Skip to main content
Top

2021 | OriginalPaper | Chapter

9. A New Type of Possibility Degree of Interval Number and Its Application in Interval Optimization

Authors : Chao Jiang, Xu Han, Huichao Xie

Published in: Nonlinear Interval Optimization for Uncertain Problems

Publisher: Springer Singapore

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

This chapter first proposes a new possibility degree model of interval number to realize quantitative comparison for not only overlapping intervals but also separate intervals, and then applies it to the nonlinear interval optimization.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Sengupta A, Pal TK (2009) Fuzzy preference ordering of interval numbers in decision problems. Springer, Berlin HeidelbergCrossRef Sengupta A, Pal TK (2009) Fuzzy preference ordering of interval numbers in decision problems. Springer, Berlin HeidelbergCrossRef
2.
go back to reference Moore RE (1966) Interval analysis. Prentice-Hall, New JerseyMATH Moore RE (1966) Interval analysis. Prentice-Hall, New JerseyMATH
3.
go back to reference Moore RE (1979) Methods and applications of interval analysis. Prenice-Hall, LondonCrossRef Moore RE (1979) Methods and applications of interval analysis. Prenice-Hall, LondonCrossRef
4.
go back to reference Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225CrossRef Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48(2):219–225CrossRef
5.
go back to reference Chanas S, Kuchta D (1996a) Multiobjective programming in optimization of interval objective functions—a generalized approach. Eur J Oper Res 94(3):594–598CrossRef Chanas S, Kuchta D (1996a) Multiobjective programming in optimization of interval objective functions—a generalized approach. Eur J Oper Res 94(3):594–598CrossRef
6.
go back to reference Chanas S, Kuchta D (1996b) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets Syst 82(3):299–305MathSciNetCrossRef Chanas S, Kuchta D (1996b) A concept of the optimal solution of the transportation problem with fuzzy cost coefficients. Fuzzy Sets Syst 82(3):299–305MathSciNetCrossRef
7.
go back to reference Nakahara Y, Sasaki M, Gen M (1992) On the linear programming problems with interval coefficients. Comput Ind Eng 23(1–4):301–304CrossRef Nakahara Y, Sasaki M, Gen M (1992) On the linear programming problems with interval coefficients. Comput Ind Eng 23(1–4):301–304CrossRef
8.
go back to reference Sevastjanov P, Venberg A (1998) Modelling and simulation of power units work under interval uncertainty. Energy 3:66–70 Sevastjanov P, Venberg A (1998) Modelling and simulation of power units work under interval uncertainty. Energy 3:66–70
9.
go back to reference Sevastjanov PV, Rog P (2003) A probabilistic approach to fuzzy and crisp interval ordering. Task Quart 7(1):147–156 Sevastjanov PV, Rog P (2003) A probabilistic approach to fuzzy and crisp interval ordering. Task Quart 7(1):147–156
10.
go back to reference Wagman D, Schneider M, Shnaider E (1994) On the use of interval mathematics in fuzzy expert systems. Int J Intell Syst 9(2):241–259CrossRef Wagman D, Schneider M, Shnaider E (1994) On the use of interval mathematics in fuzzy expert systems. Int J Intell Syst 9(2):241–259CrossRef
11.
go back to reference Kundu S (1997) Min-transitivity of fuzzy leftness relationship and its application to decision making. Fuzzy Sets Syst 86(3):357–367MathSciNetCrossRef Kundu S (1997) Min-transitivity of fuzzy leftness relationship and its application to decision making. Fuzzy Sets Syst 86(3):357–367MathSciNetCrossRef
12.
go back to reference Kundu S (1998) Preference relation on fuzzy utilities based on fuzzy leftness relation on intervals. Fuzzy Sets Syst 97(2):183–191MathSciNetCrossRef Kundu S (1998) Preference relation on fuzzy utilities based on fuzzy leftness relation on intervals. Fuzzy Sets Syst 97(2):183–191MathSciNetCrossRef
13.
go back to reference Sevastianov P, Róg P, Venberg A (2001) The constructive numerical method of interval comparison. In: PPAM Sevastianov P, Róg P, Venberg A (2001) The constructive numerical method of interval comparison. In: PPAM
14.
go back to reference Sevastianov P, Róg P, Karczewski K (2002) A probabilistic method for ordering group of intervals. Informatyka Teoretyczna I Stosowana 2(2):45–53 Sevastianov P, Róg P, Karczewski K (2002) A probabilistic method for ordering group of intervals. Informatyka Teoretyczna I Stosowana 2(2):45–53
15.
go back to reference Yager RR, Detyniecki M, Bouchon-Meunier B (2001) A context-dependent method for ordering fuzzy numbers using probabilities. Inf Sci 138(1):237–255MathSciNetCrossRef Yager RR, Detyniecki M, Bouchon-Meunier B (2001) A context-dependent method for ordering fuzzy numbers using probabilities. Inf Sci 138(1):237–255MathSciNetCrossRef
16.
