 (2013), 65-77.
67
[27] S. P. Wan and J. Y. Dong, Possibility method for triangular intuitionistic fuzzy multi-
68
attribute group decision making with incomplete weight information, International Journal
69
of Computational Intelligence Systems, 7(1) (2014), 65-79.
70
[28] S. P. Wan, F. Wang and L. L. Lin, Some new generalized aggregation operators for tri-
71
angular intuitionistic fuzzy numbers and application to multi-attribution group decision
72
making, Computers and Industrial Engineering, 93 (2016), 286-301.
73
[29] S. P. Wan, L. L. Lin and J. Y. Dong, MAGDM based on triangular Atanassov's intuition-
74
istic fuzzy information aggregation, Neural Computing and Applications, 27(2) (2016),
75
http://dx.doi.org/ 10.1007/s00521-016-2196-9.
76
[30] J. Q.Wang, R. R. Nie, H. Y. Zhang and X. H. Chen, New operators on triangular intuition-
77
istic fuzzy numbers and their applications in system fault analysis, Information Sciences,
78
251 (2013), 79-95.
79
[31] G. W. Wei, FIOWHM operator and its application to multiple attribute group decision
80
making, Expert Systems with Applications, 38 (2011), 2984-2989.
81
[32] M. M. Xia, Z. S. Xu and B. Zhu, Generalized intuitionistic fuzzy Bonferroni means, International
82
Journal of Intelligent Systems, 27(1) (2012), 23-47.
83
[33] Z. S. Xu, An overview of methods for determining OWA weights, International Journal of
84
Intelligent Systems, 20(8) (2005), 843-865.
85
[34] Z. S. Xu and R. R. Yager, Intuitionistic fuzzy Bonferroni means, IEEE Transactions on
86
System, Man, and Cybernetics-part B, 46 (2010), 568-578.
87
[35] Z. S. Xu, Fuzzy harmonic mean operator, International Journal of Intelligent Systems, 24
88
(2009), 152-172.
89
[36] R. R. Yager, Prioritized OWA aggregation, Fuzzy Optimization and Decision Making, 8
90
(2009), 245-262.
91
[37] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338-356.
92
ORIGINAL_ARTICLE
On the multivariate process capability vector in fuzzy environment
The production of a process is expected to meet customer demands, specifications or engineering tolerances. The ability of a process to meet these expectations is expresed as a single number using a process capability index. When the quality of the products relates to more than one characteristic, multivariate process capability indices are applied. As it is known, in some circumstances we are faced with imprecise data. So, fuzzy logic is engaged to deal with them. In this article, the specification limits and the target value of each characteristic and also, the data gathered from the process are assumed to be imprecise and a new fuzzy multivariate capability vector is introduced. As a whole, the present article provides a research of the application of fuzzy logic in multivariate capability vector.
http://ijfs.usb.ac.ir/article_2758_55259566d04db53b519cf379495ec255.pdf
2016-10-30T11:23:20
2018-12-16T11:23:20
147
159
10.22111/ijfs.2016.2758
Multivariate normal distribution
Multivariate process capability vector
fuzzy logic
Triangular fuzzy matrix
Fuzzy linear equation system
Ranking function
Zainab
Abbasi Ganji
abbasiganji@stu.um.ac.ir
true
1
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences,
Ferdowsi University of Mashhad, Mashhad, Iran
AUTHOR
Bahram
Sadeghpour Gildeh
sa deg hpour@umz.ac.ir
true
2
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
Department of Statistics, Faculty of Mathematical Sciences, Ferdowsi University of Mashhad, Mashhad, Iran
LEAD_AUTHOR
[1] M. A. Basaran, Calculating fuzzy inverse matrix using fuzzy linear equation system, Applied
1
Soft Computing, 12 (2012), 1810{1813.
2
[2] K. S. Chen and W. L. Pearn, Capability indices for processes with asymmetric tolerances,
3
Journal of the Chinese Institute of Engineers, 24(5) (2001), 559{568.
4
[3] M. Dehghan, M. Ghatee and B. Hashemi, Inverse of a fuzzy matrix of fuzzy numbers, International
5
Journal of Computer Mathematics, 86(8) (2009), 1433{1452.
6
[4] P. Fortemps and M. Roubens, Ranking and defuzzification methods based on area compensation,
7
Fuzzy Sets and Systems, 82 (1996) 319{330.
8
[5] J. E. Jackson, Quality control methods for two related variables, Industrial Quality Control,
9
(1956), 4{8.
10
[6] I. Kaya and C. Kahraman, Fuzzy process capability analyses: An application to teaching
11
processes, Journal of Intelligent and Fuzzy Systems, 19(4-5) (2008), 259{272.
12
[7] I. Kaya and C. Kahraman, Fuzzy robust process capability indices for risk assessment of air
13
pollution, Stochastic Environmental Research and Risk Assessment, 23(4) (2009), 529{541.
14
[8] I. Kaya and C. Kahraman, Development of fuzzy process accuracy index for decision making
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problems, Information Sciences, 180(6) (2010), 861{872.
16
[9] A. Parchami, M. Mashinchi and H. R. Maleki, Fuzzy confidence interval for fuzzy process
17
capability index, Journal of Intelligent and Fuzzy Systems, 17 (2006), 287{295.
