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A fuzzy ranking of negotiation packages for the INSPIRE negotiation support system

Piasecki Krzysztof

Control and Cybernetics

2021

Vol. 50, No. 1

69--82

Preferential information may be visualized in many different ways, and this constitutes an important issue in the principal- agent decision-making context, e.g., in representative negotiations. In the INSPIRE negotiation support system, the principal’s preferences are visualized by circles with different radii. Agents evaluate the principal’s preferences in such a manner that they digitize these preferences using numbers directly proportional to the size of the circles, drawn by the principal. The manner, in which an agent understands the concept of the circle size is unknown. The main goal of this paper is to propose such an image of principal’s preferences, which is independent of an individual agent’s evaluation. Individual negotiators may differ in their understanding of this concept. This means that the notion of “circle size” is a linguistic variable that may be described by a fuzzy set. The empirical studies referred to show that the size of the circle is a value between the radius and the area of this circle. In this paper, the principal’s preferences are defined as a fuzzy preorder between fuzzy “circle sizes”. We distinguish here two kinds of the INSPIRE method. All considerations are illustrated by means of a short case study based on INSPIRE data.

Using an analytic hierarchy process to develop a scoring system for a set of continuous feasible alternatives in negotiation

Brzostowski J., Roszkowska E., Wachowicz T.

Operations Research and Decisions

2012

Vol. 22, No. 4

21--40

The use of an Analytic Hierarchy Approach (AHP) for scoring offers in continuous negotiation problems has been studied. AHP has already proven its usefulness in constructing a ranking of alternatives in discrete decision making problems. In negotiations, however, some issues may have a quantitative character and be defined by feasible ranges, which results in uncountably large sets of feasible offers. This is a problem to which AHP cannot be applied in its original form. Therefore we propose an approach to building a scoring system that operates within AHP and a predefined discrete subset of feasible alternatives, then a method for determining global scores for all the feasible alternatives is proposed. When this subset has been built, the notion of border alternatives is applied. Assuming that these border alternatives have been ranked, single-issue utility functions are constructed using linear interpolation over the set of selected border alternatives. Single-issue utility functions are then aggregated using issue weights in order to form the final utility function. The issue weights are also determined using AHP. Such an approach means that a relatively small number of comparisons are required for a negotiator in AHP process to build a comprehensive scoring system, which makes the process of eliciting the negotiator’s preferences simple and rapid.