Digital Color Image Processing Using Intuitionistic Fuzzy Hypergraphs

Hypergraphs are considered a useful mathematical tool for digital image processing and analysis since they can represent digital images as complex relationships between pixels or block of pixels. The notion of hypergraphs has been extended in fuzzy theory leading to the concept of fuzzy hypergraphs, then in intuitionistic fuzzy theory conducting to the concept of intuitionistic fuzzy hypergraphs or IFHG. The latter is very suitable to model digital images with uncertain or imprecise knowledge. This paper deals with color image denoising, segmentation, and edge detection in a color image initially represented in RGB space using intuitionistic fuzzy hypergraphs. First, the RGB image is transformed to HLS space resulting in three separated components. Then each component is intuitionistically fuzzified based on entropy measure from which an intuitionistic fuzzy hypergraph is generated automatically. The generated hypergraphs will be used for denoising, segmentation, and edge detection.

Environmental Adaptation of Construction Barriers under Intuitionistic Fuzzy Theory

The project of construction barriers removal is a comprehensive planning task and it demands a suitable support for identification, and priority ranking of facilities necessary for barriers removal. This paper proposes a multicirteria Intuitionistic Fuzzy (IF) ELECTRE model to support decision makers in the process of managing of removal project of construction barriers for physically disabled in high schools. IF ELECTRE approach is used to deal with complex problems, where decision-makers have ambiguities and dualities in evaluation of considered solution. Hereby 17 high schools are defined and seven criteria are determined by decision-makers. These criteria are further used for the alternatives assessments. Each DM is also evaluated by linguistic and numerical values, assigning them this way an importance according to their background and the years of experience. The Intuitionistic Fuzzy Weighted Average (IFWA) operator is calculated to achieve aggregated alternatives evaluations. Furthermore, concordance and discordance sets and indexes are calculated to obtain dominance matrix and final ranking of schools for the construction barriers removal. The model is validated on high schools in the city of Split. Using IF theory, the given problematic can be operated more effectively by diminishing the inaccuracy of available information.

The Method of Data Analysis in Intuitionistic Fuzzy Generalized Consistent Decision Formal Context

Concept lattice has been successfully applied to various fields as an effective tool for data analysis and knowledge discovery, with attribute reduction being the key problem. This paper combines the intuitionistic fuzzy theory with the concept lattice theory and proposes one kind of concept lattice in intuitionistic fuzzy generalized consistent decision formal context. Furthermore, an approach to attribute a reduction in the discernibility matrix is proposed and investigated, making the discovery of implicit knowledge easier and the representation simpler in the data system and perfecting the theory of concept lattice. Moreover, this paper studies, in detail, the algorithms and case study of data analysis in the intuitionistic fuzzy generalized consistent decision formal context. The potential value of the method to deal with information discussed in this paper, especially the value of forecasting and decision-making, is expected in future.