ADV MATH SCI JOURNAL Advances in Mathematics: Scientific Journal 9 (2020), no.8, 6107–6114 ISSN: 1857-8365 (printed); 1857-8438 (electronic) https://doi.org/10.37418/amsj.9.8.78 Special Issue on ICMA-2020 EXPONENTIAL OPERATIONAL LAWS OF PYTHAGOREAN FUZZY PROJECTION MODELS FOR DECISION MAKING S. JOHN BORG 1 , D. AJAY, AND J. ALDRING ABSTRACT. The aim of this paper is to investigate the idea of projection models in Pythagorean fuzzy multi criteria decision making environment. Exponen- tial operational laws are used to study the Pythagorean fuzzy ideal point, the modules of Pythagorean fuzzy numbers and the cosine of the included angle. The paper also establishes a Pythagorean projection model using exponential operational laws and the model is used to determine the degree of similar- ity between each alternative and the ideal point of exponential fuzzy data in Pythagorean fuzzy sets. Based on the proposed projection models, the alterna- tives are ranked in order to select the most desirable alternative. 1. I NTRODUCTION The concept of fuzzy set [1] was introduced by L.A. Zadeh (1965). A fuzzy Set is defined by a membership function that assigns a membership value ranging from 0 to 1. In this paper we use exponential operational laws of Pythagorean fuzzy sets [3] to create a Pythagorean projection model. Exponential opera- tional laws is a new concept for studying the ideas of Pythagorean fuzzy ideal point and cosine of the included angle. We establish two projection models for Pythagorean fuzzy decision making, where the attribute weight is completely known. 1 Corresponding author 2010 Mathematics Subject Classification. 03E72, 03B52, 94D05. Key words and phrases. Fuzzy Sets, Pythagorean Fuzzy Sets, Exponential Operational Laws, Projection model, MCDM. 6107