We briefly present the ides of a new approach to a more effective and human consistent supporting of consensus reaching based on the concept of fairness. Our approach combines a formal, fuzzy logic based direction to the derivation of the con- cept of a (degree of) soft consensus proposed by Kacprzyk and Fedrizzi [10,11], with roots in Kacprzyks [6, 7] concept of a fuzzy mnajority, and then further devel- oped and implementd by Kacprzyk and Zadrożny  and some new directions in multiperson decision theory and decision analysis that are based on some results of social, cognitive economic, psychological, etc. sciences that advocate the inclusion of some sort of fairness. In our case, we propose the idea of a fairness based consensus reaching process, and its support, taking into account two aspectss: a fair distribution (fair resource allocation) and a fair final decision. We emphsize benefits resulting from the implementation of proposed concept in group decision support systems, no- tably those related to consensus reaching, and indicate some fruitful directions of a further model development.