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Top1. Introduction
Optimizing a linear objective subject to certain constraints is one of the most pioneering problems in the field of operations research. The problem finds its application in manufacturing, construction, logistics, energy and many others. Various classes of algorithms based on simplex method (Taha, 2011), ellipsoid method and interior point method have been defined in the literature to solve a linear programming problem (LPP). But in real life situation, precision of data is not always guaranteed and a precise data may also lead to higher information cost. Ordinary methods like simplex method, graphical method, interior point method etc. cannot deal with vagueness and complexity and characteristics like certainty, simplicity and preciseness are not always guaranteed in real life problems. Thus LPP being able to deal with vague and imprecise data greatly contribute to its diffusion and application. So, in order to reduce the information costs and at the same time enhance real life modeling, the use of fuzzy coefficients (Zimmermann, 2011) in LPP was evolved.
Bellman and Zadeh (Bellman, 1970) were first to encounter the problem of decision making in such environment. Various works related to LPP in fuzzy environment have been done in last decades and some of them are (Veeramani, 2014) where Veeramani et. al used trapezoidal fuzzy numbers to denote imprecise coefficients and an algorithm based on simplex method has been used to solve the problem. In (Shaocheng, 1994), Tong S proposed methods to solve imprecise LPP with interval numbers and fuzzy numbers as its coefficients. In case of interval numbers as coefficients, the problem is further reduced to two crisp LPPs and then an optimal interval solution is sought. In case of fuzzy numbers as coefficients, 
-cuts are used to reduce fuzzy numbers to intervals and the problem is solved as an Interval Linear Programming problem (ILPP). ILPP has also been dealt by Sengupta et.al in (Sengupta A. a., 2001). He interpreted inequality constraints by the use of acceptability index and reduced ILPP to a LPP. A transformation method has been proposed by (Suprajitno, 2021) to solve ILPP. Two solution approaches to inner estimation of optimal solution set in ILPP has been proposed in (HladIk, 2020). An application of ILPP for sustainable selection of marine renewable energy projects is presented in (Akbari, 2021). Various researchers like Moore, Ishibuchi and Tanaka, Sengupta et. al have done extensive research on interval arithmetic, readers may refer (Moore, 1979), (Ishibuchi, 1990) and (Sengupta A. a., 1997). An outcome range problem in ILPP has been discussed in (Mohammadi, 2021). There are various methods by which a fuzzy LPP has been solved. Naseeri et. al (Nasseri, 2005) used simplex method to solve LPP with fuzzy variables. The problem has been solved by Maleki et. al in (Maleki, 2000) and they used the Maleki ranking function for defuzzification process. S. Suneela et. al also used a ranking function to defuzzify a LPP and reduced it to a crisp LPP in (Suneela, 2019). In (Kumar, 2011), a fully fuzzy LPP has been handled by Kumar et. al and the method proposed solves the fuzzy LPP with equality constraints without defuzzification and returns a fuzzy optimal solution. A new method for solving LPP with IT2FN has been discussed in (Javanmard, A solving method for fuzzy linear programming problem with interval type-2 fuzzy numbers, 2019). Linear programming problem with IT2TFN has also been discussed in (Dalman, 2019).