Extended GRA-Based MADM Strategy With Single-Valued Trapezoidal Neutrosophic Numbers

Multi-attribute decision-making(MADM) strategy has been proposed to handle uncertain decision-making problems. The most extensively used models of grey system theory is grey relational analysis (GRA). This strategy was flourished by Chinese Professor J. Deng. This strategy also known as Deng's grey incidence analysis model. GRA uses a generic concept of intelligence. It describes any circumstance as no information as black and perfect information as white. Nevertheless, these idealized situations appear in real-world problems. In this chapter, the authors extend GRA strategy for multi-attribute decision making in trapezoidal neutrosophic number (TrNN) environment. To develop a GRA strategy in trapezoidal neutrosophic number (TrNN) environment, the authors use score function and accuracy function. Then Hamming distance for two trapezoidal neutrosophic number (TrNN) are also described. The authors solve a numerical problem to explain the pertinence of the proposed strategy. Lastly, they provide a comparison between VIKOR strategy with existing strategy.

An Approach to Solve the Linear Programming Problem Using Single Valued Trapezoidal Neutrosophic Number

While making a decision, the neutrosophic set theory includes the uncertainty part beside certainty part (i.e., Yes or No). In the present uncertain socio-economic fashion, this pattern is highly acceptable and hence, the limitations of fuzzy set and intuitionistic fuzzy set are overcome with neutrosophic set theory. The present study provides a modified structure of linear programming problem (LP-problem) and its solution approach in neutrosophic sense. A special type of neutrosophic set defined over the set of real number, viz., single valued trapezoidal neutrosophic number (SVTN-number) is adopted here as the coefficients of the objective function, right-hand side coefficients and decision variables itself of an LP-problem. In order to solve such problem, a parameter based ranking function of SVTN-number is newly constructed from the geometrical configuration of the trapezium. It plays a key role in the development of the solution algorithm. An LP-problem is normally solved under the asset of some given constraints. Besides that, there may be some hidden parameters (e.g., awareness level of nearer society for the smooth run of a clinical pharmacy, ruined structure of road to be met a profit from a bus, etc) of an LP-problem and these affect the solution badly when experts ignore them. This study makes an attempt to solve an LP-problem by giving importance to all these to attain a fair outcome. The efficiency of the proposed concept is illustrated in a real field. A real example is stated and is solved numerically under the present view.