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Top1. Introduction
Multi-Criteria Decision-Making (MCDM) often discusses to create or rank the alternatives from a set of likely ones in the existence of numerous, frequently differing criteria. Linguistic terms are generally used for evaluation ratings of the alternative w.r.t. criteria, weights as provided by decision makers. Decision-maker often faces problem where the information under consideration are vague or incomplete. The concept of type-2 fuzzy set is an important tool that has been developed to deal with uncertainty and the ranking of type-2 fuzzy set is very challenging problem in multi-criteria multi attributes decision making problems. The objective of this paper is to present a procedure for solving multi-criteria multi attribute decision making problems with interval type-2 fuzzy variables. Type-2 fuzzy sets are relatively new in the world of fuzzy sets and systems. Although they were originally introduced by Zadeh (1975), type-2 sets did not gain popularity until their reintroduction by Mendel (2001). These newer fuzzy sets were now thought of as an extension of the already popular fuzzy sets (now labelled type-1) to include additional uncertainties in the set. Type-2 fuzzy sets are unique and conceptually appealing, because they are fuzzy extension rather than crisp. Type-2 fuzzy sets have membership functions as type-1 fuzzy sets. The advantage of type-2 fuzzy sets is that they are helpful in some cases where it is difficult to find the exact membership functions for a fuzzy sets. There are wide variety of applications of type-2 fuzzy sets in science and technology like computing with words Mendel (2007), human resource management Gilan (2012), forecasting of time-series Karnik et al. (1999), clustering Aliev et al. (2011), pattern recognition Choi et al. (2009), fuzzy logic controller Wu et al. (2006), industrial application Dereli (2011), simulation Ramirez et al. (2011), neural network Chakravarty et al. (2012), and solid transportation problem Kundu et al. (2015).
MCDM methods have been introduced by Tzeng et al. (2011) in recent years and has wide number of applications in many areas such as, supplier selection Liu et al. (2011), construction and project management Taylan et al. (2014), energy planning Beccali et al. (2003), engineering management Gray et al. (2013), and tourism management Mardani et al. (2016). The ranking of type-2 fuzzy number plays an important role in type-2 fuzzy decision-making. The motivation behind this paper is to rank type-2 fuzzy variables. There are various methods of ranking of type-2 fuzzy sets introduced in recent years. Kundu et al. (2017) investigated fuzzy MCDM based on the ranking of interval type-2 fuzzy variables and applied it to transportation mode selection problem. Kaur et al. (2011) introduced a new ranking function in order to solve the fuzzy transportation problems. Mitchell (2006) introduced a method to rank a set of type-2 fuzzy numbers using statistical view point and and deduced each type-2 fuzzy number as an group of ordinary fuzzy numbers. Runkler et al. (2017) introduces a new method to solve decision-making using interval type-2 fuzzy sets. Javanmard et al. (2017) proposed a new ranking function method to solve interval type-2 fuzzy linear programming problem where all parameters, including coefficients in objective function, coefficients in the constraints and right hand sides of the constraints are interval type-2 fuzzy numbers (IT2FN). Nehi et al. (2017) introduced a new ranking method for interval type-2 triangular variables and evaluated some important properties on it. Gong et al. (2017) studied a new magnitude mean-variance possibility degree method to rank interval type-2 trapezoidal fuzzy variables.
A brief sketch of the paper is as follows: Section 2 introduces some basic definitions related to the concept. We have defined value and ambiguity of interval type-2 triangular fuzzy variables, interval type-2 trapezoidal fuzzy variables and studied some properties of it in Section 3. Section 4 deals with the method of ranking interval type-2 trapezoidal fuzzy variables. Section 5 describes an application of the proposed fuzzy multi-criteria group decision making method (FMCGDM) method problem description. Section 6 shows the procedure for the solution of the of the proposed FMCGDM method.