Solving fuzzy inequalities with concave membership functions

Hu, Cheng-Feng; Fang, Shu‐Cherng

doi:10.1016/s0165-0114(97)00013-4

Cited by 15 publications

(9 citation statements)

References 7 publications

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“…Moreover, an algorithm for fuzzy linear programming with piecewise linear membership functions was presented by Inuiguchi et al [18]. A group of inequalities with fuzzy numbers, their membership functions are linear, were investigated by Hu and Fang [19]. They turned fuzzy inequalities into convex programming problems.…”

Section: Introductionmentioning

confidence: 99%

“…Wang and Liao [23,24] established fuzzy variational inequalities based on fuzzy convex cone and fuzzy resolution. For some related works associated with variational inequalities, discontinuous implicit quasi-variational inequalities with applications to fuzzy mappings, linear programming with fuzzy coefficients in constraints, maximum feasibility problems for continuous linear inequalities with applications to fuzzy linear programming, and bilevel decision with generalized semi-infinite optimization for fuzzy mappings as lower level problems, we refer the reader to [15,16,[19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34]. In [35], the authors discussed the existence of a solution to the fuzzy variational-like inequality and some extended properties of the fuzzy variational-like inequality were found.…”

Section: Introductionmentioning

confidence: 99%

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A Class of Nonlinear Fuzzy Variational Inequality Problems

Jia

Liou

2019

Mathematics

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In this paper, we consider nonlinear variational inequality problems with fuzzy variables. The fuzzy variables were introduced to deal with the variational inequality containing noise for which historical data is not available. The fuzzy expected residual minimization (FERM) problems were established. We discussed the S C 1 property of the FERM model. Furthermore, results of convergence analysis were obtained based on an approximation model of the FERM model. The convergence of global optimal solutions and the convergence of stationary points were analysed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Class of Nonlinear Fuzzy Variational Inequality Problems

Jia

Liou

2019

Mathematics

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“…Recently, Hu and Fang [15] studied a system of fuzzy inequalities with linear membership functions which can be converted to a regular convex programming problem. Fang and Hu [16] and Hu [17][18][19] introduced and studied some fuzzy variational inequalities in a fuzzy environment, and proved the existence of the optimal solution for the fuzzy variational inequalities by using the tolerance approach and the entropic regularization technique.…”

Section: Introductionmentioning

confidence: 99%

An approach for solving fuzzy implicit variational inequalities with linear membership functions

Lan

2008

Computers & Mathematics with Applications

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In this paper, we consider a class of fuzzy implicit variational inequalities with linear membership functions. By using the "tolerance approach", we show that solving such problems can be reduced to a semi-infinite programming problem. A version of the "method of centres" with "entropic regularization" techniques, only used a quasi-Newton line search using MATLAB software is required in our implementation. We also give a numerical example to illustrate the validity of our approach.

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“…The entropy regularization procedure approximates the max function by a certain "smooth function" [6,7]. Problem (9) is equivalent to the following '"in-max" problem:…”

Section: Entropy Regularization Proceduresmentioning

confidence: 99%

“…For (9), because the objective is non-differentiable in general, so we solve it with "entropy regularization procedure" [7,6], although it can not get the optimal solution exactly, but it can transforms (9) into a one continuous objective programming problem with one constraint. For (lo), it can be solved with the ordinary nonlinear programming approach, and its constraints can also be transformed into one.…”

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confidence: 99%

A note on the interdependence of the objectives and their entropy regularization solution

Liu

Qing-li

Chen

Proceedings of the 2003 International Conference on Machine Learning and Cybernetics (IEEE Cat. No.03EX693)

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Considering that the concept of interdependence concept proposed by Carlsson and Fnll'er [If$], we found that it can only be applied to one dimension decision space, In this paper, we generalize the concept of objectives interdependence under the multidimensional conditions based on the gradients of the objectives. The new interdependence concept can reflect both the relationship and the degrees of the objectives' support or conflict. Then the application functions are constructed based on the interdependence grades of the objectives, and they are aggregated by entropy regularization procedure to solve the multiobjective programming problems. A numerical example shows the effect of the approach.

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Solving fuzzy inequalities with concave membership functions

Cited by 15 publications

References 7 publications

A Class of Nonlinear Fuzzy Variational Inequality Problems

A Class of Nonlinear Fuzzy Variational Inequality Problems

An approach for solving fuzzy implicit variational inequalities with linear membership functions

A note on the interdependence of the objectives and their entropy regularization solution

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