An Improved Intuitionistic Fuzzy Set TOPSIS Method Based on a New Distance Measure with an Application to Marine Aquaculture Water Quality Evaluation

With the rapid development of intensive marine aquaculture, water quality has become a key factor affecting both economic benefits and ecological safety in marine aquaculture. In the process of actual water quality evaluation, due to the great uncertainty and ambiguity of evaluation indicators, experts find it difficult to evaluate in real number form and are more inclined to use linguistic variables to evaluate indicators, which poses challenges for the construction of water quality evaluation models. An intuitionistic fuzzy set (IFS) is an effective tool for dealing with uncertainty and fuzziness in complex problems. Based on a detailed analysis of existing distance measures for IFS, this study proposes a new distance measure that not only considers membership and non-membership information, but also constructs an allocation function for membership and non-membership, introducing hesitation information into distance metrics. We proposed the definitions and proved the properties. The comparative experiments show that the new distance measure can overcome the shortcomings of existing distance measures. Furthermore, based on the newly proposed distance measure, the IFS TOPSIS method is improved in multi-attribute decision-making applications. Finally, a practical application of marine aquaculture water quality evaluation is used. The results illustrate that when α = 1 the closeness declines from 0.741 to 0.432, when =2 the closeness declines from 0.662 to 0.46, and when =6 the closeness declines from 0.566 to 0.82. The convenience and effectiveness of the new method is demonstrated.