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

Abstract

This study proposes a novel fuzzy framework for eliciting and organizing the preference information of the negotiator to allow for the evaluation of negotiation offers. The approach is based on verbal evaluation of negotiation options that operates with linguistic variables to handle vague preferences and operationalizes them through oriented trapezoidal fuzzy numbers. Two variants of the linguistic method based on Hellwig’s approach and oriented fuzzy numbers are proposed, which can be applied to building a scoring system for the negotiation template. Then, an example of determining such a scoring system and using it to evaluate the negotiation offers in typical multi-issue negotiation is shown. The results are discussed and compared with other methods known from the literature, in which the preference information is organized similarly but processed differently. The comparison shows that the presented methods can be an alternative to Simple Additive Weighting or TOPSIS methods that may also operate with oriented fuzzy numbers, but some of their characteristics may be problematic from the viewpoint of data interpretation. The former requires defuzzification of the global scores determined, while the latter requires the compulsory use of two reference points derived mechanically out of the negotiation space. By applying modified Hellwig’s approaches, the former and the latter may be easily avoided.

Modifying Hellwig’s Method for Multi-Criteria Decision-Making with Mahalanobis Distance for Addressing Asymmetrical Relationships

“…Hellwig's method has been extended to address different problems with crisp data [10] and incorporates fuzzy sets [10], intuitionistic fuzzy sets [37][38][39][40], interval-valued fuzzy sets [41], and oriented fuzzy sets [42]. This method has been applied in various practical contexts, including the circular economy [43], quality of human capital in the EU countries [44], socio-economic region development [45][46][47][48], sustainable development [49,50], quality of life [38,39,42], evaluation negotiation offers [40,42], analysis agriculture development [51][52][53][54], competitive balance of the Italian Football League [55], innovation in UE countries [56], evaluation of theater activity in Poland [57], and selection of locations [58], among others.…”

Extended Hellwig’s Method Utilizing Entropy-Based Weights and Mahalanobis Distance: Applications in Evaluating Sustainable Development in the Education Area

“…The classical Hellwig's method, as described in [13], has undergone various modifications to deal with real data [17], as well as extensions to fuzzy sets [18], intuitionistic fuzzy sets [19][20][21][22], and interval-valued fuzzy sets [23]. The classical Hellwig's method and its modifications or extensions have found applications in the analysis of complex socioeconomic phenomena across a wide range of domains, including but not limited to the circular economy [15], quality of human capital in the EU countries [14], socio-economic region development [18], sustainable development [24], quality of life [20,21], and evaluation negotiation offers [22,25].…”

The Impact of the Intuitionistic Fuzzy Entropy-Based Weights on the Results of Subjective Quality of Life Measurement Using Intuitionistic Fuzzy Synthetic Measure

“…Hellwig's classic algorithm was presented by UNESCO [76] (1972a) as a tool for measuring health development in a group of countries. Over the years, this procedure [72] has been applied in many areas [77][78][79][80][81] and modified for real data [82], fuzzy sets [83,84], intuitionistic fuzzy sets [11,35], interval-valued fuzzy sets [85], and ordered fuzzy sets [86]. It is worth noting that TOPSIS and VIKOR methods were also adapted to the intuitionistic environment (see e.g., [19,87,88] and [89,90], respectively).…”