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.
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.
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