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.
Highlights
Introduction published maps and institutional affilNegotiation analysis is a subdiscipline of decision theory, which is focused on developing tools and techniques for efficient negotiation support [1]
The paper makes an impact in the analysis of preferences in representative negotiations in the following aspects: (i) we discuss the problem of interpretation by an agent of the principal preferences visualised imprecise by circles; (ii) we design a new procedure for building a fuzzy scoring system by an agent using simultaneous recommendations provided by many independent interpreters; (iii) we identify some problems with an evaluation of preferential information by such interpreters linked with the normalisation procedures
While determining the scoring systems, they follow the prenegotiation protocol that is classically implemented in Inspire, i.e., they assigned the cardinal ratings to the options and issues according to their individual understanding of the differences in circles’ sizes using crisp values V C Ri,j
Summary
An imprecise quantity is a family of real numbers belonging to it at a varying degree. Orlovsky [47] shows that in agreement with Zadeh’s Extension Principle, this relation is a fuzzy preorder [ GE] described on F2Tr by its membership function ν[GE] ∈ [0, 1]FTr determined as follows ν[GE] (K, L) = sup{min{μK ( x ), μ L (y)} : x ≥ y}. The defuzzification may give the false perception of operating with precise and sound information, which changes the true picture of the problem under consideration [39,60], and may have negative consequences for decision making For this reason, we will stay with the fuzzy preorder [ GE] when comparing TrFNs. For any set A ⊂ FTr , we can determine the fuzzy set maxA of its non-dominated elements.
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