Ranking fuzzy quantities based on the angle of the reference functions

Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, eac...

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Veröffentlicht in:Applied mathematical modelling Jg. 37; H. 22; S. 9230 - 9241
Hauptverfasser: Nasseri, S.H., Zadeh, M.M., Kardoost, M., Behmanesh, E.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: Elsevier Inc 15.11.2013
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ISSN:0307-904X
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Abstract Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, each proposed method may has some shortcoming. So we are going to present a novel method based on the angle of the reference functions to cover a wide range of fuzzy quantities by over coming the draw backs of some existing methods. In the mentioned firstly, the angle between the left and right membership functions (the reference functions) of every fuzzy set is called Angle of Fuzzy Set (AFS), and then in order to extend ranking of two fuzzy sets the angle of fuzzy sets and α-cuts is used. The method is illustrated by some numerical examples and in particular the results of ranking by the proposed method and some common and existing methods for ranking fuzzy sets is compared to verify the advantage of the new approach. In particular, based on the results of comparison of our method with well known methods which are exist in the literature, we will see that against of most existing ranking approaches, our proposed approach can rank fuzzy numbers that have the same mode and symmetric spreads. In fact, the proposed method in this paper can effectively rank symmetric fuzzy numbers as well as the effective methods which are appeared in the literature. Moreover, unlike of most existing ranking approaches, our proposed approach can rank non-normal fuzzy sets. Finally, we emphasize that the concept of fuzzy ordering is one of key role in establishing the numerical algorithms in operations research such as fuzzy primal simplex algorithms, fuzzy dual simplex algorithms and as well as discussed in the works of Ebrahimnejad and Nasseri and coworkers [1–7].
AbstractList Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, each proposed method may has some shortcoming. So we are going to present a novel method based on the angle of the reference functions to cover a wide range of fuzzy quantities by over coming the draw backs of some existing methods. In the mentioned firstly, the angle between the left and right membership functions (the reference functions) of every fuzzy set is called Angle of Fuzzy Set (AFS), and then in order to extend ranking of two fuzzy sets the angle of fuzzy sets and α-cuts is used. The method is illustrated by some numerical examples and in particular the results of ranking by the proposed method and some common and existing methods for ranking fuzzy sets is compared to verify the advantage of the new approach. In particular, based on the results of comparison of our method with well known methods which are exist in the literature, we will see that against of most existing ranking approaches, our proposed approach can rank fuzzy numbers that have the same mode and symmetric spreads. In fact, the proposed method in this paper can effectively rank symmetric fuzzy numbers as well as the effective methods which are appeared in the literature. Moreover, unlike of most existing ranking approaches, our proposed approach can rank non-normal fuzzy sets. Finally, we emphasize that the concept of fuzzy ordering is one of key role in establishing the numerical algorithms in operations research such as fuzzy primal simplex algorithms, fuzzy dual simplex algorithms and as well as discussed in the works of Ebrahimnejad and Nasseri and coworkers [1–7].
Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, each proposed method may has some shortcoming. So we are going to present a novel method based on the angle of the reference functions to cover a wide range of fuzzy quantities by over coming the draw backs of some existing methods. In the mentioned firstly, the angle between the left and right membership functions (the reference functions) of every fuzzy set is called Angle of Fuzzy Set (AFS), and then in order to extend ranking of two fuzzy sets the angle of fuzzy sets and [alpha]-cuts is used. The method is illustrated by some numerical examples and in particular the results of ranking by the proposed method and some common and existing methods for ranking fuzzy sets is compared to verify the advantage of the new approach. In particular, based on the results of comparison of our method with well known methods which are exist in the literature, we will see that against of most existing ranking approaches, our proposed approach can rank fuzzy numbers that have the same mode and symmetric spreads. In fact, the proposed method in this paper can effectively rank symmetric fuzzy numbers as well as the effective methods which are appeared in the literature. Moreover, unlike of most existing ranking approaches, our proposed approach can rank non-normal fuzzy sets. Finally, we emphasize that the concept of fuzzy ordering is one of key role in establishing the numerical algorithms in operations research such as fuzzy primal simplex algorithms, fuzzy dual simplex algorithms and as well as discussed in the works of Ebrahimnejad and Nasseri and coworkers [1-7],
Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge number of researches is attracted to this filed but until now there is any unique accepted method to rank the fuzzy quantities. In fact, each proposed method may has some shortcoming. So we are going to present a novel method based on the angle of the reference functions to cover a wide range of fuzzy quantities by over coming the draw backs of some existing methods. In the mentioned firstly, the angle between the left and right membership functions (the reference functions) of every fuzzy set is called Angle of Fuzzy Set (AFS), and then in order to extend ranking of two fuzzy sets the angle of fuzzy sets and alpha -cuts is used. The method is illustrated by some numerical examples and in particular the results of ranking by the proposed method and some common and existing methods for ranking fuzzy sets is compared to verify the advantage of the new approach. In particular, based on the results of comparison of our method with well known methods which are exist in the literature, we will see that against of most existing ranking approaches, our proposed approach can rank fuzzy numbers that have the same mode and symmetric spreads. In fact, the proposed method in this paper can effectively rank symmetric fuzzy numbers as well as the effective methods which are appeared in the literature. Moreover, unlike of most existing ranking approaches, our proposed approach can rank non-normal fuzzy sets. Finally, we emphasize that the concept of fuzzy ordering is one of key role in establishing the numerical algorithms in operations research such as fuzzy primal simplex algorithms, fuzzy dual simplex algorithms and as well as discussed in the works of Ebrahimnejad and Nasseri and coworkers , , , , , and .
Author Behmanesh, E.
Kardoost, M.
Nasseri, S.H.
Zadeh, M.M.
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  surname: Behmanesh
  fullname: Behmanesh, E.
  organization: Department of Mathematics, University of Mazandaran, Babolsar, Iran
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Cites_doi 10.1016/j.eswa.2007.05.009
10.1016/j.ins.2005.03.013
10.1016/j.camwa.2008.10.090
10.4018/joris.2011010105
10.1016/j.fss.2007.05.005
10.1016/j.eswa.2010.08.002
10.1080/01969720302866
10.1016/0165-0114(85)90012-0
10.1016/S0165-0114(96)00272-2
10.1504/EJIE.2012.046670
10.1016/0165-0114(85)90050-8
10.1080/01969720590961727
10.1016/j.camwa.2010.11.020
10.1016/0165-0114(93)90374-Q
10.1016/j.camwa.2007.07.015
