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Top1. Introduction
When resolving real problems, we are frequently blocked with the fuzziness encompassed. Zadeh introduced Fuzzy Sets (FS) in 1965 (Zadeh, 1965), that were adapted to the decision making framework in 1970 (Bellman & Zadeh, 1970). Later, the first Fuzzy Linear Programming (FLP) model in which only parameters were fuzzy was proposed in (Zimmermann, 1978). Since that, other methods were proposed to model the fuzzy aspect in linear programming (Carlsson & Korhonen, 1986; Ebrahimnejad & Verdegay, 2018; Ma et al., 2017; Verdegay, 1982). Nevertheless, the selected problems were partially fuzzy. In other words, only some parts of the treated problems (decision variables or parameters) were tolerated to be fuzzy, while others were forced to be crisp. Recently, authors aimed to solve the problem where all components are fuzzy, the so called fully fuzzy problem (Aggarwal & Sharma, 2016; Albayrak, 2017; S. K. Das, 2017; Sapan Kumar Das et al., 2017; Ezzati et al., 2015; A. Hosseinzadeh & Edalatpanah, 2016; Kaur & Kumar, 2012; Kumar et al., 2011; Kumar & Kaur, 2014; Puri & Yadav, 2016). Still, the models proposed, permitted to consider only type 1 fuzzy numbers. However, as pointed by the founder of fuzzy logic (Zadeh, 1975); it is counterintuitive to ask for an exact membership function, while the main objective is to permit fuzziness. While type 2 fuzzy logic handles these situations. The use of perfectly normal interval type 2 fuzzy numbers, as a special kind of type 2 fuzzy sets, permits a satisfactory compromise between acceptable representation and complexity.
Similarly to type 1 fuzzy programming, first extensions treated Right Hand Side (RHS) parameters and the objective function (J. C. Figueroa Garcia, 2008; J. C. Figueroa García, 2009, 2011; J. C. Figueroa García & G. Hernández, 2013). Then other parts of the optimized problem were also considered to be fuzzy (García, 2012; J. C. Figueroa García & G. Hernández-Pérez, 2015; Moslem Javanmard & Mishmast Nehi, 2019; Srinivasan & Geetharamani, 2016). In (E. Hosseinzadeh et al., 2015), a weighted goal programming approach was proposed to solve linear regression problem, in which inputs were crisp, and outputs Type 2 Fuzzy Sets (T2FS). Another regression model with T2FS was proposed in (Elham Hosseinzadeh et al., 2016). Authors in (Kundu et al., 2018), aimed to solve a problem involving type 2 fuzzy parameters in the RHS coefficients. They also used chance constraint programming and credibility theory to treat inequalities. The resolution approach was adapted to the shortest path algorithm and to a minimum spanning tree problem. A comparison between fuzzy type 1 and fuzzy type 2 credibility measures was presented in (Jana et al., 2017). Non-linear programming approaches dealing with type 2 fuzzy quantities were presented in (H. Dalman & Bayram, 2017; Hasan Dalman & Bayram, 2018). A comparison of recently developed transportation models was proposed in (Majumder et al., 2019). Further models and approaches were proposed in (Figueroa-García & Hernández, 2014; Haghighi et al., 2019; Jin et al., 2014; Kundu et al., 2014, 2015).