Tomasz Wachowicz

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

Inaccuracy in Defining Preferences by the Electronic Negotiation System Users

In this paper we analyze how preferences are defined by negotiators in electronic negotiations if a SAW-based negotiation offer scoring system is used. We analyze a dataset of the Inspire electronic negotiation system, containing the transcripts of bilateral negotiation experiments and study how the negotiators use the preferential information provided in the case description and map it into a system of issues and options ratings in the discrete negotiation problem. We measure the accuracy of the preference systems by comparing the user-defined scoring systems with the reference ideal ones that stem directly from precise initial graphical information. Two notions of accuracy are used: (1) ordinal accuracy which measures if the negotiators followed the ranking order only; and (2) cardinal accuracy, defined by means of an original formula that takes into account weighted normalized distances between the negotiator’s own system and the reference scoring one.

Defining Preferences and Reference Points – A Multiple Criteria Decision Making Experiment

In this paper we study how do the decision makers proceed in analyzing the multiple criteria decision making (MCDM) problem. Based on the results of the questionnaire-based experiment, we investigate how do they define the reference points in the decision problem and specify their preferences. We also study what kind of problems do they encounter while analyzing such a multiple criteria decision making problem. Finally, we consider what MCDM methods could be used to fit the decision makers way of analyzing the preferences and conducting the decision process.

SAW-Based Rankings vs. Intrinsic Evaluations of the Negotiation Offers – An Experimental Study

In this paper we discuss the issue of evaluating the negotiation offers represented in a form of the complete packages and the negotiators’ consistency in scoring such packages. We analyze the results of an experiment, in which the negotiators were asked to build the ranking of fourteen negotiation offers and then compare it with two predefined rankings obtained by means of SAW method. We verify how do the negotiators evaluate these SAW-based rankings and how they correspond to the negotiators’ intrinsic ones. We discuss then both the negotiators’ consistency in defining their preferences and the applicability of some formal methods in supporting them in such a definition.

The Multi-Criteria Negotiation Analysis Based on the Membership Function

Abstract In this paper we propose a multi-criteria model based on the fuzzy preferences approach which can be implemented in the prenegotiation phase to evaluate the negotiations packages. The applicability of some multi-criteria ranking methods were discussed for building a scoring function for negotiation packages. The first one is Simple Additive Weighting (SAW) technique which determines the sum of the partial satisfactions from each negotiation issue and aggregate them using the issue weights. The other one is Distance Based Methods (DBM), with its extension based on the distances to ideal or anti-ideal package, i.e. the TOPSIS procedure. In our approach the negotiators preferences over the issues are represented by fuzzy membership functions and next a selected multi-criteria decision making method is adopted to determine the global rating of each package. The membership functions are used here as the equivalents of utility functions spread over the negotiation issues, which let us compare different type of data. One of the key advantages of the approach proposed is its usefulness for building a general scoring function in the ill-structured negotiation problem, namely the situation in which the problem itself as well as the negotiators preferences cannot be precisely defined, the available information is uncertain, subjective and vague. Secondly, all proposed variants of scoring functions produce consistent rankings, even though the new packages are added (or removed) and do not result in rank reversal.

Supporting Ill-Structured Negotiation Problems

The negotiation is a complex decision-making process in which two or more parties talk with one another in afford to resolve their opposing interests. It can be divided into consecutive stages, namely: pre-negotiation phase involving structuring the problem and the analysis of preferences, the intention phase involving the iterative exchange of offers and counter-offers, and the postoptimization phase aiming at the improvement of the agreement obtained in the intention phase. In this chapter, we focus on the analysis of negotiators\({^\prime }\) preferences in ill-structured negotiation problems. We employ the modified FTOPSIS approach and the AHP method for determining the negotiation offers\({^\prime }\) scoring system, which allows for the easy evaluation of both the incoming offers as well as the packages under preparation. The imprecision and vagueness of the packages and option\(\text {s}{^\prime }\) descriptions is modeled by the fuzzy triangular numbers. The Analytic Hierarchy Process is used to derive the negotiation issue weights instead of directly assigning such values to the issues (a classic approach). The FTOPSIS method is used to build the final scoring system allowing for the evaluation of any potential negotiation package. The whole process of negotiation supported by the approach we proposed is illustrated with an numerical example.

Can the Holistic Preference Elicitation be Used to Determine an Accurate Negotiation Offer Scoring System? A Comparison of Direct Rating and UTASTAR Techniques

In this paper we study the prenegotiation process of eliciting the negotiators’ preferences and building the negotiation offer scoring system. We analyze how the agents build the formal and quantitative scoring systems based on the preferential information provided by their principals. The results of the bilateral negotiation experiment conducted in Inspire negotiation system are analyzed, in which the simple direct rating technique (SMARTS-like approach) is implemented to evaluate the negotiation problem and build scoring systems. The concordance of such scoring systems with the principal’s preferences was determined using the cardinal and ordinal inaccuracy measures. Then for each agent the scoring system was determined using UTASTAR method based on the same preference structures subjectively declared for direct rating. Finally, the inaccuracy of scoring systems obtained by means of both methods was compared.

The Application of Item Response Theory for Analyzing the Negotiators’ Accuracy in Defining Their Preferences

In this paper we analyze how some notions of Item Response Theory (IRT) may be used to analyze the process of scoring the negotiation template and building the negotiation offer scoring system. In particular we focus on evaluating and analyzing the accuracy and concordance of such scoring systems with the preferential information provided to negotiators by the represented party. In our research we use the dataset of bilateral electronic negotiations conducted by means of Inspire negotiation support system, which provides users with decision support tools for preference analysis and scoring system building based on SMART/SAW method. IRT allows us to consider how the potential accuracy of individual scoring systems can be explained by both negotiators’ intrinsic abilities to use decision support tool and understand the scoring mechanism, and the difficulty of applying this scoring mechanism.

Representative Decision-Making and the Propensity to Use Round and Sharp Numbers in Preference Specification

This paper analyzes the agents’ predisposition to produce round numbers during preference elicitation of the pre-negotiation phase. The agents negotiate on behalf of their principals and are asked to use information presented in terms of bar graphs and text to provide their principals’ preferences numerically. In doing that, they tend to use round numbers more often than sharp numbers. Also, more agents use round numbers than sharp numbers, however, the majority of agents use a mix of numbers. The results show that the increased use of round numbers results in greater inaccuracy; the most accurate are agents who use a mix or round and sharp numbers.

Some Methodological Considerations for the Organization and Analysis of Inter- and Intra-cultural Negotiation Experiments

In this paper we analyze some problems related to the design and analysis of the inter- and intra-cultural online negotiation experiments in which university students participate. We discuss factors that may impact the negotiation performance. Apart from national culture, which is an evident factor the impact of which is traditionally measured in cross-country negotiations, we discuss also the potential influences of university or students’ individual or group culture. When analyzing the negotiation performance, we focus not only on the bargaining process, but also on the pre-negotiation preparation. The paper provides a statistical analysis of the negotiation experiments organized in Inspire, which – unfortunately – were not designed to study all the issues raised in the paper, yet allow us to capture some of the ideas and notions discussed.