The aim of this research paper is to derive the solution of a problem related to flux condition involving the multivariable H-function.

The TOPSIS method, commonly known as the technique for order performance by similarity to ideal solutions, is one of the most popular approaches used in the multi-attribute decision making (MADM). In this method has some advantages are simplicity, rationality, comprehensibility, good computational efficiency and ability to measure the relative performance for each alternative in a simple mathematical form. In the last four decades world is getting warmer. It is whether the cause of human activity or natural variability. The thermometer reading all round the world have risen steadily since the beginning of the industrial revolution. According to the ongoing temperature analysis conducted by scientist at NASA’s Goddard Institute for Space Studies (GISS), the average global temperature on the Earth has increased about 0.80 Celsius since 1880. So, applying this method to determines the best solution from a set of alternatives with certain attributes. The best alternative is chosen based on its Euclidean distance from the ideal solution. The aim of this paper to systematizes the knowledge within the scope of techniques of decision taking with the use of the TOPSIS method. Simple numerical examples that reference real situations show practical applications of different aspects of this method.

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The Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) is a multi-criteria decision analysis method which is currently one of the most popular methods and has been shown to provide helpful outputs in various application areas. In this paper, we identify the set of important parameters of the decision making system and concept of TOPSIS, and calculate the distance of each alternative from the shortest geometric distance from positive ideal solution (SGDFPIS) and longest geometric distance from negative ideal solution (LGDFNIS). Finally, we use a numerical experiment to illustrate the procedure of the proposed approach.