Note: [1] Work on Sect. 1 and 2 is supported by the Asen Zlatarov University through project Ref. No. NIX-449/2021 “Modern methods for making management decisions”. Work on Sect. 3 and Sect. 4 is supported by the Ministry of Education and Science under the Programme “Young scientists and postdoctoral students”, approved by DCM # 577/17.08.2018.
Abstract: Analysis of variance (ANOVA) is an important method in data analysis, which was developed by Fisher. There are situations when there is impreciseness in data In order to analyze such data, the aim of this paper is to introduce for the first time an intuitionistic fuzzy two-factor ANOVA (2-D IFANOVA) without replication as an extension of the classical ANOVA and the one-way IFANOVA for a case where the data are intuitionistic fuzzy rather than real numbers. The proposed approach employs the apparatus of intuitionistic fuzzy sets (IFSs) and index matrices (IMs). The paper also analyzes a unique set of data on daily ticket sales for a year in a multiplex of Cinema City Bulgaria, part of Cineworld PLC Group, applying the two-factor ANOVA and the proposed 2-D IFANOVA to study the influence of “ season ” and “ ticket price ” factors. A comparative analysis of the results, obtained after the application of ANOVA and 2-D IFANOVA over the real data set, is also presented.
Keywords: Decision making, index matrix, intuitionistic fuzzy sets, variation analysis
