Fuzzy multi-objective optimization for optimum allocation in multivariate stratified sampling with quadratic cost and parabolic fuzzy numbers

This article deals with the uncertainties in a multivariate stratified sampling problem. The uncertain parameters of the problem, such as stratum standard deviations, measurement costs, travel costs and total budget of the survey, are considered as parabolic fuzzy numbers and the problem is formulat...

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Published in:Journal of statistical computation and simulation Vol. 87; no. 12; pp. 2372 - 2383
Main Authors: Gupta, Neha, Bari, Abdul
Format: Journal Article
Language:English
Published: Abingdon Taylor & Francis 13.08.2017
Taylor & Francis Ltd
Subjects:
Allocations
Budgeting
compromise allocation
Cost function
Fuzzy numbers
fuzzy programming
Fuzzy sets
Marketing
multi-objective programming
Multiple objective analysis
Nonlinear programming
Optimization
Parameter uncertainty
Sampling
stratified sampling
travel cost
ISSN:0094-9655, 1563-5163
Online Access:Get full text
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Abstract This article deals with the uncertainties in a multivariate stratified sampling problem. The uncertain parameters of the problem, such as stratum standard deviations, measurement costs, travel costs and total budget of the survey, are considered as parabolic fuzzy numbers and the problem is formulated as a fuzzy multi-objective nonlinear programming problem with quadratic cost function. Using α-cut, parabolic fuzzy numbers are defuzzified and then the compromise allocations of the problem are obtained by fuzzy programming for a prescribed value of α. To demonstrate the utility of the proposed problem a numerical example is solved with the help of [LINGO User?s Guid. Lindo Systems Inc., 1415 North Dayton Street, Chicago,Illinois-60622, (USA), 2013] software and the derived compromise optimum allocation is compared with deterministic and proportional allocations.
AbstractList This article deals with the uncertainties in a multivariate stratified sampling problem. The uncertain parameters of the problem, such as stratum standard deviations, measurement costs, travel costs and total budget of the survey, are considered as parabolic fuzzy numbers and the problem is formulated as a fuzzy multi-objective nonlinear programming problem with quadratic cost function. Using α-cut, parabolic fuzzy numbers are defuzzified and then the compromise allocations of the problem are obtained by fuzzy programming for a prescribed value of α. To demonstrate the utility of the proposed problem a numerical example is solved with the help of [LINGO User?s Guid. Lindo Systems Inc., 1415 North Dayton Street, Chicago,Illinois-60622, (USA), 2013] software and the derived compromise optimum allocation is compared with deterministic and proportional allocations.
Author Bari, Abdul
Gupta, Neha
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  givenname: Abdul
  surname: Bari
  fullname: Bari, Abdul
  organization: Department of Statistics & Operations Research, Aligarh Muslim University
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SubjectTerms Allocations
Budgeting
compromise allocation
Cost function
Fuzzy numbers
fuzzy programming
Fuzzy sets
Marketing
multi-objective programming
Multiple objective analysis
Nonlinear programming
Optimization
Parameter uncertainty
Sampling
stratified sampling
travel cost
Title Fuzzy multi-objective optimization for optimum allocation in multivariate stratified sampling with quadratic cost and parabolic fuzzy numbers
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