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Mathematical Problems in Engineering
Volume 2017, Article ID 8605652, 9 pages
Research Article

An Improvement for Fuzzy Stochastic Goal Programming Problems

1Department of Hotel Management, Lee-Ming Institute of Technology, New Taipei, Taiwan
2Department of Computer Science and Information Management, Hungkuang University, Taichung, Taiwan
3Department of Traffic Science, Central Police University, Taoyuan, Taiwan

Correspondence should be addressed to Peterson Julian; moc.liamg@82344nailujnosretep

Received 2 January 2017; Revised 5 June 2017; Accepted 11 June 2017; Published 25 July 2017

Academic Editor: Leonid Shaikhet

Copyright © 2017 Shu-Cheng Lin et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We examined the solution process for linear programming problems under a fuzzy and random environment to transform fuzzy stochastic goal programming problems into standard linear programming problems. A previous paper that revised the solution process with the lower-side attainment index motivated our work. In this paper, we worked on a revision for both-side attainment index to amend its definition and theorems. Two previous examples were used to examine and demonstrate our improvement over previous results. Our findings not only improve the previous paper with both-side attainment index, but also provide a theoretical extension from lower-side attainment index to the both-side attainment index.