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

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.

KEYWORDS:

• Fuzzy numbers
• fuzzy programming
• multi-objective programming
• compromise allocation
• stratified sampling
• travel cost

SUBJECT CLASSIFICATION CODES:

• 90C70
• 90C29
• 90C30
• 49M37

Acknowledgements

The authors are grateful to the editor and anonymous referees for a careful checking of the details and for fruitful comments that improved the quality of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.