Tomada de decisão em grupo e multi-atributos baseada na Lógica fuzzy intuicionista de Atanassov intervalarmente valorada

Abstract

Fuzzy logic emerged in 1965 with the work of Lotfi Zadeh that aims rigorously deal with the uncertainty inherent in the definition of notions and inaccurate or vague properties in several everyday situations, such as high temperature, sharp drop, etc. For this, Zadeh considered a degree (a value in the range [0,1]) in order to express how much an element belongs to a set, i.e. satisfies a given property. However, some criticism of this theory have been made, mainly because that this theory deal with uncertainties using exact values, which led to several researchers (including himself Zadeh) in 1975 and independently, to extend this theory relaxing the set where the membership degrees take their values. One of these extensions, interval-valued Atanassov’s intuitionistic fuzzy logic, proposed in 1989 by Atanassov and Gargov, uses a pair of subintervals of [0,1], the first represent how much, considering some inaccuracy, it is believed that the element satisfies the property while the second describes how much it is believed that does not satisfy the property. This pair of interval degrees aim to capture the hesitation and inaccuracy present at the time of assigning the degree to which the element satisfies the property. Fuzzy logic and its various extensions, has been successfully applied in various areas, such as: medicine, engineering, agriculture, economics and management. In particular, one of the main applications of fuzzy logic in management concerns with the support to the decision making. A typical decision-making problem is the choice of the best alternative among a set of them or the obtention of a ranking of the alternatives, considering some criteria to be satisfied, as well as the opinion of one or more experts. The fuzzy methods for decision making problems based on decision matrices, use fuzzy degrees (or of their extensions) to express how much an alternative satisfies a particular attribute or criterion. On the other hand, the methods of fuzzy decision making problems based on preference relations, use fuzzy degrees (or of their extensions) to express how much an alternative is preferred to other alternative. In both cases, the opinion of all experts is aggregated to determine only a single decision matrix or preference relation, according be the case, and from them extract a score (which can be a numeric value or not) in order to decide which is the potentially best alternative. In this thesis are presents significant theoretical advances in the theory of intervalvalued Atanassov’s intuitionistic fuzzy sets as well as are proposed two new decisionmaking methods, considering multiple attributes (or criteria) and a group of experts, these methods are applyed on specific problems and made a comparison with the results obtained by others decision-making methods. On the other hand, one of the major problems with the methods or processes of decision-making is that, when applied to real problems, in general, can not determine the quality of the solution (ranking of the alternatives) obtained by the method. In fact, different decision making methods to the same problem may result in different solutions. In this thesis, it is proposed to consider the results obtained by different methods (independent of the fuzzy extension considered and of the type of decision-making problem) as information that can be used by another method capable of determining a ranking of the alternatives representing the fusion or consensus of these rankings.