The objective of this paper is to develop matrix games with pay-offs of triangular hesitant fuzzy elements (THFEs). To solve such games, a new methodology has been derived based on the notion of weighted average operator and score function of THFEs. Firstly, we formulate two non-linear programming problems with THFEs. Then applying the score function of THFEs, we transform these two problems in...

In this paper, a quadratic programming (FFQP) problem is considered in which all of the cost coefficients, constraints coefficients, and right hand side of the constraints are characterized by L-R fuzzy numbers. Through this paper, the concept of α- level of fuzzy numbers for the objective function, and the order relations on the fuzzy numbers for the constraints are considered.  To optimize th...

This paper proposes a compromise model, based on a new method, to solve the multi-objective large-scale linear programming (MOLSLP) problems with block angular structure involving fuzzy parameters. The problem involves fuzzy parameters in the objective functions and constraints. In this compromise programming method, two concepts are considered simultaneously. First of them is that the optimal ...

Real time PCR is a powerful tool for studying the expression of genes involved in the pathophysiology of human diseases. Recent studies of the RAN (6p21), ZHX-2 (8q24.3), CHC1L (13q14.3) loci highlight the importance of these genes in multiple myeloma (MM) prognosis and therapeutic applications. Here, we described a detailed Real-Time PCR method for the detection of RAN, ZHX-2, and CHC1L expres...