Research Article A New Method for Defuzzification and Ranking of Fuzzy Numbers Based on the Statistical Beta Distribution A. Rahmani, F. Hosseinzadeh Lotfi, M. Rostamy-Malkhalifeh, and T. Allahviranloo Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, Iran Correspondence should be addressed to M. Rostamy-Malkhalifeh; mohsen rostamy@yahoo.com Received 25 March 2016; Revised 22 June 2016; Accepted 18 October 2016 Academic Editor: Rustom M. Mamlook Copyright © 2016 A. Rahmani et al. Tis is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defned as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy information could be of special interest for the applications where fuzzy sets must be converted to crisp sets to avoid uncertainty. Tis paper proposes a novel method of defuzzifcation based on the mean value of statistical Beta distribution and an algorithm for ranking fuzzy numbers based on the crisp number ranking system on R. Te proposed method is quite easy to use, but the main reason for following this approach is the equality of lef spread, right spread, and mode of Beta distribution with their corresponding values in fuzzy numbers within (0,1) interval, in addition to the fact that the resulting method can satisfy all reasonable properties of fuzzy quantity ordering defned by Wang et al. Te algorithm is illustrated through several numerical examples and it is then compared with some of the other methods provided by literature. 1. Introduction Granular computing is an emerging computing paradigm that is concerned with the processing of information entities created from the process of data abstraction and is intrinsi- cally linked with the adjustable nature of human perception [1, 2]. Information granularity and granular computing have been widely used in development of verbal and linguistic concepts and particularly those concerned with fuzzy and rough sets [3] and are valuable assets for creating realistic models for real-world decision-making processes, as they provide the means to understand and solve abstract problems of the real world with simplicity, clarity, good approximation, and tolerance of uncertainty [1, 4]. Granular computing is the science of building heterogeneous and multilevel models for the processing of granular information by incorporating distinct concepts such as probabilistic sets, rough sets, and especially fuzzy sets and their membership functions into a single framework, thereby allowing the verbal, linguistic, and human-centered concepts to be processed. Since the introduction of the term “granular computing,” its related concepts have appeared in many diferent felds such as artifcial intelligence, decision-making, and cluster analysis [5–7]. Although there have been some works in regard with granular models, granular computing is yet to be fully and exclusively explored, and its current structures and especially those related to fuzzy sets seem to be underdevel- oped. In 1997, Zadeh [8] introduced a strong relationship between granular data and fuzzy sets and developed the theory of fuzzy information granulation to provide a new angle of approach for tackling the problem of ambiguity and uncertainty. Te theory of fuzzy information granulation (TFIG) is an informal method of using linguistic variables and fuzzy IF-THEN rules to make rational decisions in an environment full of uncertainty. Tus, this article is focused on this aspect of fuzzy theory and provides a method for defuzzifcation of fuzzy sets to achieve certainty in solution of real-world problems. Te concept of fuzzy sets (referring to the sets with imprecise and ambiguous nature) was frst introduced in 1965 by Zadeh [9]. He expanded the notion of membership beyond the “zero-one” logic and utilized the dynamic infnite Hindawi Publishing Corporation Advances in Fuzzy Systems Volume 2016, Article ID 6945184, 8 pages http://dx.doi.org/10.1155/2016/6945184