10.1504/EJIE.2010.033336
10.1016/0020-0255(81)90017-7
10.1016/S0165-0114(98)00122-5
10.1016/S0898-1221(01)00277-2
10.1016/S0165-0114(83)80082-7
10.1504/EJIE.2010.031077
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Issue 22
Keywords Fuzzy quantities
Fuzzy ranking
α-Cut
Angle of fuzzy number
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References Ebrahimnejad, Nasseri, Hosseinzadeh Lotfi, Soltanifar (b0010) 2010; 4
Chen, Sanguansat (b0090) 2011; 38
Yager (b0100) 1981; 24
Thomas, Finney (b0120) 1972
Mahdavi-Amiri, Nasseri, Yazdani (b0025) 2009; 1
Chu, Tsao (b0070) 2002; 43
Nasseri (b0130) 2010; 4
Choobineh, Li (b0060) 1993; 54
Chen (b0055) 1985; 17
Wang, Lee (b0075) 2008; 55
Chen, Chen (b0140) 2003; 34
Deng, Liu (b0145) 2005; 36
Mahdavi-Amiri, Nasseri (b0020) 2007; 158
Jain (b0040) 1976; 6
Bortolan, Degani (b0050) 1985; 15
Van Larrhoven, Pedrycz (b0105) 1983; 11
Ebrahimnejad, Nasseri, Mansourzaded (b0015) 2011; 2
Nasseri, Attari, Ebrahimnejad (b0035) 2012; 6
Yao, Wu (b0125) 2000; 116
Dubois, Prade (b0045) 1980
Ebrahimnejad, Nasseri, Mansourzaded (b0005) 2012; 23
Abbasbandy, Hajjari (b0085) 2009; 57
Nasseri, Ebrahimnejad (b0030) 2010; 4
Nasseri, Sohrabi (b0135) 2010; 4
Lee, Chen (b0150) 2008; 34
Abbasbandy, Asady (b0080) 2006; 176
Nejad, Mashinchi (b0095) 2011; 61
Zimmermann (b0115) 1991
Kaufmann, Gupta (b0110) 1991
Cheng (b0065) 1998; 95
Chu (10.1016/j.apm.2013.04.002_b0070) 2002; 43
Abbasbandy (10.1016/j.apm.2013.04.002_b0080) 2006; 176
Ebrahimnejad (10.1016/j.apm.2013.04.002_b0010) 2010; 4
Jain (10.1016/j.apm.2013.04.002_b0040) 1976; 6
Nasseri (10.1016/j.apm.2013.04.002_b0135) 2010; 4
Chen (10.1016/j.apm.2013.04.002_b0140) 2003; 34
Ebrahimnejad (10.1016/j.apm.2013.04.002_b0015) 2011; 2
Zimmermann (10.1016/j.apm.2013.04.002_b0115) 1991
Nejad (10.1016/j.apm.2013.04.002_b0095) 2011; 61
Ebrahimnejad (10.1016/j.apm.2013.04.002_b0005) 2012; 23
Wang (10.1016/j.apm.2013.04.002_b0075) 2008; 55
Kaufmann (10.1016/j.apm.2013.04.002_b0110) 1991
Cheng (10.1016/j.apm.2013.04.002_b0065) 1998; 95
Mahdavi-Amiri (10.1016/j.apm.2013.04.002_b0025) 2009; 1
Lee (10.1016/j.apm.2013.04.002_b0150) 2008; 34
Chen (10.1016/j.apm.2013.04.002_b0090) 2011; 38
Nasseri (10.1016/j.apm.2013.04.002_b0030) 2010; 4
Van Larrhoven (10.1016/j.apm.2013.04.002_b0105) 1983; 11
Yao (10.1016/j.apm.2013.04.002_b0125) 2000; 116
Dubois (10.1016/j.apm.2013.04.002_b0045) 1980
Bortolan (10.1016/j.apm.2013.04.002_b0050) 1985; 15
Abbasbandy (10.1016/j.apm.2013.04.002_b0085) 2009; 57
Yager (10.1016/j.apm.2013.04.002_b0100) 1981; 24
Mahdavi-Amiri (10.1016/j.apm.2013.04.002_b0020) 2007; 158
Choobineh (10.1016/j.apm.2013.04.002_b0060) 1993; 54
Thomas (10.1016/j.apm.2013.04.002_b0120) 1972
Deng (10.1016/j.apm.2013.04.002_b0145) 2005; 36
Nasseri (10.1016/j.apm.2013.04.002_b0035) 2012; 6
Chen (10.1016/j.apm.2013.04.002_b0055) 1985; 17
Nasseri (10.1016/j.apm.2013.04.002_b0130) 2010; 4
References_xml – volume: 116
  start-page: 275
  year: 2000
  end-page: 288
  ident: b0125
  article-title: Ranking fuzzy numbers based on decomposition principle and signed distance
  publication-title: Fuzzy Sets Syst.
– volume: 6
  start-page: 698
  year: 1976
  end-page: 703
  ident: b0040
  article-title: Decision-making in the presence of fuzzy variable
  publication-title: IEEE Trans. Syst. Man Cybern.
– volume: 4
  start-page: 189
  year: 2010
  end-page: 209
  ident: b0010
  article-title: A primal dual method for linear programming problems with fuzzy variables
  publication-title: Eur. J. Ind. Eng.
– volume: 34
  start-page: 109
  year: 2003
  end-page: 137
  ident: b0140
  article-title: A new method for handling multicriteria fuzzy decision-making problems using FN-IOWA operators
  publication-title: Cybern. Syst.
– volume: 36
  start-page: 581
  year: 2005
  end-page: 595
  ident: b0145
  article-title: A TOPSIS-Based centroid-index ranking method of fuzzy numbers and its application in decision-making
  publication-title: Cybern. Syst.
– volume: 54
  start-page: 287
  year: 1993
  end-page: 294
  ident: b0060
  article-title: An index for ordering fuzzy numbers
  publication-title: Fuzzy Sets Syst.
