Fuzzy decision making of profit function in production planning using S-curve membership function

Any modern industrial manufacturing unit inevitably faces problems of vagueness in various aspects such as raw material availability, human resource availability, processing capability and constraints and limitations imposed by marketing department. Such a complex problem of vagueness and uncertainty can be handled by the theory of fuzzy linear programming. In this paper, a new fuzzy linear programming based methodology using a modified S-curve membership function is used to solve fuzzy mix product selection problem in Industrial Engineering. Profits and satisfactory level have been computed using fuzzy programming approach. Since there are several decisions to be taken, a performance measure has been defined to identify the decision for high level of profit with high degree of satisfaction.     

Detection of level of satisfaction and fuzziness patterns for MCDM model with modified flexible S-curve MF

The present research work deals with a logistic membership function (MF), within non-linear MFs, in finding out fuzziness patterns in disparate level of satisfaction for Multiple Criteria Decision-Making (MCDM) problem. This MF is a modified form of general set of S-curve MF. Flexibility of this MF in applying to real world problem has also been validated through a detailed analysis. An example illustrating an MCDM model applied in an industrial engineering problem has been considered to demonstrate the veracity of the proposed technique. The approach presented here provides feedback to the decision maker, implementer and analyst and gives a clear indication about the appropriate application and usefulness of the MCDM model. The key objective of this paper is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction with lesser degree of vagueness under tripartite fuzzy environment.     

Sensing degree of fuzziness in MCDM model using modified flexible S -curve MF

It is hard to sense the degree of vagueness while using a Multiple Criteria Decision-Making (MCDM) model in industrial engineering problems. Selection of best candidate-alternative is an important issue when the attributes of the candidate-alternatives are conflicting in nature and they have incommensurable units. An MCDM model makes it possible to select the candidate-alternative that suits best for the investor. An example illustrating an MCDM model applied in plant-site selection problem has been considered in this article to demonstrate the veracity of the proposed methodology. The degree of vagueness hidden in the proposed approach has been investigated using a flexible modified logistic membership function (MF). The approach presented here provides feedback to the decision maker, implementer and analyst and gives a clear indication about the appropriate application and usefulness of the MCDM model. The key objective of this article is to guide decision makers in finding out the best candidate-alternative with higher degree of satisfaction and lesser degree of vagueness.     

Interactive fuzzy random cooperative two-level linear programming through level sets based probability maximization

In this paper, assuming cooperative behavior of the decision makers, two-level linear programming problems under fuzzy random environments are considered. To deal with the formulated fuzzy random two-level linear programming problems, α-level sets of fuzzy random variables are introduced and an α-stochastic two-level linear programming problem is defined for guaranteeing the degree of realization of the problem. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced and the α-stochastic two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. Through probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example is provided to demonstrate the feasibility and efficiency of the proposed method.     

An Interactive Satisfying Method Based on Alternative Tolerance for Multiple Objective Optimization With Fuzzy Parameters

An interactive satisfying method based on alternative tolerance is presented for the multiple objective optimization problem with fuzzy parameters. Using the $alpha $ -level sets of the fuzzy numbers, all the objectives are modeled as the fuzzy goals, and the tolerances of the objectives are iteratively changed according to a decision maker for a satisfying solution. Via a specific attainable point programming model, the membership functions can be modified, and then, a lexicographic two-phase programming procedure is constructed correspondingly to find the final solution. In a special case, the objective constraint is added instead of changing the membership functions; therefore, the dissatisfying objectives for the decision maker can be improved step by step. The presented method not only acquires the $alpha $ -Pareto optimal or weak $alpha $-Pareto optimal solution of the fuzzy multiple objective optimization, but also satisfies the progressive preference of the decision maker. A numerical example shows its power.      

An integrated fuzzy multi criteria group decision making approach for ERP system selection

This paper aims to ease group decision-making by using an integration of fuzzy AHP (analytic hierarchy process) and fuzzy TOPSIS (technique for order preference by similarity to ideal solution) and its application to software selection of an electronic firm. Firstly, priority values of criteria in software selection problem have been determined by using fuzzy extension of AHP method. Fuzzy extension of AHP is suggested in this paper because of little computation time and much simpler than other fuzzy AHP procedures. Then, the result of the fuzzy TOPSIS model can be employed to define the most appropriate alternative with regard to this firm's goals in uncertain environment. Fuzzy numbers are presented in all phases in order to overcome any vagueness in decision making process. The final decision depends on the degree of importance of each decision maker so that wrong degree of importance causes the mistaken result. The researchers generally determine the degrees of importance of each decision maker according to special characteristics of each decision maker as subjectivity. In order to overcome this subjectivity in this paper, the judgments of decision makers are degraded to unique decision by using an attribute based aggregation technique. There is no study about software selection using integrated fuzzy AHP-fuzzy TOPSIS approach with group decision-making based on an attribute based aggregation technique. The results of the proposed approach and the other approaches are compared. Results indicate that our methodology allows decreasing the uncertainty and the information loss in group decision making and thus, ensures a robust solution to the firm.     

An interactive fuzzy satisficing method for multiobjectivenonconvex programming problems with fuzzy numbers through coevolutionarygenetic algorithms

In this paper, by considering the experts' fuzzy understanding of the nature of the parameters in the problem-formulation process, multiobjective nonconvex nonlinear programming problems with fuzzy numbers are formulated and an interactive fuzzy satisficing method through coevolutionary genetic algorithms is presented. Using the alpha-level sets of fuzzy numbers, the corresponding nonfuzzy alpha-programming problem is introduced. After determining the fuzzy goals of the decision maker, if the decision maker specifies the degree alpha and the reference membership values, the corresponding extended Pareto optimal solution can be obtained by solving the augmented minimax problems for which the coevolutionary genetic algorithm, called GENOCOP III, is applicable. In order to overcome the drawbacks of GENOCOP III, the revised GENOCOP III is proposed by introducing a method for generating an initial feasible point and a bisection method for generating a new feasible point efficiently. Then an interactive fuzzy satisficing method for deriving a satisficing solution for the decision maker efficiently from an extended Pareto optimal solution set is presented together with an illustrative numerical example.     

Fuzzy Production Planning and its Application to Decision Making

This paper presents new methods for solving a production-planning problem. First the modified s-curve membership function as a methodology is constructed. Then fuzzy production planning problems with vagueness parameters alpha and fuzzy objective coefficients, fuzzy technical coefficients and fuzzy resource variables are outlined. The objective of this paper is to find a satisfactory solution for optimal profit in which vagueness is playing major factor in selecting the solution. Finally a practical application of decision-making in production planning is illustrated.     

Finding the maximal membership in a fuzzy set of an element from another fuzzy set

The problem of finding the maximal membership grade in a fuzzy set of an element from another fuzzy set is an important class of optimisation problems manifested in the real world by situations in which we try to find what is the optimal financial satisfaction we can get from a socially responsible investment. Here, we provide a solution to this problem. We then look at the proposed solution for fuzzy sets with various types of membership grades, ordinal, interval value and intuitionistic.     

Interactive fuzzy programming for fuzzy random two-level linear programming problems through probability maximization with possibility

This paper considers two-level linear programming problems involving fuzzy random variables under cooperative behavior of the decision makers. Through the introduction of fuzzy goals together with possibility measures, the formulated fuzzy random two-level linear programming problem is transformed into the problem to maximize the satisfaction degree for each fuzzy goal. By adopting probability maximization, the transformed stochastic two-level programming problem can be reduced to a deterministic one. Interactive fuzzy programming to derive a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.