The importance of fuzzy numbers to express uncertainty in certain applications, concerned with decision making, is observed in a large number of problems of different kinds. In Decision making problems, the best of available alternatives is chosen to the possible extent. In the process of ordering the alternatives, ranking of fuzzy numbers plays a key role. A large volume of ranking methods, based on different features, have been available in this domain. Owing to the complicated nature of fuzzy numbers, the so far introduced methods suffered setbacks or posed difficulties or showed drawbacks in one context or other. In addition, some methods are lengthy and complicated to apply on concerned problems. In this article, a new ranking procedure based on defuzzification, stemmed from the concepts of geometric mean and height of a fuzzy number, is proposed. Finally, numerical comparisons are made with other existing procedures for testing and validation of proposed method with the support of some standard numerical examples.

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The main aim of this paper is to obtain a unique common tripled fixed point theorem in partial ordered metric space using Caristi type contraction.