The subject of this work is to establish a mathematical framework that provides the basis and tool for synthesis and evaluation analysis in decision making, especially from the logic point of view. This paper focuses on a flexible and realistic approach, i.e., the use of linguistic assessment in decision making, specially, the symbolic approach acts by direct computation on linguistic values. A lattice-valued linguistic algebra model, which is based on a logical algebraic structure, i.e., lattice implication algebra, is applied to represent imprecise information and deal with both comparable and incomparable linguistic values (i.e., non-ordered linguistic values). Within this framework, some known weighted aggregation functions are analyzed and extended to deal with these kinds of lattice-value linguistic information.

Performance appraisal is a process used for some firms in order to evaluate the employees' efficiency and productivity for planning their promotion policy. Initially this process was carried out just by the executive staff, but recently it has evolved to an evaluation process based on the opinion of different reviewers, supervisors, collaborators, clients and the employee himself (360-degree method). In such a evaluation process the reviewers evaluate some indicators related to the employee performance appraisal. The sets of Reviewers involve in the evaluation process might have different degree of knowledge about the evaluated employee. It then seems suitable to offer a flexible framework in which different reviewers can express their assessments in different domains according to their knowledge, i.e., an heterogeneous evaluation framework. The final aim is to design an performance appraisal model in such a framework that computes a final evaluation for each employee. That will be used by the management team to make their decisions regarding their incentive and promotion policy.

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