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Many decision-making problems can solve successfully by traditional optimization methods with a well-defined configuration. The formulation of such optimization problems depends on crisply objective functions and a specific system of constraints. Nevertheless, in reality, in any decision-making process, it is often observed that due to some doubt or hesitation, it is pretty tricky for decision-maker(s) to specify the precise/crisp value of any parameters and compelled to take opinions from different experts which leads towards a set of conflicting values regarding satisfaction level of decision-maker(s). Therefore the real decision-making problem cannot always be deterministic. Various types of uncertainties in parameters make it fuzzy. This paper presents a practical mathematical framework to reflect the reality involved in any decision-making process. The proposed method has taken advantage of the hesitant fuzzy aggregation operator and presents a particular way to emerge in a decision-making process. For this purpose, we have discussed a couple of different hesitant fuzzy aggregation operators and developed linear and hyperbolic membership functions under hesitant fuzziness, which contains the concept of hesitant degrees for different objectives. Finally, an example based on a multiobjective optimization problem is presented to illustrate the validity and applicability of our proposed models. [ABSTRACT FROM AUTHOR]

Some of the actual life decisions are made in decentralized manner under uncertainty. This paper formulates a quadratic fractional bi-level (QFBL) programming problem with probabilistic constraints in both first (leader) and second level (follower) having two parameter exponential random variables with known probability distributions and fuzziness is considered as triangular and trapezoidal fuzzy number. These fuzzy numbers of the membership functions related with the proportional probability density function has been used to introduce a defuzzification approach for finding the crisp values of fuzzy numbers. In the proposed model the problem is first converted into an equivalent deterministic quadratic fractional fuzzy bi level programming model by applying chance constrained programming technique. Secondly, in the suggested model, each objective function of the bi-level quadratic fractional programming problem has its own nonlinear membership function. The fuzzy goal programming (FGP) approach is used to find a compromise solution for the BLQFP problem. Finally, to demonstrate the applicability and performance of the proposed approach an illustrative numerical example is given. [ABSTRACT FROM AUTHOR]

In any decision-making process, it is often observed that due to some doubt or hesitation, it is quite difficult for decision maker(s) to specify the precise/crisp value of any parameters which results in the existence of uncertainty among parameter. In this study, a multiobjective nonlinear transportation problem (MO-NTP) has been formulated with fuzzy parameters. The nonlinearity occurs in cost function due to the existence of extra cost in the fixed cost which has been discussed briefly. The solution method, neutrosophic compromise programming approach (NCPA), based on neutrosophic decision set has been investigated which contains the concept of indeterminacy degree along with membership and non-membership degree of different objectives. It also provides an effective framework which reflects the reality involved in any decision making process. In order to show the validity and suitability of NCPA, a numerical example has been presented. The superiority of the NCPA has been shown by doing a comparative study with other existing approaches. [ABSTRACT FROM AUTHOR]

In many real-life situations, it is often observed that the degree of indeterminacy (neutrality) plays an important role along with the satisfaction and dissatisfaction levels of the decision maker(s) (DM(s)) in any decision making process. Due to some doubt or hesitation, it may necessary for DM(s) to take opinions from experts which leads towards a set of conflicting values regarding satisfaction, indeterminacy and dis-satisfaction level of DM(s). In order to highlight the above-mentioned insight, we have developed an effective framework which reflects the reality involved in any decision-making process. In this study, a multiobjective nonlinear programming problem (MO-NLPP) has been formulated in the manufacturing system. A new algorithm, neutrosophic hesitant fuzzy programming approach (NHFPA), based on singlevalued neutrosophic hesitant fuzzy decision set has been proposed which contains the concept of indeterminacy hesitant degree along with truth and falsity hesitant degrees of different objectives. In order to show the validity and applicability of the proposed approach, a numerical example has been presented. The superiority of the proposed approach has been shown by comparing with other existing approaches. Based on the present work, conclusions and future scope have been presented. [ABSTRACT FROM AUTHOR]

Supplier selection plays a vital role in evolving an effective supply chain and the overall performance of organisations. Choosing suppliers may involve different levels arranged in a hierarchical structure. Decisions are made successively starting from the first level to the last level. Decision variables are partitioned between different levels and are called controlling factors. In the paper, we propose a multilevel supplier selection problem with uncertain or fuzzy demand and supply. Since objectives may be conflicting in nature, possible relaxations in the form of tolerances are provided by the upper level decision makers to avoid decision deadlocks. We use (linear) membership functions to fuzzily describe objective functions, as well as the controlling factors, and generate satisfactory solutions. We extend and present an approach to solving multilevel decision making problems when fuzzy constraints are employed. Different scenarios are constructed within a numerical illustration, based on the selection of controlling factors by the upper level decision makers. [ABSTRACT FROM AUTHOR]