Abstract
Practical nonlinear programming problem often encounters uncertainty and indecision due to various factors that cannot be controlled. To overcome these limitations, fully fuzzy rough approaches are applied to such a problem. In this paper, an effective two approaches are proposed to solve fully fuzzy rough multi-objective nonlinear programming problems (FFRMONLP) where all the variables and parameters are fuzzy rough triangular numbers. The first, based on a slice sum technique, a fully fuzzy rough multi-objective nonlinear problem has turned into five equivalent multi-objective nonlinear programming (FFMONLP) problems. The second proposed method for solving FFRMONLP problems is α-cut approach, where the triangular fuzzy rough variables and parameters of the FFRMONLP problem are converted into rough interval variables and parameters by α-level cut, moreover the rough MONLP problem turns into four MONLP problems. Furthermore, the weighted sum method is used in both proposed approaches to convert multi-objective nonlinear problems into an equivalent nonlinear programming problem. Finally, the effectiveness of the proposed procedure is demonstrated by numerical examples.
Highlights
There are many 1-D optimum path problems existing in universal and diary life
This paper aims to set up relationship between the 1-D optimum path problem and the “Principle of Minimum
The optimum path problem of 1-D two end-points A and B fixed is reduced to an optimum of an vector integral equation of Fredholm type, i.e
Summary
There are many 1-D (one dimension) optimum path problems existing in universal and diary life. Optimum path in logistics navigation, optimum path in military design-attacking target, optimum path in wind moving track, and typhoon track, etc. The 1-D optimum path problem with constraint(s), usually, it can be changed to un-constraint problem by method of Lagrange multipliers [3]. The optimum problem of integrand with given scalar function have been summery in mathematical hand books, e.g., [4]. There are many principles on energy relating to mechanical problems or relating to scientific problems. These principles have no connection with the optimum path problem
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