Aggreagation operators in fuzzy decision making and applications

Multiple Attribute Decision Making refers to select the most desirable option among a finitenumber of options (alternatives) using attributes to evaluate the alternatives. Real lifesituations are not stable and generally data is uncertain, incomplete or imprecise. Fuzzy settheory is a good tool to deal with such problems. In fuzzy set theory, an element belongs to aset with a certain degree of membership. The degree of membership specifies the extent towhich a given element belongs to a set or is related to a concept. Aggregation operatorsreduce a set of numbers into a unique, representative or meaningful number. In order toprovide an overall score from scores which represent degrees of satisfaction, aggregationoperators are used. A large number of aggregation operators exist in literature. When makinga decision, decision makers may have a behavior such as pessimistic, optimistic or neutral.There are different aggregation operators representative of the different behaviors. Thesebehaviors reflect the decision by aggregating with t-norm, t-conorm and average operatorsrespectively. The best known and more extensively used aggregation operator is weightedarithmetic mean which computes a linear combination of values according to the set ofweights which account for the importance or reliability of the information sources. Thisfunction behaves well when the information sources are independent; there are no interactionsbetween them. When interaction exists, using fuzzy integrals is much appropriate to reducethe effect of having redundant sources. An OWA operator is both a weighted arithmetic meanand a fuzzy integral. The main feature of this operator is to give a bridge between t-norm andt-conorm operators. In this thesis, aggregation operators which we can give such examples,their properties and applications to multiple attribute decision making problems are given.Keywords: Aggregation Operators, Multiple Criteria Decision Making, Fuzzy Set Theory.