Application of fuzzy TOPSIS to scoring the negotiation offers in ill-structured negotiation problems

• We formulate a model of the decision problem in ill-structured negotiations.
• We modify the classic fuzzy TOPSIS algorithm by changing the PIS and NIS definition.
• The notion of unstable negotiation problem is introduced.
• We provide three alternative mechanisms for scoring offers in unstable problems.

In this paper we analyze the applicability of the TOPSIS method to support the process of building the scoring system for negotiation offers in ill-structured negotiations. When discussing the ill-structured negotiation problem we consider two major issues: the imprecisely defined negotiation space, and the vagueness of the negotiator's preferences that cannot be defined by means of crisp values. First we introduce the traditional fuzzy TOPSIS model showing the alternative ways of normalizing the data and measuring the distances, which allows to avoid the problem of ranking reversals. Then we formalize ill-structured negotiations using a model which allows the negotiation problem to be defined in a simplified way by means of the aspiration and reservation levels only. Such a definition requires changes in the traditional fuzzy TOPSIS algorithm the development of a mechanism for scoring the offers that fall outside of the negotiation space defined independently and subjectively by the negotiator. We propose three different approaches to handle this problem, that keep the scoring system stable and unchanged throughout the whole negotiation process.