Multiobjective programming in optimization of the interval objective function

Ishibuchi, Hisao; Tanaka, Hideo

doi:10.1016/0377-2217(90)90375-l

Cited by 663 publications

(319 citation statements)

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“…Ishibuchi and Tanaka (1990) ranked the interval numbers more prominently and did not compare pairs of the interval numbers. Sengupta and Pal (2000) constructed a premise which implied that an interval number is inferior to the other interval numbers in terms of the values.…”

Section: The Comparison Of Different Interval Numbersmentioning

confidence: 99%

Limited public resources allocation model based on social fairness using an extended VIKOR method

Jiang

2016

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Article information:To cite this document: Wenqi Jiang, (2016) "Limited public resources allocation model based on social fairness using an extended VIKOR method", Kybernetes, Vol. 45 Issue: 7, pp.998-1012, https For AuthorsIf you would like to write for this, or any other Emerald publication, then please use our Emerald for Authors service information about how to choose which publication to write for and submission guidelines are available for all. Please visit www.emeraldinsight.com/authors for more information. About Emerald www.emeraldinsight.comEmerald is a global publisher linking research and practice to the benefit of society. The company manages a portfolio of more than 290 journals and over 2,350 books and book series volumes, as well as providing an extensive range of online products and additional customer resources and services.Emerald is both COUNTER 4 and TRANSFER compliant. The organization is a partner of the Committee on Publication Ethics (COPE) and also works with Portico and the LOCKSS initiative for digital archive preservation.*Related content and download information correct at time of download. Limited public resources allocation model based on social fairness using an extended VIKOR method Wenqi JiangNanjing University of Science and Technology, Nanjing, China Abstract Purpose -Different from manufacturing resources allocation problems, the prices and amounts of limited public service resources could not be changed with the consumers' requirements and social fairness is the most important objective for improving allocation efficiency. To measure social fairness reasonably, the purpose of this paper is fourfold: first, divide social fairness into longitudinal comparative fairness and crosswise comparative fairness, therefore providing their calculation formula and describing the comprehensive fair degree by using the interval numbers. Second, the comparison regulations of interval numbers are given and the corresponding features are also described. Third, an extension of VIKOR method is put forward for evaluating social fairness of different allocation alternatives with interval numbers. Finally, a numerical example illustrates the proposed method and clarifies the main results developed in the paper. Design/methodology/approach -In this paper, the author depicts the social fair degree as an interval number, and thus proposes the comparison method between any two interval numbers. Based on the basis procedure of the VIKOR method, the paper proposes an extension of the fuzzy VIKOR method with the interval numbers to rank and select the compromise allocation alternatives. Finally, a numerical example illustrates the practicability of the proposed method.Findings -The comparison of interval numbers is very important when the author evaluates the decision alternatives. Through analyzing the present comparison methods, the paper proposes the simple method of comparing the interval numbers, which can obtain the same results with the above two methods. The fuzzy VIKOR method, a popular multi-...

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Section: The Comparison Of Different Interval Numbersmentioning

confidence: 99%

Limited public resources allocation model based on social fairness using an extended VIKOR method

Jiang

2016

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“…Steuer [11] proposed three algorithms, called the F-cone algorithm, E-cone algorithm and all emanating algorithms to solve the linear programming problems with interval-valued objective functions. 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].…”

Section: Introductionmentioning

confidence: 99%

“…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 the interval objective function

Cited by 663 publications

References 5 publications

Limited public resources allocation model based on social fairness using an extended VIKOR method

Limited public resources allocation model based on social fairness using an extended VIKOR method

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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