Supporting Ill-Structured Negotiation Problems

Abstract

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 preferences in ill-structured negotiation problems. We employ the modified FTOPSIS approach and the AHP method for determining the negotiation offers 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 options 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. E. Roszkowska (B)

The Intuitionistic Fuzzy Framework for Evaluation and Rank Ordering the Negotiation Offers

“…It is assumed [3,5] that the alternative is a negotiation package, which the negotiator can present as an offer or receive from an opponent, the criteria are negotiating issues, i.e. points to be agreed upon, the option is a resolution level of a negotiation issue.…”

“…Therefore, a negotiation package is represented by a vector P = [x 1 , ..., x j , ..., x n ] where x j ∈ N j (j = 1, 2, ..., n). In the prenegotiation phase, the negotiator builds a so-called scoring system that assigns score ratings to negotiation packages that allow to organize offers from best to worst and help to make decisions during the negotiation process (see [3,5]). Let us denote by ℘ = {P 1 , ..., P m } a finite set of negotiating offers which are evaluated based on the issues from the set C.…”

“…The options of negotiation issues may be real, interval, fuzzy, or expressed in words. In a series of papers [4][5][6][7] to set up the problems mentioned above, the building negotiation scoring systems based on fuzzy multi-criteria methods are proposed, where data of various types, was converted into triangular fuzzy numbers (e.g. fuzzy TOPSIS or fuzzy SAW).…”

The Multi-Criteria Negotiation Analysis Based on the Membership Function

“…The Pareto-optimal packeges are: P 1 , P 3 , P 5 , P 8 , P 11 , P 13 and P 14 (see Figure 9). The recommended compromise ("fair") solutions could be P 8 or P 10 , depending on the notion of fair solutions that can be applied in the negotiation symmetrical analysis (see Roszkowska et al, 2014).…”

The Extended Linguistic Hellwig’s Methods Based on Oriented Fuzzy Numbers and Their Application to the Evaluation of Negotiation Offers

“…On the other hand, FMCDM can be applied in the ill-structured negotiation problem where the negotiators express ratings and criteria weights imprecisely, subjectively, or vaguely. Such imprecise evaluations can result from the lack of information, measurement error, cognitive limitations, or subjective evaluation of the options, which are often observed in real-life negotiation [ 15 ]. Applications of fuzzy multiple criteria decision-making methods to determine the scoring systems can be found in many papers, e.g., [ 7 , 15 , 16 , 17 ].…”