2 research outputs found
Complex Atanassov's Intuitionistic Fuzzy Relation
This paper presents distance measure between two complex Atanassov's intuitionistic fuzzy sets (CAIFSs). This distance measure is used to illustrate an application of CAIFSs in solving one of the most core application areas of fuzzy set theory, which is multiattributes decision-making (MADM) problems, in complex Atanassov's intuitionistic fuzzy realm. A new structure of relation between two CAIFSs, called complex Atanassov's intuitionistic fuzzy relation (CAIFR), is obtained. This relation is formally generalised from a conventional Atanassov's intuitionistic fuzzy relation, based on complex Atanassov's intuitionistic fuzzy sets, in which the ranges of values of CAIFR are extended to the unit circle in complex plane for both membership and nonmembership functions instead of [0, 1] as in the conventional Atanassov's intuitionistic fuzzy functions. Definition and some mathematical concepts of CAIFS, which serve as a foundation for the creation of complex Atanassov's intuitionistic fuzzy relation, are recalled. We also introduce the Cartesian product of CAIFSs and derive two properties of the product space. The concept of projection and cylindric extension of CAIFRs are also introduced. An example of CAIFR in real-life situation is illustrated in this paper. Finally, we introduce the concept of composition of CAIFRs
Supplier evaluation and selection in fuzzy environments: a review of MADM approaches
In past years, the multi-attribute decision-making (MADM)
approaches have been extensively applied by researchers to the
supplier evaluation and selection problem. Many of these studies
were performed in an uncertain environment described by fuzzy sets.
This study provides a review of applications of MADM approaches
for evaluation and selection of suppliers in a fuzzy environment. To
this aim, a total of 339 publications were examined, including papers
in peer-reviewed journals and reputable conferences and also some
book chapters over the period of 2001 to 2016. These publications
were extracted from many online databases and classified in some
categories and subcategories according to the MADM approaches,
and then they were analysed based on the frequency of approaches,
number of citations, year of publication, country of origin and
publishing journals. The results of this study show that the AHP and
TOPSIS methods are the most popular approaches. Moreover, China
and Taiwan are the top countries in terms of number of publications
and number of citations, respectively. The top three journals with
highest number of publications were: Expert Systems with Applications,
International Journal of Production Research and The International
Journal of Advanced Manufacturing Technology