Multiobjective programming in optimization of interval objective functions — A generalized approach

Chanas, Stefan; Kuchta, Dorota

doi:10.1016/0377-2217(95)00055-0

Cited by 217 publications

(116 citation statements)

References 2 publications

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“…a y c x 0 a y c x 0 (P) Max z = [29,31]x + [22,24]x + [28,30]x subject to constraints 6x + 5x + 3x [25,27] 4x + 2x + 5x [6,8] and x , x , x 0.…”

Section: Resultsmentioning

confidence: 99%

“…Min w [25,27]y + [6,8]y subject to constraints 6y + 4y [29,31] 5y + 2y [22,24] 3y + 5y [28,30] Max z 30,1 x + 23,1 x + 29,1 x + 0s + 0s subject to constraints 6x + 5x + 3x + s + 0s 26,1 4x + 2x + 5x + 0s + s 7,1 and x , x , x ,s ,s 0. …”

Section: Resultsmentioning

confidence: 99%

“…Linear programming problems with interval coefficients have been studied by several authors, such as Atanu Sengupta et al [2,3], Bitran [5], Chanas and Kuchta [6], Nakahara et al [20], Steuer [26] and Tong Shaocheng [31]. Numerous methods for comparison of interval numbers can be found as in Atanu Sengupta and Tapan Kumar Pal [2,3], Ganesan and Veeramani [8,9] etc.…”

Section: Introductionmentioning

confidence: 99%

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Duality Theory for Interval Linear Programming Problems

Ramesh¹

2012

IOSR-JM

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“…a y c x 0 a y c x 0 (P) Max z = [29,31]x + [22,24]x + [28,30]x subject to constraints 6x + 5x + 3x [25,27] 4x + 2x + 5x [6,8] and x , x , x 0.…”

Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Duality Theory for Interval Linear Programming Problems

Ramesh¹

2012

IOSR-JM

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“…Ishibuchi and Tanaka [12] focused their study on an extremum problem whose objective function has interval coefficients and proposed the ordering relation between two closed intervals by considering the maximization and minimization problems separately. In [13], Chanas and Kuchta presented an approach to unify the solution methods proposed by Ishibuchi and Tanaka [12]. Jiang et al [14] suggested to solve the nonlinear interval number programming problem with uncertain coefficients both in nonlinear objective function and nonlinear constraints.…”

Section: Introductionmentioning

confidence: 99%

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

Antczak

2017

J Optim Theory Appl

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In the paper, the classical exact absolute value function method is used for solving a nondifferentiable constrained interval-valued optimization problem with both inequality and equality constraints. The property of exactness of the penalization for the exact absolute value penalty function method is analyzed under assumption that the functions constituting the considered nondifferentiable constrained optimization problem with the interval-valued objective function are convex. The conditions guaranteeing the equivalence of the sets of LU-optimal solutions for the original constrained interval-valued extremum problem and for its associated penalized optimization problem with the interval-valued exact absolute value penalty function are given.Keywords Interval-valued optimization problem · Exact absolute value penalty function method · Penalized optimization problem with the interval-valued exact absolute value penalty function · Exactness of the exact absolute value penalty function method · LU-convex function Mathematics Subject Classification 49M30 · 90C25 · 90C30Communicated by

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“…This paper is focused on the application of interval valued intuitionistic fuzzy numbers in mathematical optimization problems. In the field of interval linear programming, Ishibuchi and Tanaka (1990), Inuiguchi and Sakawa (1995), Chanas and Kuchta (1996), Chinneck and Ramadan (2000) or Sengupta et al (2001) developed different procedures to deal with these problems. Some frameworks were proposed to solve multi-objective problems with interval parameters by Ida (1999) or Wang and Wang (2001).…”

Section: Introductionmentioning

confidence: 99%

A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

Vidhya

Hepzibah

2017

International Journal of Applied Mathematics and Computer Science

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In a real world situation, whenever ambiguity exists in the modeling of intuitionistic fuzzy numbers (IFNs), interval valued intuitionistic fuzzy numbers (IVIFNs) are often used in order to represent a range of IFNs unstable from the most pessimistic evaluation to the most optimistic one. IVIFNs are a construction which helps us to avoid such a prohibitive complexity. This paper is focused on two types of arithmetic operations on interval valued intuitionistic fuzzy numbers (IVIFNs) to solve the interval valued intuitionistic fuzzy multi-objective linear programming problem with pentagonal intuitionistic fuzzy numbers (PIFNs) by assuming different α and β cut values in a comparative manner. The objective functions involved in the problem are ranked by the ratio ranking method and the problem is solved by the preemptive optimization method. An illustrative example with MATLAB outputs is presented in order to clarify the potential approach.Keywords: pentagonal intuitionistic fuzzy number, interval valued intuitionistic fuzzy number, interval valued intuitionistic fuzzy arithmetic, modified interval valued intuitionistic fuzzy arithmetic, interval valued intuitionistic fuzzy multi-objective linear programming problem.

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Multiobjective programming in optimization of interval objective functions — A generalized approach

Cited by 217 publications

References 2 publications

Duality Theory for Interval Linear Programming Problems

Duality Theory for Interval Linear Programming Problems

Exactness Property of the Exact Absolute Value Penalty Function Method for Solving Convex Nondifferentiable Interval-Valued Optimization Problems

A comparative study on interval arithmetic operations with intuitionistic fuzzy numbers for solving an intuitionistic fuzzy multi–objective linear programming problem

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