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This study evaluates the assignment system by FMCDM for Turkish Army Forces (TAF). TAF personnel are assigned to Garrisons (a headquarter or a certain geographical place in Turkey), for fixed periods. Selecting the optimal Garrison is an important problem for personnel, and is based on a number of alternatives and criteria. The system includes eight city centers, evaluated as alternatives. For defining the criteria, a questionnaire is designed and applied to army officers and sergeants. The criteria weights are determined by four randomly selected experts. Experts described the weights depending on their assessments, which may vary depending on their own necessities, experiences and priorities. They used linguistic weights, such as "very good, good, medium, low, very low". Hence, the assessments are away from certainty. This uncertainty implies fuzziness in weights. Besides, the criteria were determined by factor analysis, applied on the responses of the questionnaire, which also gives a sense of uncertainty. In the analysis under imprecision judgements, the criteria weights are presented as trapezoidal fuzzy numbers to get more reasonable and realistic solutions. Ideal and anti-ideal points are calculated for different optimism indexes and the final results are obtained based on these points. It is observed that different optimality indexes changed the rankings of alternatives.

As international corporate activities increase, the staffing of their operations involves more strategic concerns. However, foreign assignments have many differences, and dissatisfaction with host country is a known cause of expatriate failure. This study distinguishes from previous studies, which focused on the expatriate selection process from the viewpoint of the human resource managers. From the view of expatriate candidate's points, this paper describes a fuzzy analytic hierarchy process (fuzzy AHP) to determine the weighting of subjective judgments. When the expatriate assignments are evaluated from various aspects, such as employee personal factors, employee competencies, job characteristics, family factors, environmental factors and organization relocation support activities, it can be regarded as an fuzzy multiple criteria decision making (FMCDM) problem. Since expatriate candidates cannot clearly estimate the relative importance of each considered criterion in terms of numerical values, fuzziness is applicable. Consequently, this paper uses triangular fuzzy numbers by fuzzy AHP to establish weights for expatriate candidates, thus determining the relative importance for criteria of expatriate assignments. From the insights of this study, this article addresses this expatriate problem and offers guidelines for managers concerned with a successful expatriate assignment program.

To encompass uncertainty and vagueness of information, the analytic hierarchy process (AHP) was often extended into fuzzy multi-criteria decision-making (FMCDM) under an uncertain environment. However, the extension of AHP was rarely constructed on interval-valued fuzzy numbers. Recently, interval-valued fuzzy numbers were utilized for decision-making to obtain more messages than others. For AHP extended under a fuzzy environment into fuzzy AHP, fuzzy computations are critical to derive priorities of pairwise comparison matrices. Although AHP’s approximate computations including the normalization of row arithmetic averages may be adopted to the fuzzy environment, the fuzzy extension of AHP is still complicated for division and multiplication of fuzzy numbers, especially interval-valued fuzzy numbers. To resolve complicated ties, a utility representation function of interval-valued fuzzy numbers in fuzzy AHP is used for yielding vectors consisting of priority representations of fuzzy pairwise comparison matrices on evaluation criteria based on objective, alternatives based on evaluation criteria, and more hierarchies. Then, sum product of multiplying the priority representation vectors is derived to form the utility representations of alternative performance indices, and alternative performance indices are represented by their corresponding utility representations. Therefore, FMCDM problems are easily solved by fuzzy AHP, i.e., combining AHP with the utility representation function under an interval-valued fuzzy environment.

This work applies the Fuzzy Multiple Criteria Decision Making (FMCDM) approach to assist in making stock investment decisions. The proposed approach applies to quantitative data and can accommodate qualitative information which is normally difficult to be integrated by traditional finance and accounting methods. A major-sub-criteria hierarchy is established to reduce the possibility of over-weighing some dependent criteria existing in a single-level structure. The ratings of stocks versus qualitative sub-criteria and the weights of major and sub-criteria are assessed in linguistic terms represented by fuzzy numbers. Each sub-criterion is in a benefit, cost, or balanced nature. New standardization methods for cost-nature and balanced-nature criteria are presented. The algorithms of membership functions of the final aggregation are derived from the roots of cubic equations of multiplications of triple fuzzy numbers. Since these algorithms are clearly developed, the investor can easily calculate the fuzzy aggregation values. The defuzzified final aggregation judges the performance of alternative stocks. Moreover, the ratio of the market price to performance (PP) is suggested to filter the over and under-pricing of alternative stocks. A set of buying and selling rules are recommended based on the performance and PP ratio. Finally, an empirical example of evaluating a set of TSE-listed stocks tests the proposed approach.