Pareto-optimal solutions for multi-objective flexible linear programming

作者: Dipti Dubey , Aparna Mehra

DOI: 10.3233/IFS-151778

关键词: Optimization problemSolution conceptLinear programmingRepresentation (mathematics)Fuzzy setSet (abstract data type)Mathematical optimizationConstraint (information theory)Interval (mathematics)Mathematics

摘要: The aim of this paper is twofold. Firstly, to define a solution concept Pareto-optimality for multi-objective flexible linear programming (MOFLP) problem (or fuzzy problem) and design method extract Pareto-optimal MOFLP from the set optimal solutions equivalent optimization formulated by Dubey Mehra (2013). Secondly, extend study involving hard constraints with interval uncertainty. A constraint uncertainty generalizes allowing preferences be expressed in form intervals. An optimistic-pessimistic approach proposed solve multi- objective (MOFLPIU) using an interval-valued representation Hurwicz optimism-pessimism criterion.

参考文章(31)
Brigitte M. Werners, Aggregation Models in Mathematical Programming Springer, Berlin, Heidelberg. pp. 295- 305 ,(1988) , 10.1007/978-3-642-83555-1_19
Edurne Barrenechea, Alberto Fernández, Francisco Herrera, Humberto Bustince, Construction of Interval-Valued Fuzzy Preference Relations Using Ignorance Functions: Interval-Valued Non Dominance Criterion Eurofuse. pp. 243- 255 ,(2011) , 10.1007/978-3-642-24001-0_23
RC Nayak, RK Panda, None, Integrated Management of a Canal Command in a River Delta using Multi-Objective Techniques Water Resources Management. ,vol. 15, pp. 383- 401 ,(2001) , 10.1023/A:1015593417769
Hirotaka Nakayama, Naoko Kagaku, Pattern Classification by Linear Goal Programming and its Extensions Journal of Global Optimization. ,vol. 12, pp. 111- 126 ,(1998) , 10.1023/A:1008244409770
Jiuping Xu, Xiaoyang Zhou, Fuzzy Multiple Objective Decision Making Springer Berlin Heidelberg. pp. 57- 133 ,(2011) , 10.1007/978-3-642-16895-6_2
Didier Dubois, Henri Prade, Gradualness, uncertainty and bipolarity: Making sense of fuzzy sets Fuzzy Sets and Systems. ,vol. 192, pp. 3- 24 ,(2012) , 10.1016/J.FSS.2010.11.007
Hsiao-Fan Wang, Miao-Ling Wang, A fuzzy multiobjective linear programming Fuzzy Sets and Systems. ,vol. 86, pp. 61- 72 ,(1997) , 10.1016/0165-0114(95)00393-2
Glad Deschrijver, Etienne E. Kerre, On the relationship between some extensions of fuzzy set theory Fuzzy Sets and Systems. ,vol. 133, pp. 227- 235 ,(2003) , 10.1016/S0165-0114(02)00127-6
S.S. Rao, K. Sundararaju, B.G. Prakash, C. Balakrishna, Multiobjective fuzzy optimization techniques for engineering design Computers & Structures. ,vol. 42, pp. 37- 44 ,(1992) , 10.1016/0045-7949(92)90534-7
Dipti Dubey, Suresh Chandra, Aparna Mehra, Fuzzy linear programming under interval uncertainty based on IFS representation Fuzzy Sets and Systems. ,vol. 188, pp. 68- 87 ,(2012) , 10.1016/J.FSS.2011.09.008