– volume: 6
  start-page: 259
  year: 2012
  end-page: 280
  ident: b0035
  article-title: Revised simplex method and its application for solving fuzzy linear programming problem
  publication-title: Eur. J. Ind. Eng.
– volume: 1
  start-page: 68
  year: 2009
  end-page: 84
  ident: b0025
  article-title: Fuzzy primal simplex algorithms for solving fuzzy linear programming problems
  publication-title: Iran. J. Oper. Res.
– volume: 95
  start-page: 307
  year: 1998
  end-page: 317
  ident: b0065
  article-title: A new approach for ranking fuzzy numbers by distance method
  publication-title: Fuzzy Sets Syst.
– year: 1991
  ident: b0115
  article-title: Fuzzy Sets Theory and its Application
– volume: 38
  start-page: 2163
  year: 2011
  end-page: 2171
  ident: b0090
  article-title: Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers
  publication-title: Expert Syst. Appl.
– year: 1972
  ident: b0120
  article-title: Calculus and Analytic Geometry
– volume: 61
  start-page: 431
  year: 2011
  end-page: 442
  ident: b0095
  article-title: Ranking fuzzy numbers based on the areas on the left and right sides of fuzzy number
  publication-title: Comput. Math. Appl.
– volume: 4
  start-page: 3519
  year: 2010
  end-page: 3525
  ident: b0130
  article-title: Ranking trapezoidal fuzzy numbers by using Hadi method
  publication-title: Aust. J. Basic Appl. Sci.
– volume: 15
  start-page: 1
  year: 1985
  end-page: 19
  ident: b0050
  article-title: A review of some methods for ranking fuzzy numbers
  publication-title: Fuzzy Sets Syst.
– volume: 55
  start-page: 2033
  year: 2008
  end-page: 2042
  ident: b0075
  article-title: The revised method of ranking fuzzy numbers with an area between the centroid and original points
  publication-title: Comput. Math. Appl.
– volume: 34
  start-page: 2763
  year: 2008
  end-page: 2771
  ident: b0150
  article-title: Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations
  publication-title: Expert Syst. Appl.
– volume: 11
  start-page: 229
  year: 1983
  end-page: 241
  ident: b0105
  article-title: A fuzzy extension of satty’s priority theory
  publication-title: Fuzzy Sets Syst.
– volume: 2
  start-page: 100
  year: 2011
  end-page: 124
  ident: b0015
  article-title: Bounded primal simplex algorithm for bounded linear programming with fuzzy cost coefficients
  publication-title: Int. J. Oper. Res. Inf. Syst.
– volume: 43
  start-page: 11
  year: 2002
  end-page: 117
  ident: b0070
  article-title: Ranking fuzzy numbers with an area between the centroid point and original point
  publication-title: Comput. Math. Appl.
– volume: 57
  start-page: 413
  year: 2009
  end-page: 419
  ident: b0085
  article-title: A new approach for ranking of trapezoidal fuzzy numbers
  publication-title: Comput. Math. Appl.
– volume: 158
  start-page: 1961
  year: 2007
  end-page: 1976
  ident: b0020
  article-title: Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables
  publication-title: Fuzzy Sets Syst.
– volume: 17
  start-page: 113
  year: 1985
  end-page: 129
  ident: b0055
  article-title: Ranking fuzzy numbers with maximizing set and minimizing set
  publication-title: Fuzzy Sets Syst.
– volume: 176
  start-page: 2405
  year: 2006
  end-page: 2416
  ident: b0080
  article-title: Ranking of fuzzy numbers by sign distance
  publication-title: Inf. Sci.
– volume: 4
  start-page: 372
  year: 2010
  end-page: 389
  ident: b0030
  article-title: A fuzzy primal simplex algorithm and its application for solving the flexible linear programming problem
  publication-title: Eur. J. Ind. Eng.
– year: 1980
  ident: b0045
  article-title: Fuzzy Sets Systems: Theory and Applications
– year: 1991
  ident: b0110
  article-title: Introduction to Fuzzy Arithmetic: Theory and Application
– volume: 4
  start-page: 4630
  year: 2010
  end-page: 4637
  ident: b0135
  article-title: Hadi’s method and it’s advantage in ranking fuzzy numbers
  publication-title: Aust. J. Basic Appl. Sci.
