Fuzzy Representation of Principal’s Preferences in Inspire Negotiation Support System

Abstract

We consider the negotiation problem, in which an agent negotiates on behalf of a principal. Our considerations are focused on the Inspire negotiation support system in which the principal’s preferences are visualised by circles. In this way, the principal describes the importance of each negotiation issue and the relative utility of each considered option. The paper proposes how this preference information may be implemented by the agent for determining a scoring function used to support decisions throughout the negotiation process. The starting point of our considerations is a discussion regarding the visualisation of the principal’s preferences. We assume here that the importance of each issue and the utility of each option increases with the size of the circle representing them. The imprecise meaning of the notion of “circle size” implies that in a considered case, the utility of an option should be evaluated by a fuzzy number. The proposed utility fuzzification is justified by a simple analysis of results obtained from the empirical prenegotiation experiment. A novel method is proposed to determine trapezoidal fuzzy numbers, which evaluates an option’s utility using a series of answers given by the participants of the experiment. The utilities obtained this way are applied to determine the fuzzy scoring function for an agent. By determining such a common generalised fuzzy scoring system, our approach helps agents handle the differences in human cognitive processes associated with understanding the principal’s preferences. This work is the first approach to fuzzification of the preferences in the Inspire negotiation support system.

The Use of Trapezoidal Oriented Fuzzy Numbers in Portfolio Analysis

“…In this paper, PV is modelled by oriented fuzzy numbers (OFN) defined in [13]. In recent years, OFNs have been increasingly used to describe and analyze economic [14,15], financial [16][17][18][19][20][21][22][23][24][25] and decision-making [26][27][28][29][30][31][32][33] problems. The application of OFNs in financial analysis may minimize imprecision risk, which was presented, for instance, in [32].…”