go back to reference Sevastjanow P (2004) Interval comparison based on dempster-shafer theory of evidence. In: Wyrzykowski R, Dongarra J, Paprzycki M, Waśniewski J (eds) Parallel processing and applied mathematics: 5th international conference, PPAM 2003, Czestochowa, Poland, September 7–10, 2003. Revised Papers. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 668–675 Sevastjanow P (2004) Interval comparison based on dempster-shafer theory of evidence. In: Wyrzykowski R, Dongarra J, Paprzycki M, Waśniewski J (eds) Parallel processing and applied mathematics: 5th international conference, PPAM 2003, Czestochowa, Poland, September 7–10, 2003. Revised Papers. Springer Berlin Heidelberg, Berlin, Heidelberg, pp 668–675
17.
go back to reference Sevastjanov P, Róg P (2006) Two-objective method for crisp and fuzzy interval comparison in optimization. Comput Oper Res 33(1):115–131CrossRef Sevastjanov P, Róg P (2006) Two-objective method for crisp and fuzzy interval comparison in optimization. Comput Oper Res 33(1):115–131CrossRef
18.
go back to reference Jiang C, Han X, Liu GR, Liu GP (2008) A nonlinear interval number programming method for uncertain optimization problems. Eur J Oper Res 188(1):1–13MathSciNetCrossRef Jiang C, Han X, Liu GR, Liu GP (2008) A nonlinear interval number programming method for uncertain optimization problems. Eur J Oper Res 188(1):1–13MathSciNetCrossRef
20.
go back to reference Sengupta A, Pal TK, Chakraborty D (2001) Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets Syst 119(1):129–138CrossRef Sengupta A, Pal TK, Chakraborty D (2001) Interpretation of inequality constraints involving interval coefficients and a solution to interval linear programming. Fuzzy Sets Syst 119(1):129–138CrossRef
21.
go back to reference Wang YM, Yang JB, Xu DL (2005) A preference aggregation method through the estimation of utility intervals. Comput Oper Res 32(8):2027–2049CrossRef Wang YM, Yang JB, Xu DL (2005) A preference aggregation method through the estimation of utility intervals. Comput Oper Res 32(8):2027–2049CrossRef
22.
go back to reference Sun HL, Yao WX (2008) The basic properties of some typical systems’ reliability in interval form. Struct Saf 30(4):364–373CrossRef Sun HL, Yao WX (2008) The basic properties of some typical systems’ reliability in interval form. Struct Saf 30(4):364–373CrossRef
23.
go back to reference Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13(7):613–622CrossRef Facchinetti G, Ricci RG, Muzzioli S (1998) Note on ranking fuzzy triangular numbers. Int J Intell Syst 13(7):613–622CrossRef
24.
go back to reference Liu XW, Da QL (1999) A satisfactory solution for interval linear programming. J Syst Eng 14(2):123–128MathSciNet Liu XW, Da QL (1999) A satisfactory solution for interval linear programming. J Syst Eng 14(2):123–128MathSciNet
25.
go back to reference Abbasi MA, Khorram E (2008) Linear programming problem with interval coefficients and an interpretation for its constraints. Iran J Sci Tech (Sci) 32(4):369–390MathSciNetMATH Abbasi MA, Khorram E (2008) Linear programming problem with interval coefficients and an interpretation for its constraints. Iran J Sci Tech (Sci) 32(4):369–390MathSciNetMATH
26.
go back to reference Tseng TY, Klein CM (1989) New algorithm for the ranking procedure in fuzzy decision-making. IEEE Trans Syst Man Cyber 19(5):1289–1296CrossRef Tseng TY, Klein CM (1989) New algorithm for the ranking procedure in fuzzy decision-making. IEEE Trans Syst Man Cyber 19(5):1289–1296CrossRef
27.
go back to reference Xu ZS, Da QL (2003) Possibility degree method for ranking interval numbers and its application. J Syst Eng 18(1):67–70 Xu ZS, Da QL (2003) Possibility degree method for ranking interval numbers and its application. J Syst Eng 18(1):67–70
28.
go back to reference Jiang C, Han X, Li D (2012) A new interval comparison relation and application in interval number programming for uncertain problems. Comput Mater Contin 27(3):275–303 Jiang C, Han X, Li D (2012) A new interval comparison relation and application in interval number programming for uncertain problems. Comput Mater Contin 27(3):275–303
29.
go back to reference Hu YD (1990) Practical multi-objective optimization. Shanghai Technological Press, Shanghai Hu YD (1990) Practical multi-objective optimization. Shanghai Technological Press, Shanghai
30.
31.
go back to reference Jiang C, Bai YC, Han X, Ning HM (2010) An efficient reliability-based optimization method for uncertain structures based on non-probability interval model. Comput Mater Contin (CMC) 18(1):21–42 Jiang C, Bai YC, Han X, Ning HM (2010) An efficient reliability-based optimization method for uncertain structures based on non-probability interval model. Comput Mater Contin (CMC) 18(1):21–42
32.
go back to reference Elishakoff I, Haftka RT, Fang J (1994) Structural design under bounded uncertainty—optimization with anti-optimization. Comput Struct 53(6):1401–1405CrossRef Elishakoff I, Haftka RT, Fang J (1994) Structural design under bounded uncertainty—optimization with anti-optimization. Comput Struct 53(6):1401–1405CrossRef
Metadata
Title
A New Type of Possibility Degree of Interval Number and Its Application in Interval Optimization
Authors
Chao Jiang
Xu Han
Huichao Xie
Copyright Year
2021
Publisher
Springer Singapore
DOI
https://doi.org/10.1007/978-981-15-8546-3_9

Premium Partner