– volume: 24
  start-page: 143
  year: 1981
  end-page: 161
  ident: b0100
  article-title: A procedure for ordering fuzzy subsets of the unit interval
  publication-title: Inf. Sci.
– volume: 23
  start-page: 1
  year: 2012
  end-page: 8
  ident: b0005
  article-title: Modified bounded dual network simplex algorithm for solving minimum cost flow problem with fuzzy costs based on ranking functions
  publication-title: J. Intell. Fuzzy Syst.
– volume: 34
  start-page: 2763
  year: 2008
  ident: 10.1016/j.apm.2013.04.002_b0150
  article-title: Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations
  publication-title: Expert Syst. Appl.
  doi: 10.1016/j.eswa.2007.05.009
– volume: 176
  start-page: 2405
  year: 2006
  ident: 10.1016/j.apm.2013.04.002_b0080
  article-title: Ranking of fuzzy numbers by sign distance
  publication-title: Inf. Sci.
  doi: 10.1016/j.ins.2005.03.013
– year: 1980
  ident: 10.1016/j.apm.2013.04.002_b0045
– volume: 57
  start-page: 413
  year: 2009
  ident: 10.1016/j.apm.2013.04.002_b0085
  article-title: A new approach for ranking of trapezoidal fuzzy numbers
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2008.10.090
– volume: 2
  start-page: 100
  issue: 1
  year: 2011
  ident: 10.1016/j.apm.2013.04.002_b0015
  article-title: Bounded primal simplex algorithm for bounded linear programming with fuzzy cost coefficients
  publication-title: Int. J. Oper. Res. Inf. Syst.
  doi: 10.4018/joris.2011010105
– volume: 6
  start-page: 698
  year: 1976
  ident: 10.1016/j.apm.2013.04.002_b0040
  article-title: Decision-making in the presence of fuzzy variable
  publication-title: IEEE Trans. Syst. Man Cybern.
– volume: 158
  start-page: 1961
  year: 2007
  ident: 10.1016/j.apm.2013.04.002_b0020
  article-title: Duality results and a dual simplex method for linear programming problems with trapezoidal fuzzy variables
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/j.fss.2007.05.005
– volume: 38
  start-page: 2163
  year: 2011
  ident: 10.1016/j.apm.2013.04.002_b0090
  article-title: Analyzing fuzzy risk based on a new fuzzy ranking method between generalized fuzzy numbers
  publication-title: Expert Syst. Appl.
  doi: 10.1016/j.eswa.2010.08.002
– year: 1991
  ident: 10.1016/j.apm.2013.04.002_b0110
– volume: 4
  start-page: 3519
  issue: 8
  year: 2010
  ident: 10.1016/j.apm.2013.04.002_b0130
  article-title: Ranking trapezoidal fuzzy numbers by using Hadi method
  publication-title: Aust. J. Basic Appl. Sci.
– volume: 1
  start-page: 68
  issue: 2
  year: 2009
  ident: 10.1016/j.apm.2013.04.002_b0025
  article-title: Fuzzy primal simplex algorithms for solving fuzzy linear programming problems
  publication-title: Iran. J. Oper. Res.
– year: 1991
  ident: 10.1016/j.apm.2013.04.002_b0115
– volume: 34
  start-page: 109
  issue: 2
  year: 2003
  ident: 10.1016/j.apm.2013.04.002_b0140
  article-title: A new method for handling multicriteria fuzzy decision-making problems using FN-IOWA operators
  publication-title: Cybern. Syst.
  doi: 10.1080/01969720302866
– volume: 15
  start-page: 1
  year: 1985
  ident: 10.1016/j.apm.2013.04.002_b0050
  article-title: A review of some methods for ranking fuzzy numbers
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(85)90012-0
– volume: 95
  start-page: 307
  year: 1998
  ident: 10.1016/j.apm.2013.04.002_b0065
  article-title: A new approach for ranking fuzzy numbers by distance method
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(96)00272-2
– volume: 6
  start-page: 259
  issue: 3
  year: 2012
  ident: 10.1016/j.apm.2013.04.002_b0035
  article-title: Revised simplex method and its application for solving fuzzy linear programming problem
  publication-title: Eur. J. Ind. Eng.
