Linear Programming Method for Solving Semi-Latticized Fuzzy Relation Geometric Programming with Max-Min Composition

被引：25

作者：

Yang, Xiao-Peng ^{[1
]}

机构：

[1] Hanshan Normal Univ, Dept Math & Stat, Chaozhou 521041, Guangdong, Peoples R China

来源：

INTERNATIONAL JOURNAL OF UNCERTAINTY FUZZINESS AND KNOWLEDGE-BASED SYSTEMS | 2015年 / 23卷 / 05期

基金：

中国博士后科学基金;

关键词：

Fuzzy relation equation; geometric programming; latticized programming; max-min composition; nonlinear optimization; Peer-to-Peer network system; RELATION EQUATION CONSTRAINTS; RELATION INEQUALITY CONSTRAINTS; NONLINEAR OPTIMIZATION PROBLEMS; OBJECTIVE FUNCTION; PRODUCT COMPOSITION; ALGORITHM; SUBJECT; RECONSTRUCTION; SYSTEM; IMAGES;

D O I：

10.1142/S0218488515500348

中图分类号：

TP18 [人工智能理论];

学科分类号：

081104 ; 0812 ; 0835 ; 1405 ;

摘要：

Motivated by application in BitTorrent-like Peer-to-Peer resource sharing system, we introduce the maximization and minimization semi-latticized fuzzy relation geometric programming problems with max-min composition in this paper. The objective function in the proposed problem in nonlinear and the feasible domain is non-convex. The maximization problem is converted into a fuzzy relation monomial geometric programming and then solved. However, this approach is not effective for the minimization one. The linear programming method is applied to deal with the minimization problem. A step-to-step algorithm is develop to carried out the linear programming method and tow illustrative examples are provided at last.

引用

页码：781 / 804

页数：24

共 46 条

[1] Numerical solution of fuzzy max-min systems
Abbasbandy, S
Babolian, E
Allame, M
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 174 (02) : 1321 - 1328
[2] Iteration algorithm for solving Ax = b in max-min algebra
Allame, Masould
Vatankhahan, Behnaz
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 175 (01) : 269 - 276
[3] [Anonymous], 2010, OPTIMAL MODELS METHO
[4] Linear optimization problem constrained by fuzzy max-min relation equations
Chang, Cheung-Wen
Shieh, Bih-Sheue
[J]. INFORMATION SCIENCES, 2013, 234 : 71 - 79
[5] Chen L., 2002, Soft Computing, V6, P428, DOI 10.1007/S00500-001-0157-3
[6] FUZZY RELATION EQUATIONS ON A FINITE-SET
CZOGALA, E
DREWNIAK, J
PEDRYCZ, W
[J]. FUZZY SETS AND SYSTEMS, 1982, 7 (01) : 89 - 101
[7] Lukasiewicz transform and its application to compression and reconstruction of digital images
Di Nola, A.
Russo, C.
[J]. INFORMATION SCIENCES, 2007, 177 (06) : 1481 - 1498
[8] Di Nola A., 1989, Fuzzy Relation Equations and Their Applications to Knowledge Engineering
[9] Solving fuzzy relation equations with a linear objective function
Fang, SC
Li, GZ
[J]. FUZZY SETS AND SYSTEMS, 1999, 103 (01) : 107 - 113
[10] Solving a linear programming problem with the convex combination of the max-min and the max-average fuzzy relation equations
Ghodousian, A.
Khorram, E.
[J]. APPLIED MATHEMATICS AND COMPUTATION, 2006, 180 (01) : 411 - 418

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