Abstract:

We present a new fuzzy aggregation operator that uses the weighted average (WA) and the ordered weighted averaging (OWA) operator in the same formulation. Moreover, we use an aggregation model that it is able to deal with uncertain environments that can be assessed with fuzzy numbers (FNs). Furthermore, we also use order inducing variables in the reordering step of the aggregation process. Thus, we are able to consider complex attitudinal characters that do not depend only on the values of the arguments. We call it the fuzzy induced ordered weighted averaging weighted averaging (FIOWAWA) operator. We study some of its main properties and we see that it has a lot of particular cases such as the WA and the OWA operator. The main advantage of the FIOWAWA operator is that it is possible to use the degree of importance (or subjective probability) of the characteristics and the attitudinal character (degree of orness) of the decision maker. Moreover, by using FNs, we are able to represent the information considering the minimum and the maximum and the possibility that the internal values will occur. We further generalize this approach by using generalized and quasi-arithmetic means, obtaining the fuzzy induced generalized OWAWA (FIGOWAWA) and the fuzzy induced quasi-arithmetic OWAWA (Quasi-FIOWAWA) operator. We analyze the applicability of this new approach and we see that it is very broad because it can be applied in a wide range of fields such as statistics, economics, decision theory and engineering. Theoretically, we could state that all the previous models and applications based on the WA and the OWA can be revised and improved with this new approach because the previous analysis will be included in this framework as a particular case. Thus, this new approach will give a more complete representation of the problem. In this paper, we focus on a decision making problem about human resource management where we are considering the selection of professors for a faculty position in a university. We analyze the criteria that should be taken into account in the selection process and we see that depending on the interests of the university about the expertise of the candidates, the selection will be different. Note that this analysis follows the methodology used in different studies about human resource selection with the difference that we apply it in a university context about selecting the most appropriate professor for the university.

Keywords:

Decision making, selection of professors, uncertainty, fuzzy numbers, aggregation operators.