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In 1937 the Hungarian-born mathematician John von Neumann analyzed a steadily expanding economy based on alternative methods of production and fixed technological coefficients.
In this equation, A is the technological coefficients' matrix, y represents the vector of final demand and x is a vector that shows the level of output.
Dejuan et al. (2013) consider the impact of the prices of energy on technological coefficients, but in their analyses price evolvements are exogenous.
It is shown how the problem can be modeled and efficiently solved in a multi-phase approach in which objective function and technological coefficients are derived in the first phases and incorporated into the formulation and solution of a mathematical model in the final phase.
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B, C and e demonstrate random technological coefficient matrix and right- hand side vector, respectively.
The main objective of this research paper is to solve non-linear fuzzy optimization problem where the technological coefficient in the constraints involved are fuzzy numbers, which was represented by logistic membership functions using the hybrid evolutionary optimization approach.
Regarding the risk threatening estimated demands, all OF coefficients, technological multipliers, and right-hand side coefficients may take a vague quantity.
For instance, consider the following problem in which C ˜ ′ = c ˜ 1 ′, c ˜ 2 ′, … c ˜ n ′ Open image in new window, A ˜ ″ = a ˜ ij ″ m × n Open image in new window, and B ˜ ′ = b ˜ 1 ′, b ˜ ′, … b ˜ m ′ t Open image in new window are the fuzzy parameters representing the OF coefficients, technological multiplies, and right-hand side coefficients, respectively.
Table 4 Discriminant validity of the reflexive variables Constructs AVE AVE Square Root Correlation coefficient Technological capability Financial network Technological network Planning effort Technological capability 0.604 0.777 1 – – – Financial network 0.742 0.861 0.658 1 – – Technological network 0.623 0.789 0.774 0.527 1 – Planning effort 0.607 0.779 0.333 0.408 0.510 1.
Although this coefficient remains fixed, changes to the relative factor price change the physical input output coefficient, ξ ij (the technological structure), such that (a_{textit {ij}} = left (p_{i}/ p_{j} right) xi _{textit {ij}}), where p indicates price.
In terms of the specialized development of trade, it indicates that specialization is more helpful for technological innovation than equalization if the regression coefficient of the 60% quantile is less than that at the 40%and20%0% quantiles.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com