Min-Max Programming Problem Subject to Addition-Min Fuzzy Relation Inequalities

A BitTorrent-like peer-to-peer file-sharing system can be reduced into a system of addition-min fuzzy relation inequalities. Addition-min is a new composition, and the solution set of addition-min fuzzy relation inequalities differs much from that of general max-t-norm fuzzy relation inequalities or equations. In order to avoid network congestion and improve the stability of data transmission, a min-max programming problem is proposed subject to addition-min fuzzy relation inequalities in this paper. Based on some relevant theorems on resolution, a novel algorithm is developed step by step to find an optimal solution of the proposed problem. Moreover, an application example is given to illustrate the feasibility and efficiency of the algorithm. Finally, some further discussions are made concerning the optimal solution of the proposed problem.

[1]  Yan-Kuen Wu,et al.  Minimizing a linear function under a fuzzy max-min relational equation constraint , 2005, Fuzzy Sets Syst..

[2]  Dan Meng,et al.  An algorithm for solving optimization problems with fuzzy relational inequality constraints , 2013, Inf. Sci..

[3]  Shao-Jun Yang,et al.  An algorithm for minimizing a linear objective function subject to the fuzzy relation inequalities with addition-min composition , 2014, Fuzzy Sets Syst..

[4]  Wen-June Wang,et al.  Matrix-pattern-based computer algorithm for solving fuzzy relation equations , 2003, IEEE Trans. Fuzzy Syst..

[5]  Bih-Sheue Shieh,et al.  Minimizing a linear objective function under a fuzzy max-t norm relation equation constraint , 2011, Inf. Sci..

[6]  B. Baets.  Analytical solution methods for fuzzy relational equations. , 2000 .

[7]  XueGang Zhou,et al.  Geometric programming problem with single-term exponents subject to max-product fuzzy relational equations , 2011, Math. Comput. Model..

[8]  Bing-yuan Cao,et al.  The more-for-less paradox in fuzzy posynomial geometric programming , 2012, Inf. Sci..

[9]  Shu-Cherng Fang,et al.  Solving nonlinear optimization problems with fuzzy relation equation constraints , 2001, Fuzzy Sets Syst..

[10]  C. Bing-yuan.  Fuzzy Geometric Programming , 2002 .

[11]  Esmaile Khorram,et al.  Monomial geometric programming with fuzzy relation inequality constraints with max-product composition , 2009, Comput. Ind. Eng..

[12]  Yuzhen Wang,et al.  A Matrix Approach to Latticized Linear Programming With Fuzzy-Relation Inequality Constraints , 2013, IEEE Transactions on Fuzzy Systems.

[13]  G. Klir,et al.  Resolution of finite fuzzy relation equations , 1984 .

[14]  B. Cao,et al.  Geometric programming with max-product fuzzy relation equation constraints , 2005, NAFIPS 2005 - 2005 Annual Meeting of the North American Fuzzy Information Processing Society.

[15]  Jianxin Li.  A new algorithm for minimizing a linear objective function with fuzzy relation equation constraints , 2008, Fuzzy Sets Syst..

[16]  Yan-Kuen Wu.  Optimizing the geometric programming problem with single-term exponents subject to max-min fuzzy relational equation constraints , 2008, Math. Comput. Model..

[17]  Shu-Cherng Fang,et al.  On the unique solvability of fuzzy relational equations , 2011, Fuzzy Optim. Decis. Mak..

[18]  Jian-Xin Li,et al.  Fuzzy relation inequalities about the data transmission mechanism in BitTorrent-like Peer-to-Peer file sharing systems , 2012, 2012 9th International Conference on Fuzzy Systems and Knowledge Discovery.

[19]  E. Babolian,et al.  Numerical solution of fuzzy max-min systems , 2006, Appl. Math. Comput..

[20]  Esmaile Khorram,et al.  Solving nonlinear optimization problems subjected to fuzzy relation equation constraints with max-average composition using a modified genetic algorithm , 2008, Comput. Ind. Eng..

[21]  Bih-Sheue Shieh,et al.  Linear optimization problem constrained by fuzzy max-min relation equations , 2013, Inf. Sci..

[22]  Yang Ji-hui,et al.  Geometric Programming with Fuzzy Relation Equation Constraints , 2006 .

[23]  Jiranut Loetamonphong,et al.  Optimization of fuzzy relation equations with max-product composition , 2001, Fuzzy Sets Syst..

[24]  W. Pedrycz,et al.  Fuzzy relation equations on a finite set , 1982 .

[25]  Li Jian-Xin.  A new algorithm for minimizing a linear objective function with fuzzy relation equation constraints , 2008 .

[26]  Da Ruan,et al.  Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part I , 1997, Fuzzy Sets Syst..

[27]  Dhaneshwar Pandey,et al.  Satisficing solutions of multi-objective fuzzy optimization problems using genetic algorithm , 2012, Appl. Soft Comput..

[28]  Da Ruan,et al.  Novel neural algorithms based on fuzzy δ rules for solving fuzzy relation equations: Part III , 2000, Fuzzy Sets Syst..

[29]  Wen-June Wang,et al.  New algorithms for solving fuzzy relation equations , 2002, Math. Comput. Simul..

[30]  Elie Sanchez,et al.  Resolution of Composite Fuzzy Relation Equations , 1976, Inf. Control..

[31]  Chi-Tsuen Yeh,et al.  On the minimal solutions of max-min fuzzy relational equations , 2008, Fuzzy Sets Syst..

[32]  Cheng Lichun,et al.  The fuzzy relation equation with union or intersection preserving operator , 1988 .

[33]  George J. Klir,et al.  Fuzzy sets and fuzzy logic - theory and applications , 1995 .

[34]  Jun-Lin Lin,et al.  On fuzzy relational equations and the covering problem , 2011, Inf. Sci..

[35]  Bing-yuan Cao,et al.  Optimal Models and Methods with Fuzzy Quantities , 2010, Studies in Fuzziness and Soft Computing.

[36]  Jihui Yang,et al.  Monomial geometric programming with fuzzy relation equation constraints , 2007, Fuzzy Optim. Decis. Mak..

[37]  Shu-Cherng Fang,et al.  Latticized Linear Optimization on the Unit Interval , 2009, IEEE Transactions on Fuzzy Systems.

[38]  Paul P. Wang,et al.  Fuzzy relation equations (I): the general and specialized solving algorithms , 2002, Soft Comput..

[39]  Pei-Zhuang Wang,et al.  Latticized linear programming and fuzzy relation inequalities , 1991 .