Supplier selection decisions are usually made by multiple decision makers according to multiple criteria. A method combining the technique for preference by similarity to ideal solution (TOPSIS) and 0-1 programming was proposed for supplier selection in supply chain management. First, the priority orders of suppliers under each criteria given by individual decision makers were aggregated to the ranking orders in the group's view by TOPSIS considering weights of decision makers. Then, the final integrated ranking orders of all suppliers were derived from the group's priority orders of them with respect to each criteria by 0-1 programming. A numerical example was presented to demonstrate the application of the proposed method and the comparisons of the results have shown the method is effective.

Aiming at the triangular fuzzy (TF) multi-attribute decision making (MADM) problem with a preference for the distribution density of attribute (DDA), a decision making method with TF number two-dimensional density (TFTD) operator is proposed based on the density operator theory for the decision maker (DM). Firstly, a simple TF vector clustering method is proposed, which considers the feature of TF number and the geometric distance of vectors. Secondly, the least deviation sum of squares method is used in the program model to obtain the density weight vector. Then, two TFTD operators are defined, and the MADM method based on the TFTD operator is proposed. Finally, a numerical example is given to illustrate the superiority of this method, which can not only solve the TF MADM problem with a preference for the DDA but also help the DM make an overall comparison.

The TOPSIS and Cook-Seiford social choice function are generalized and integrated for multicriteria group decision-making (MCGDM) with both cardinal evaluations and ordinal preferences of the alternatives. Unlike traditional TOPSIS, at first, the group’s positive ideal solution and negative ideal solution under cardinal and ordinal preferences are defined, respectively. Thus the group rankings of the alternatives with respect to each criterion are derived from the individual preferences by the modified group TOPSIS considering the weights of decision makers under each criterion. Then the weighted distance function representing the total inconsistency between the comprehensive rankings of all alternatives and the ones under all criteria is presented after the criteria weights are taken into account. Form the perspective of minimizing the criteria-weighted distance of the rankings, a nonlinear integer programming is developed and transformed into an assignment problem to obtain the final rankings of all alternatives. An illustrative case is presented and some comparisons on the results show that the developed approach is practical and effective. This study extends TOPSIS to group decision-making with ordinal preferences and generalizes Cook-Seiford social choice function to multicriteria decision-making considering the criteria weights and can be a novel benchmark for MCGDM with both cardinal and ordinal data.

Distance and similarity measures are very important in clustering, pattern recognition, decision-making and other scientific fields. For the existing hesitant fuzzy distance, most of them do not consider the hesitance degree. Even if the hesitance degree is considered, only the degree of dispersion or the number of hesitant fuzzy values are considered. Aiming at these shortages, a new hesitance degree is defined, which has better accuracy and applicability. Then, some hesitant fuzzy distance measures based on the proposed hesitance degree are proposed, which can overcome some shortcomings of the existing distance measures. Finally, the new hesitant fuzzy distance is applied to the hierarchical hesitant fuzzy k-means clustering algorithm, and an illustration example is given to illustrate the effectiveness of the proposed method.

The problem of how to make good use of the expenditure of books procurement is discussed. The authors present a pattern for books procurement decision-making which takes into account both the values of books and the requirements of the readers, and develop the mathematical models for books estimate, budget allocation by subject, and books selection in every single subject. Then a decision support system for books purchase based on the library automation system is developed and which is benefit to improve the quality of books procurement.