,z:t;OK.JIa,l.\H Ha B'hJlI'apcKaTa aKa,ll;eMIDI Ha HayKJITe Comptes rendus de l' Academie bulgare des Sciences Tome 62, No 5,2009 MATHEMATIQUES Sous-ensembles flous MODELS FOR FUZZY MULTICRITERIA DECISION MAKING BASED ON FUZZY RELATIONS Vania Peneva, Ivan Popchev (Submitted on March 16, 2009) . Abstract The paper presents models and corresponding algorithms for solving fuzzy multicriteria decision making problems. The models use or transform the initial information to fuzzy preference relations by each criterion. These relations possess required properties to solve the problems of choice or ordering of the alternatives. The weights of the criteria are real numbers or weighting functions. Key words: multicriteria decision making, fuzzy relations, aggregation operators, fuzzy relations' properties, weighting function 2000 Mathematics Subject Classification: 03E72 1. Introduction. The multicriteria decision making models in fuzzy envi- ronment are based on: • a finite set of alternatives, among which a decision maker has to choose (choice problem), or to rank (ranking problem), or to part (cluster problem); • a finite set of judges or criteria on the base of which the"alternatives are evaluated; • a criteria importance, i.e. weights of the criteria. The alternatives in decision making problems are usually evaluated from different points of views that correspond to particular criteria. criteria can be quantitative and qualitative ones. Usually quantitative criteria are assessed by means of crisp numerical values. The qualitative criteria are presented in This work was supported by the Bulgarian Academy of Sciences under grant 010077. 551