Analytic hierarchy process based on interval type-2 intuitionistic fuzzy sets with their application to multicriteria decision making

Article type: Research Article

Authors: Debnath, Joy | Biswas, Animesh^*

Affiliations: Department of Mathematics, University of Kalyani, Kalyani, India

Correspondence: [*] Corresponding author: Animesh Biswas, Department of Mathematics, University of Kalyani, Kalyani 741235, India. E-mail: abiswaskln@rediffmail.com

Abstract: Based on the concepts of interval type-2 fuzzy sets and intuitionistic fuzzy sets, this paper introduces the concept of interval type-2 intuitionistic fuzzy set that provides an extra dimension to intuitionistic fuzzy sets for the first time. Different arithmetic operations on interval type-2 intuitionistic fuzzy set are defined and a defuzzification method of interval type-2 intuitionistic fuzzy sets is developed for ranking purpose. Also, existing analytic hierarchy processes are further generalized with the introduction of interval type-2 intuitionistic fuzzy analytic hierarchy process to assess the relative importance among the alternatives in a convenient way under multi criteria decision-making environment. This process is efficient enough to evaluate the differences among the alternatives more prominently than the existing method that plays an important role in multi criteria decision-making contexts. Finally, a case example on supplier selection problem is considered and is solved to illustrate the applicability and validity of the proposed methodology.

Keywords: Interval type-2 intuitionistic fuzzy set, operations on fuzzy sets, defuzzification processes, fuzzy analytic hierarchy process, multicriteria decision making

DOI: 10.3233/IDT-180341

Journal: Intelligent Decision Technologies, vol. 12, no. 3, pp. 359-370, 2018