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 |
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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]. |
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| 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. |
| Author_xml | – sequence: 1 givenname: S.H. surname: Nasseri fullname: Nasseri, S.H. email: nasseri@umz.ac.ir organization: Department of Mathematics, University of Mazandaran, Babolsar, Iran – sequence: 2 givenname: M.M. surname: Zadeh fullname: Zadeh, M.M. organization: Department of Mathematics, University of Mazandaran, Babolsar, Iran – sequence: 3 givenname: M. surname: Kardoost fullname: Kardoost, M. organization: Young Researchers Club, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran – sequence: 4 givenname: E. 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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| 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 |
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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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