In this paper, a decision model based on a fuzzy soft set and ideal solution approaches is proposed. This new decision-making method uses the divide-and-conquer algorithm, and it is different from the existing algorithm (the choice value based approach and the comparison score based approach). The ideal solution is generated according to each attribute (pros or cons of the attributes, with or without constraints) of the fuzzy soft sets. Finally, the weighted Hamming distance is used to compute all possible alternatives and get the final result. The core of the decision process is the design phase, the existing decision models based on soft sets mostly neglect the analysis of attributes and decision objectives. This algorithm emphasizes the correct expression of the purpose of the decision maker and the analysis of attributes, as well as the explicit decision function. Additionally, this paper shows the fact that the rank reversal phenomenon occurs in the comparison score algorithm, and an example is provided to illustrate the rank reversal phenomenon. Experiments indicate that the decision model proposed in this paper is efficient and will be useful for practical problems. In addition, as a general model, it can be extended to a wider range of fields, such as classifications, optimization problems, etc.

The processing of uncertain information is increasingly becoming a hot topic in the artificial intelligence field, and the information measures of uncertainty information processing are also becoming of importance. In the process of decision-making, decision-makers make decisions mostly according to information measures such as similarity, distance, entropy, and cross-entropy in order to choose the best one. However, we found that many researchers apply cross-entropy to multi-attribute decision-making according to the minimum principle, which is in accordance with the principle of distance measures. Thus, among all the choices, we finally chose the one with the smallest cross-entropy (distance) from the ideal one. However, the relation between cross-entropy and distance measures in fuzzy sets or neutrosophic sets has not yet been verified. In this paper, we mainly consider the relation between the discrimination measure of fuzzy sets and distance measures, where we found that the fuzzy discrimination satisfied all the conditions of distance measure; that is to say, the fuzzy discrimination was found to be consistent with distance measures. We also found that the cross-entropy, which improved when it was based on the fuzzy discrimination, satisfied all the conditions of distance measure, and we finally proved that cross-entropy, including fuzzy cross-entropy and neutrosophic cross-entropy, was also a distance measure.