Optimisation under hybrid uncertainty

A note on “Solving linear programming problems under fuzziness and randomness environment using attainment values”

“…One is to perform the conversion of the de-fuzzification and de-randomization in a sequential manner [16,15,9]. The other is to perform both processes in a simultaneous manner [6,12,14].…”

FSILP: Fuzzy-stochastic-interval linear programming for supporting municipal solid waste management

“…The commonly used approaches of integrating FP with SP and IP were featured by defuzzifying and derandomizing fuzzy random variables in a sequential (Luhandjula, 1996(Luhandjula, , 2004Iskander, 2005) or in a simultaneous manner (Liu, 2001;Liu andLiu, 2002, 2005). Either defuzzification or derandomization could only be applied before or after the SP or IP approach, which limited their abilities in dynamic integration.…”

Solving fuzzy (stochastic) linear programming problems using superiority and inferiority measures

“…The new measures are used to evaluate any violation of the constraints to convert the fuzzy (stochastic) linear program into the standard deterministic linear program (LP). In literature, the general direction to handle the challenge of solving fuzzy (stochastic) linear programming problems is to defuzzify and/or derandomize fuzzy numbers/fuzzy stochastic variables [11,6,4,2,10,3,9,7,17,18,16,13,14,12,15,8]. The main difference between the developed methods is the way to defuzzify and/or derandomize fuzzy numbers/fuzzy stochastic variables.…”

“…The most popular approach to convert the fuzzy linear program (FLP) into the conventional deterministic linear program (LP) is the method of ordering fuzzy numbers such as the area compensation method [5], the expected mid-point of fuzzy numbers [9], the grade of possibility and necessity [1], the signed distance method [3]. Similarly, the fuzzy stochastic linear program (FSLP) has also been handled by defuzzifying and derandomizing fuzzy random variables in the sequential manner [17,18,16,8] or in the simultaneous manner [13,14,21,12,20,15,19]. In the sequential approaches, the defuzzifying process is performed first.…”