A Hypervolume Based Approach to Rank Intuitionistic Fuzzy Sets and Its Extension to Multi-criteria Decision Making Under Uncertainty

Ranking intuitionistic fuzzy sets with distance based ranking methods requires to calculate the distance between intuitionistic fuzzy set and a reference point which is known to have either maximum (positive ideal solution) or minimum (negative ideal solution) value. These group of approaches assume that as the distance of an intuitionistic fuzzy set to the reference point is decreases, the similarity of intuitionistic fuzzy set with that point increases. This is a misconception because an intuitionistic fuzzy set which has the shortest distance to positive ideal solution does not have to be the furthest from negative ideal solution for all circumstances when the distance function is nonlinear. This paper gives a mathematical proof of why this assumption is not valid for any of the non-linear distance functions and suggests a hypervolume based ranking approach as an alternative to distance based ranking. In addition, the suggested ranking approach is extended as a new multicriteria decision making method, HyperVolume based ASsessment (HVAS). HVAS is applied for multicriteria assessment of Turkey's energy alternatives. Results are compared with three well known distance based multicriteria decision making methods (TOPSIS, VIKOR, and CODAS).Comment: 8 pages, 3 figure

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