A Kind of Nonlinear Programming Problem Based on Mixed Fuzzy Relation Equations Constraints

Li, Jinquan; Shuang, Feng; Mi, Honghai

doi:10.1016/j.phpro.2012.05.276

Cited by 4 publications

(6 citation statements)

References 20 publications

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“…It is not difficult to see that the mixed fuzzy relation equation (MFRE) expressed by Li et al (2012) can also be viewed as MFRI. Consequently, MFRE can be seen as a special case of MFRI.…”

Section: Formulation Of Mfri Programming Problem and Motivations Behimentioning

confidence: 99%

“…Consequently, MFRE can be seen as a special case of MFRI. MFRE has only been studied by Li et al (2012) and Feng et al (2012) up to now. The MFRI structure and the problem (1)- (5) have not been studied in the literature up to now.…”

Section: Formulation Of Mfri Programming Problem and Motivations Behimentioning

confidence: 99%

“…Recently, Li et al (2012) investigated a kind of nonlinear programming problem with a non-differential objective function subject to a system of MFREs with the max-min and the max-product composition operator. They presented some properties of the optimization problem and designed a polynomial-time algorithm to solve this problem based on the properties.…”

Section: Relevant Literature Review and Motivationsmentioning

confidence: 99%

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Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

Molai

2014

Soft Comput

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This paper studies the minimization problem of a linear objective function subject to mixed fuzzy relation inequalities (MFRIs) over finite support with regard to max-T 1 and max-T 2 composition operators, where T 1 and T 2 are two pseudo-t-norms. We first determine the structure of its feasible domain and then show that the solution set of a MFRI system is determined by a maximum solution and a finite number of minimal solutions. Moreover, sufficient and necessary conditions are proposed to check whether the feasible domain of the problem is empty or not. The MFRI path is defined to determine the minimal solutions of its feasible domain. The resolution process of the optimization problem is also designed based on the structure of its feasible domain. Procedures are proposed to reduce the size of the problem. With regard to the above points and the procedures, an algorithm is designed to solve the problem. Its application is expressed in the area of investing and covering. Finally, the algorithm is compared with other approaches.

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“…It is not difficult to see that the mixed fuzzy relation equation (MFRE) expressed by Li et al (2012) can also be viewed as MFRI. Consequently, MFRE can be seen as a special case of MFRI.…”

Section: Formulation Of Mfri Programming Problem and Motivations Behimentioning

confidence: 99%

Section: Formulation Of Mfri Programming Problem and Motivations Behimentioning

confidence: 99%

Section: Relevant Literature Review and Motivationsmentioning

confidence: 99%

See 1 more Smart Citation

Linear optimization with mixed fuzzy relation inequality constraints using the pseudo-t-norms and its application

Molai

2014

Soft Comput

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show abstract

“…This kind of system is called Mixed Bipolar Fuzzy Relation Equations (MBFREs). Recently, Li et al [17] investigated a kind of nonlinear programming problem with a non-differential objective function subject to a system of MFREs with the max-min and the max-product composition operator. They presented some properties of the optimization problem and designed a polynomial-time algorithm to solve this problem based on the properties.…”

Section: Introductionmentioning

confidence: 99%

“…With regard to the importance of MFREs [1,10,17] and BFREs [11,20,21], we consider the linear optimization problem with BFRE constraints with max-parametric hamacher composition operators and bipolar variables, simultaneously. In this problem, the composition operator of each its constraint can be associated to a different members of the parametric hamacher family.…”

Section: Introductionmentioning

confidence: 99%