AN INTERACTIVE APPROACH TO PROBABILISTIC INTUITIONISTIC FUZZY MULTI-CRITERIA DECISION MAKING IN STOCK SELECTION PROBLEM
The concurrence of randomness and imprecision exists in decision making problems (DMPs). To describe unpredictability, fuzziness and statistical uncertainty in a single frame, we have developed an interactive approach to probabilistic intuitionistic fuzzy MCDM method, in which assessment of alternative over attributes are provided by probabilistic intuitionistic fuzzy elements (PIFEs). In proposed methodology a conversion method to convert fuzzy sets to intuitionistic fuzzy sets is also used. To completely describe statistical and non-statistical uncertainty, suitable probability distribution function is associated to the both belongingness values and non-belongingness values of each one entity in constructed IFS. The core intention of this paper is to propose a PIF-TOPSIS (Technique for Order Preference by Similarity to Ideal Solution) method for MCDM problem. Firstly, we develop distance measures for PIFEs. Probabilistic intuitionistic fuzzy positive and negative ideal solutions are also defined. A real life case study is in use as an example to illustrate the methodology of developed PIF-TOPSIS method and to find the ranking of organizations using real data. The decision making framework of proposed PIF-TOPSIS method is superior to other MCDM methods, because of introducing probabilistic information in IFEs, which can be useful to ensure the integrality and accuracy of intuitionistic fuzzy information.