Development of Multi-Choice Goal Programming by Applying the Interval- Valued Fuzzy Principal Component Analysis for Goal Selection

Determining a unique goal in Goal Programming (GP) method for each objective function due to restriction of information is difficult and inefficient. To overcome this problem, a type of goal programing methods called multiple-choice goal programing has been developed, in which multiple levels introduced for each objective. In this paper, the goals are considered as alternatives, which decision-makers express their agreement or disagreement with them through interval-valued intuitive fuzzy numbers (IVIFNs). In the complex multi-attribute large-group decision making problems where attribute values are interval-valued fuzzy numbers, the number of decision attributes is often large and their correlation degrees are high, which increase the difficulty of decision making and thus influence the accuracy of the result. To integrate multiple opinion with a high degree of correlation and choosing a goal, a principal component analysis algorithm for interval-valued intuitive fuzzy numbers (IVIF-PCA) is applied. IVIF-PCA model represents major information of original attributes, effectively reduces the dimensions of attribute spaces, and synthesizes original attributes into several relatively independent comprehensive variables. The proposed approach has enabled to consider the opinions of decision makers with different interests in large groups and the degree of their Doubt in the model, also it can reduce the computational complexity through selecting a limited number of goals through a scientific and accurate method based on IVIF-PCA Algorithm. To evaluate the performance of the proposed mechanism, a numerical example is presented and solved. Previous approaches, in addition to their inability for considering the decision makers’ doubt degree in goal definition, require to identify several variables to take into account the aspirations set by a large group of decision makers, which increase the computational complexity. In contrast, the proposed approach in addition to considering the decision makers’ doubt degree in goal definition, reduce the computational complexity through IVIF- PCA Algorithm.