The main purpose of this paper is to investigate the application potential of ordered fuzzy numbers (OFN) to support evaluation of negotiation offers. The Simple Additive Weighting (SAW) and the Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) methods are extended to the case when linguistic evaluations are represented by OFN. We study the applicability of OFN for linguistic evaluation negotiation options and also provide the theoretical foundations of SAW and TOPSIS for constructing a scoring function for negotiation offers. We show that the proposed framework allows us to represent the negotiation information in a more direct and adequate way, especially in ill-structured negotiation problems, allows for holistic evaluation of negotiation offers, and produces consistent rankings, even though new packages are added or removed. An example is presented in order to demonstrate the usefulness of presented fuzzy numerical approach in evaluation of negotiation offers.
From the perspective of each evaluation criterion, any decision alternative is evaluated by means of trapezoidal ordered fuzzy numbers (TrOFN). This approach is justified in the way that some criteria are linguistically evaluated. In this paper, decision alternatives are evaluated using oriented fuzzy Simple Additive Weighting (OF-SAW) scoring function. The ranking of alternatives may be defined by means of a nonincreasing sequence of defuzzified values of a scoring function. Any defuzzification procedure distorts ordered fuzzy numbers in a way that information on imprecision and orientation is lost. This undermines the credibility of the determined alternatives' ranking. The main purpose of this paper is to avoid the defuzzification stage in the OF-SAW method. Thus, the OF-SAW method is equipped with fuzzy scoring order. This OF-SAW method is described as a negotiation scoring system. We study an empirical example of the OF-SAW application and rank some negotiation offers. Here, we focus on the effects of replacing the defuzzified scoring function by a fuzzy one. The obtained conclusions are generalized for the case of any decision alternatives.
Sustainability is a holistic and complex multi-dimensional concept comprising economic, social and environmental issues. The EU Sustainable Development Goals' indicator set, developed by European Commission, is implemented online in Eurostat's database and constitutes the basis for assessing the level of sustainability assessment in different areas. The integration of the sustainability indicators was carried out in many studies by using the multi-criteria techniques. This work proposes a new methodological framework based on extended TOPSIS procedure, which takes into account EU targets and/or national targets in building positive ideal solution and negative ideal solution. This algorithm allows compensatory and non-compensatory approach in integrated sustainability assessment from the target point of view. This framework has been applied to measure sustainable development in the area of education in 28 EU countries in 2015. The results of this research also illustrate the complexity of measuring sustainable development, where multiple sustainability criteria and targets are considered.
In this paper we analyze how the way in which the principal's preferences are visualized may affect the accuracy of representation of this principal by their agent. We study the processes of multi-issue electronic representative negotiations conducted by agents on behalf of their principals by means of the negotiation support system that implements a simple decision support tool for eliciting the preferences and building a system of cardinal ratings for feasible negotiation offers. First, we investigate the accuracy of agents' scoring systems and compare their concordance to the preferential information provided to them by their principals by means of single verbal description and two different visualization techniques, one using bar graphs and the second-circles (pies). The concordance is measured by means of the notions of ordinal and cardinal accuracy. Then we analyze how the scoring systems with various inaccuracy indexes influence the agents' perception of negotiation process, i.e. the interpretation of concessions made by parties and the structures of concession paths. We also study what is an impact of inaccurate scoring systems on the negotiation outcomes, i.e. the final contracts, their ratings and efficiency. The results obtained show that the bars are slightly better in more precise representation of principals preferences. They allow agent to determine a little more accurate scoring systems, which help to understand the negotiation process better by minimizing the cardinal error of evaluation of the offers in concession paths. Yet, no significant impact on the outcomes have been found. An interesting prescriptive conclusion that can be drawn is that to assure an adequate representation of principal's preferences the agents should be offered the bar-based visualization. Also, a checkup mechanism should be introduced to the preference elicitation procedure that assure the agents to be ordinally concordant with the priorities of their principal's preferences.
Benchmarking the analysis of countries' performance in terms of sustainable development helps to understand the success factors of countries that over perform and to target priority issues of others with lower performance. However, assessing sustainable development comes with methodological challenges, including indicator standardization, aggregation and weighting. Our study significantly contributes to the measure of sustainable development by providing a new approach based on an extended Hellwig method. After describing the main limitations of existing methodologies, this paper's aim is twofold. First, we show that the proposed analytical framework allows for comparing the sustainable performance of EU countries on the national level. The extended Hellwig method takes into consideration EU targets and/or national targets in building patterns of development. Second, this framework is tested as a part of the evaluation of the implementation of the Europe 2020 strategy in the education area. The results obtained using the extended Hellwig method were compared with those obtained by means of the Education Index, TOPSIS and Ward technique. Our analysis showed the significant disparities in the implementation of the Europe 2020 strategy recommendations in the education area in 2015.
Game theory in its several variants is widely recognized as a contribution to social and economic modeling. One relevant development of classical game theory, Generalized Game Theory (GGT), entails its extension and generalization through the formulation of the mathematical theory of rules and rule complexes. Social theory concepts such as norm, value, belief, role, social relationship, and institution as well as game can be defined in a uniform way in terms of rules and rule complexes. Among the applications, one major initiative has been the conceptualization of fuzzy games and equilibria. In this paper a GGT model of 2-person fuzzy bargaining games is outlined. Two key concepts are applied: (1) players' value (or "utility") structures consisting of ideal points or expectation levels, on the one hand, and limits of acceptance, on the other; (2) fuzzy judgment functions in which players deal with imprecise information and use approximate reasoning in making decisions and negotiating agreements. Such fuzzy judgment functions can take into account economic, socio-psychological, and cultural and institutional aspects of the bargaining context, which affect the bargaining process in specifiable ways. Several significant results are obtained from the application of this model: the opportunities (or not) for agreement, the participants' satisfaction levels with an agreement, and the question whether or not the agreed "price" is an equilibrium price.
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