  doi: 10.1504/EJIE.2012.046670
– volume: 17
  start-page: 113
  issue: 2
  year: 1985
  ident: 10.1016/j.apm.2013.04.002_b0055
  article-title: Ranking fuzzy numbers with maximizing set and minimizing set
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(85)90050-8
– volume: 36
  start-page: 581
  issue: 6
  year: 2005
  ident: 10.1016/j.apm.2013.04.002_b0145
  article-title: A TOPSIS-Based centroid-index ranking method of fuzzy numbers and its application in decision-making
  publication-title: Cybern. Syst.
  doi: 10.1080/01969720590961727
– volume: 61
  start-page: 431
  issue: 2
  year: 2011
  ident: 10.1016/j.apm.2013.04.002_b0095
  article-title: Ranking fuzzy numbers based on the areas on the left and right sides of fuzzy number
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2010.11.020
– volume: 54
  start-page: 287
  year: 1993
  ident: 10.1016/j.apm.2013.04.002_b0060
  article-title: An index for ordering fuzzy numbers
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/0165-0114(93)90374-Q
– volume: 55
  start-page: 2033
  year: 2008
  ident: 10.1016/j.apm.2013.04.002_b0075
  article-title: The revised method of ranking fuzzy numbers with an area between the centroid and original points
  publication-title: Comput. Math. Appl.
  doi: 10.1016/j.camwa.2007.07.015
– volume: 4
  start-page: 372
  issue: 3
  year: 2010
  ident: 10.1016/j.apm.2013.04.002_b0030
  article-title: A fuzzy primal simplex algorithm and its application for solving the flexible linear programming problem
  publication-title: Eur. J. Ind. Eng.
  doi: 10.1504/EJIE.2010.033336
– volume: 23
  start-page: 1
  year: 2012
  ident: 10.1016/j.apm.2013.04.002_b0005
  article-title: Modified bounded dual network simplex algorithm for solving minimum cost flow problem with fuzzy costs based on ranking functions
  publication-title: J. Intell. Fuzzy Syst.
– volume: 24
  start-page: 143
  year: 1981
  ident: 10.1016/j.apm.2013.04.002_b0100
  article-title: A procedure for ordering fuzzy subsets of the unit interval
  publication-title: Inf. Sci.
  doi: 10.1016/0020-0255(81)90017-7
– year: 1972
  ident: 10.1016/j.apm.2013.04.002_b0120
– volume: 116
  start-page: 275
  year: 2000
  ident: 10.1016/j.apm.2013.04.002_b0125
  article-title: Ranking fuzzy numbers based on decomposition principle and signed distance
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(98)00122-5
– volume: 43
  start-page: 11
  year: 2002
  ident: 10.1016/j.apm.2013.04.002_b0070
  article-title: Ranking fuzzy numbers with an area between the centroid point and original point
  publication-title: Comput. Math. Appl.
  doi: 10.1016/S0898-1221(01)00277-2
– volume: 4
  start-page: 4630
  issue: 10
  year: 2010
  ident: 10.1016/j.apm.2013.04.002_b0135
  article-title: Hadi’s method and it’s advantage in ranking fuzzy numbers
  publication-title: Aust. J. Basic Appl. Sci.
– volume: 11
  start-page: 229
  year: 1983
  ident: 10.1016/j.apm.2013.04.002_b0105
  article-title: A fuzzy extension of satty’s priority theory
  publication-title: Fuzzy Sets Syst.
  doi: 10.1016/S0165-0114(83)80082-7
– volume: 4
  start-page: 189
  issue: 2
  year: 2010
  ident: 10.1016/j.apm.2013.04.002_b0010
  article-title: A primal dual method for linear programming problems with fuzzy variables
  publication-title: Eur. J. Ind. Eng.
  doi: 10.1504/EJIE.2010.031077
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Snippet Ordering fuzzy quantities and their comparison play a key tool in many applied models in the world and in particular decision-making procedures. However a huge...
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SubjectTerms Algorithms
Angle of fuzzy number
Fuzzy
Fuzzy logic
Fuzzy quantities
Fuzzy ranking
Fuzzy set theory
Fuzzy systems
Mathematical analysis
Mathematical models
Ranking
α-Cut
Title Ranking fuzzy quantities based on the angle of the reference functions
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