Solving Fuzzy Linear Programming Problems with Fuzzy Decision Variables

Wu, Chong

doi:10.3390/math7070569

Cited by 4 publications

(3 citation statements)

References 31 publications

(45 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, Chalco-Cano et al [17] and Pirzada and Pathak [18] proposed the Newton method to solve optimization problems with fuzzy coefficients. In general, solving optimization problems with fuzzy decision variables is a difficult task; a long paper by Wu [19] provides an efficient way to solve the fuzzy linear programming problems with fuzzy decision variables.…”

Section: Introductionmentioning

confidence: 99%

“…In this algorithm, each individual must be mutated. Each individual κ (j) is mutated in the way of (19) and is assigned to κ (j+p) for j = 1, • • • , p. We want to generate N(0, σ s ). In this paper, the standard deviation σ s is taken by…”

mentioning

confidence: 99%

“…where β s is a constant of proportionality to scale τ(κ (j) ) and ζ s represents an offset. According to (19), we obtain the mutated individual κ (j) must be mutated to be κ (j+p) for j = 1, • • • , p; after this step, we shall have 2p individuals κ (j)…”

mentioning

confidence: 99%

See 2 more Smart Citations

Solving Fuzzy Optimization Problems Using Shapley Values and Evolutionary Algorithms

2023

Mathematics

Self Cite

View full text Add to dashboard Cite

The fusion of evolutionary algorithms and the solution concepts of cooperative game theory is proposed in this paper to solve the fuzzy optimization problems. The original fuzzy optimization problem is transformed into a scalar optimization problem by assigning some suitable coefficients. The assignment of those coefficients is frequently determined by the decision-makers via their subjectivity, which may cause some biases. In order to avoid these subjective biases, a cooperative game is formulated by considering the α-level functions of the fuzzy objective function. Using the Shapley values of this formulated cooperative game, the suitable coefficients can be reasonably set up. Under these settings, the transformed scalar optimization problem is solved to obtain the nondominated solution, which will depend on the coefficients. In other words, we shall obtain a bunch of nondominated solutions depending on the coefficients. Finally, the evolutionary algorithms are invoked to find the best nondominated solution by evolving the coefficients.

show abstract

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%