Hesitant Fuzzy Sets: State of the Art and Future Directions

Abstract

The necessity of dealing with uncertainty in real world problems has been a long-term research challenge that has originated different methodologies and theories. Fuzzy sets along with their extensions, such as type-2 fuzzy sets, interval-valued fuzzy sets, and Atanassov's intuitionistic fuzzy sets, have provided a wide range of tools that are able to deal with uncertainty in different types of problems. Recently, a new extension of fuzzy sets so-called hesitant fuzzy sets has been introduced to deal with hesitant situations, which were not well managed by the previous tools. Hesitant fuzzy sets have attracted very quickly the attention of many researchers that have proposed diverse extensions, several types of operators to compute with such types of information, and eventually some applications have been developed. Because of such a growth, this paper presents an overview on hesitant fuzzy sets with the aim of providing a clear perspective on the different concepts, tools and trends related to this extension of fuzzy sets. C 2014 Wiley Periodicals, Inc.

Application of Interactive Genetic Algorithm based on hesitancy degree in product configuration for customer requirement

“…By investigating the impact of the user's emotional fluctuations on individual fitness values during the evolution process, as well as hesitancy developed from uncertainty regarding the evolutionary population, we have established a hesitancy adjustment mechanism which based on the hesitant fuzzy sets [17][18] to lower noise and applied an artificial neural network and layered IGA to speed up population convergence and further decrease user fatigue. Finally, we carried out a simulation experiment where we applied the method proposed in this paper to the evolutionary design system for car consoles.…”

Hesitant Fuzzy Worth: An innovative ranking methodology for hesitant fuzzy subsets

“…This reference justifies that hesitant fuzzy elements and sets have produced an extensive theoretical and applied literature. In the recent authoritative survey of HFSs [9], the authors summarize many useful and valuable decision making methods to solve hesitant fuzzy multicriteria decision making problems and propose further applications of HFSs to decision making. Within the extended field of Hesitancy in Fuzzy Sets, application papers that contribute to multicriteria decision making include [7], [10], [11], [12], [13], [14], [15] and [16].…”

“…Multiexpert multicriteria decision making under this requirement has been explored by Xia et al [17] or Tan et al [18] among others. Rodríguez et al [9], Section 7, emphasize that "a new trend is the application of the theoretical models to real problems". In this paper we adhere to their position.…”

Applications of finite interval-valued hesitant fuzzy preference relations in group decision making

“…Most of them are centred on the concept of hesitant fuzzy sets ( [9,21,23,25]) and the aggregation of this kind of sets ( [2,26,27]). Other authors have proposed using fuzzy preference relations ( [14,17,22]), Atanassov's intuitionistic interval fuzzy information ( [24]), trapezoidal valued hesitant fuzzy sets ( [20]) or hesitant fuzzy linguistic terms ( [15]).…”