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Abstract
In this study, a novel algorithm is developed to solve the multi-level multiobjective fractional programming problems, using the idea of a neutrosophic fuzzy set. The co-efficients in each objective functions is assumed to be rough intervals. Furthermore, the objective functions are transformed into two sub-problems based on lower and upper approximation intervals. The marginal evaluation of pre-determined neutrosophic fuzzy goals for all objective functions at each level is achieved by different membership functions, such as truth, indeterminacy/neutral, and falsity degrees in neutrosophic uncertainty. In addition, the neutrosophic fuzzy goal programming algorithm is proposed to attain the highest degrees of each marginal evaluation goals by reducing their deviational variables and consequently obtain the optimal solution for all the decision-makers at all levels. To verify and validate the proposed neutrosophic fuzzy goal programming techniques, a numerical example is adressed in a hierarchical decision-making environment along with the conclusions.
Highlights
Most often, the mathematical programming problems consist of only one decision-maker who takes the decisions all alone
The proposed neutrosophic fuzzy goal programming (NFGP) solution algorithm provides an extension of the work presented by [1, 18, 21] and [24] under neutrosophic environment which deals with multi-level multiobjective fractional programming problems
The neutrosophic goals of each objective function at each level and the vector-set of neutrosophic goals for the decision variables monitored by t-th level decision makers can be stated as follows: oij(y) < ̃ lij, i = 1, 2, ..., t, j = 1, 2, ..., mi and yi = ̃ yii∗, i = 1, 2, ..., t − 1 where < ̃ and = ̃ represents the degree of neutrosophy of the aspiration levels
Summary
The mathematical programming problems consist of only one decision-maker who takes the decisions all alone. Rough linear programming is proposed by [16, 23, 24] and they introduced two solutions concepts as surely interval and possibly range for the existance of optimal solution Many researchers such as [3, 4, 17, 19, 20, 28] have worked on intuitionistic fuzzy and neutrosophic research domain. The proposed NFGP solution algorithm provides an extension of the work presented by [1, 18, 21] and [24] under neutrosophic environment which deals with multi-level multiobjective fractional programming problems It extend the work of [27] by introducing the NFGP algorithm to MLPPs with a multiple fractional objective at various level. The final model entertains the marginal evaluations for the described neutrosophic goals of the objective functions and the constraints at all levels which are determined separately for each level except the follower
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