18
[10] A. Parchami and M. Mashinchi, Fuzzy estimation for process capability indices, Information
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Sciences, 177 (2007), 1452{1462.
20
[11] A. Parchami, B. Sadeghpour Gildeh, M. Nourbakhsh and M. Mashinchi, A new generation
21
of process capability indices based on fuzzy measurements, Journal of Applied Statistics, 41
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(2014), 1122{1136.
23
[12] W. L. Pearn, S. Kotz and N. L. Johnson, Distributional and inferential properties of process
24
capability indices, Journal of Quality Technology, 24 (1992), 216{233.
25
[13] B. Sadeghpour Gildeh, Comparison of and process capability indices in the case of measurement
26
error occurrence, IFSA World Congress, Istanbul, Turkey, (2003), 563{567.
27
[14] B. Sadeghpour Gildeh, Measurement error effects on the performance of the process capability
28
index based on fuzzy tolerance interval, Annals of Fuzzy Mathematica and Informatics, 2
29
(2011), 17{32.
30
[15] B. Sadeghpour Gildeh and V. Moradi, Fuzzy tolerance region and process capability analysis,
31
Advances in Intelligent and Soft Computing, 157 (2012), 183{193.
32
[16] H. Shahriari and M. Abdollahzadeh, A new multivariate process capability vector, Quality
33
Engineering, 21(3) (2009), 290{299.
34
[17] J. J. H. Shiau, C. L. Yen, W. L. Pearn and W. T. Lee, Yield-Related process capability
35
indices for processes of multiple quality characteristics, Quality and Reliability Engineering
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International, 29 (2013), 487{507.
37
[18] L. A. Zadeh, Fuzzy sets, Information and Control, 8 (1965), 338{353.
38
[19] M. Zhang, G. A. Wang, H. E. Shuguang and H. E. Zhen, Modified multivariate process capability
39
index using principal component analysis, Chinese Journal of Mechanical Engineering,
40
27(2) (2014), 249{259.
41
ORIGINAL_ARTICLE
Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces
The definition of $L$-fuzzy Q-convergence spaces is presented by Pang and Fang in 2011. However, Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces is not investigated. This paper focuses on Cartesian-closedness of the category of $L$-fuzzy Q-convergence spaces, and it is shown that the category $L$-$\mathbf{QFCS}$ of $L$-fuzzy Q-convergence spaces is Cartesian-closed.
http://ijfs.usb.ac.ir/article_2759_89db0f2bc8a8e0f41e92811df1036a31.pdf
2016-10-30T11:23:20
2018-12-16T11:23:20
161
168
10.22111/ijfs.2016.2759
$L$-fuzzy filter
$L$-fuzzy Q-convergence space
$L$-fuzzy topology
Cartesian-closedness
Juan
Li
lijuan201209@sohu.com
true
1
School of Mathematics, Beijing Institute of Technology, Beijing 100081,
PR China
School of Mathematics, Beijing Institute of Technology, Beijing 100081,
PR China
School of Mathematics, Beijing Institute of Technology, Beijing 100081,
PR China
LEAD_AUTHOR
[1] J. Adamek, H. Herrlich and G. E. Strecker, Abstract and concrete category, Wiley, New York,
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[2] C. L. Chang, Fuzzy topological spaces, J. Math. Anal. Appl., 24 (1968), 182{190.
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4
[5] U. Hohle and A. P. Sostak, Axiomatic foundations of xed-basis fuzzy topology, in: U.Hohle,
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S.E.Rodabaugh(Eds.), Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, in:
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8
[7] G. Jager, A category of L-fuzzy convergence spaces, Quest. Math., 24 (2001), 501{517.
9
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10
[9] Y. M. Liu and M. K. Luo, Fuzzy topology, World Scientic Publication, Singapore, 1998.
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[10] B. Pang and J. M. Fang, L-fuzzy Q-convergence structures, Fuzzy Sets Syst., 182 (2011),
12
[11] B. Pang, Further study on L-fuzzy Q-convergence structures, Iranian Journal of Fuzzy Systems,
13
10(5) (2013), 147{164.
14
[12] B. Pang, On (L;M)-fuzzy convergence spaces, Fuzzy Sets Syst., 238 (2014), 46{70.
15
[13] B. Pang, Enriched (L;M)-fuzzy convergence spaces , J. Intell. Fuzzy Syst., 27 (2014), 93{103.
16
[14] B. Pang and F. G. Shi, Degree of compactness of (L;M)-fuzzy convergence spaces and its
17
applications, Fuzzy Sets Syst., 251 (2014), 1{22.
18
[15] G. Preuss, Foundations of Topology{An Approach to Convenient Topology, Kluwer Academic
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Publisher, Dordrecht, Boston, London, 2002.
20
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(1985), 89{103.
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[17] W. Yao, On L-fuzzifying convergence spaces, Iranian Journal of Fuzzy Systems, 6(1) (2009),
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24
2503{2519.
25
[19] M. S. Ying, A new approach to fuzzy topology (I), Fuzzy Sets Syst., 39 (1991), 303{321.
26
ORIGINAL_ARTICLE
Persian-translation vol. 13, no. 5, October 2016
http://ijfs.usb.ac.ir/article_2760_9fbdfe8776c649f6d864e15b27ac71fb.pdf
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171
179
10.22111/ijfs.2016.2760