•Formulation of two fixed charge transportation problems with type-2 fuzzy parameters.•Transportation Costs, supplies, demands, conveyance capacities are taken as type-2 fuzzy variables.•CV-based ...reduction methods and centroid method are applied for defuzzification.•Chance-constrained programming model is formulated using generalized credibility measure for the second problem.•Sensitivity analysis is done for different generalized credibility levels.
This paper considers two fixed charge transportation problems with type-2 fuzzy parameters. Unit transportation costs, fixed costs in the first problem and unit transportation costs, fixed costs, supplies and demands in the second problem are type-2 fuzzy variables. For the first problem, to get corresponding defuzzified values of the type-2 fuzzy cost parameters, first critical value (CV)-based reduction methods are applied to reduce type-2 fuzzy variables into type-1 fuzzy variables and then centroid method is used for complete defuzzification. Besides this, we also apply geometric defuzzification method to the type-2 fuzzy cost parameters in the first problem to provide a comparison of the results. Coming to the second problem, a chance-constrained programming model is formulated using generalized credibility measure for the objective function as well as the constraints with the CV-based reductions of corresponding type-2 fuzzy parameters. Next, the reduced model is turned into equivalent parametric programming problem. The deterministic problems so obtained are then solved by using the standard optimization solver – LINGO. We have provided numerical examples illustrating the proposed models and techniques. Some sensitivity analyzes for the second model are also presented.
Purpose
Good management strives to align and corporate processes for more attention being paid to supply chain management. Firms realize that greater co-operation and improved coordination can help ...to manage the entire supply chain more efficiently. The imperfect quality item is one of the most important issues that affect the expected profit of green supply chain. The imprecise cost with screening process of poor quality items posed in supply chain is the subject of this study.
Design/methodology/approach
The present study explores production model for imperfect items having uncertain cost parameters with three-layer supply chain encompassing supplier, manufacturer and retailer. The model is considering the impact of business tactics such as order size, production rate, production cost and appropriate times in various sectors on collaborative marketing systems. Due to imprecise cost parameters, the pentagonal fuzzy numbers are set to fuzzify the total cost and defuzzifition by using graded mean integration.
Findings
This study offers an explicit condition in uncertain environment to manage the imperfect quality item to increase the potential profit of the supply chain. The influence of changes in parameter values on the optimal inventory policy under fuzziness is provided managerial insights.
Originality/value
This model makes a significant contribution to fuzzy inference. The results of the study provide a trading strategy for the industry to avoid losses. The prescribed study can be suitable for the industries like sculpture, jewelry, pottery, etc.
Failure mode and effects analysis (FMEA) has been extensively used for examining potential failures in products, processes, designs and services. An important issue of FMEA is the determination of ...risk priorities of the failure modes that have been identified. The traditional FMEA determines the risk priorities of failure modes using the so-called risk priority numbers (RPNs), which require the risk factors like the occurrence (O), severity (S) and detection (D) of each failure mode to be precisely evaluated. This may not be realistic in real applications. In this paper we treat the risk factors O, S and D as fuzzy variables and evaluate them using fuzzy linguistic terms and fuzzy ratings. As a result, fuzzy risk priority numbers (FRPNs) are proposed for prioritization of failure modes. The FRPNs are defined as fuzzy weighted geometric means of the fuzzy ratings for O, S and D, and can be computed using alpha-level sets and linear programming models. For ranking purpose, the FRPNs are defuzzified using centroid defuzzification method, in which a new centroid defuzzification formula based on alpha-level sets is derived. A numerical example is provided to illustrate the potential applications of the proposed fuzzy FMEA and the detailed computational process of the FRPNs.
Type reduction (TR) followed by defuzzification is commonly used in interval type-2 fuzzy logic systems (IT2 FLSs). Because of the iterative nature of TR, it may be a computational bottleneck for the ...real-time applications of an IT2 FLS. This has led to many direct approaches to defuzzification that bypass TR, the simplest of which is the Nie-Tan direct defuzzification method (NT method). This paper provides some theoretical analyses of the NT method that answer the question "Why is the NT method good to use?" This paper also provides a direct relationship between TR followed by defuzzification (using KM algorithms) and the NT method. It also provides an improved NT method. Numerical examples illustrate our theoretical results and suggest that the NT method is a very good way to simplify an interval type-2 fuzzy set.
This paper proposes a new approach for defuzzification of interval type-2 fuzzy sets. The collapsing method converts an interval type-2 fuzzy set into a type-1
representative embedded set (RES), ...whose defuzzified values closely approximates that of the type-2 set. As a type-1 set, the RES can then be defuzzified straightforwardly. The novel
representative embedded set approximation (RESA), to which the method is inextricably linked, is expounded, stated and proved within this paper. It is presented in two forms:
Simple RESA: this approximation deals with the most simple interval FOU, in which a vertical slice is discretised into 2 points.
Interval RESA: this approximation concerns the case in which a vertical slice is discretised into 2 or more points. The collapsing method (simple RESA version) was tested for accuracy and speed, with excellent results on both criteria. The collapsing method proved more accurate than the Karnik–Mendel iterative procedure (KMIP) for an asymmetric test set. For both a symmetric and an asymmetric test set, the collapsing method outperformed the KMIP in relation to speed.
This research addresses the problem of restaurant locations ranking with applications for a cosmopolitan big city like Kolkata, India. A restaurant selection is based on occasions, spending ...capability, environment, location, comfort, quality of the food etc. In this research paper an exhaustive set of factors and sub-factors is taken into consideration to select and rank restaurants situated at different locations in the city of Kolkata with a population of around fifteen million. The ranking of restaurants depends on complex, conflicting qualitative attributes. In the paper hexagonal fuzzy numbers (HFN) have been used to suitably depict the imprecise uncertain environment. HFN, its distance measure and defuzzification have been applied to deal with the hesitancy and impreciseness of the decision makers. Analytic hierarchy process (AHP) has been used as a Multi Criteria Decision Making (MCDM) tool to obtain factors and sub-factors weights. TOPSIS and COPRAS methods were used for ranking different restaurant locations. Using comparative analysis it is shown that HFN with the TOPSIS and COPRAS method gives better result than other fuzzy numbers. The sensitivity analysis portion also gives a direction for taking a suitable decision in different possible scenario.
In fuzzy decision-making, incomplete information always leads to uncertain and partially reliable judgements. The emergence of fuzzy set theory helps decision-makers in handling uncertainty and ...vagueness when making judgements. Intuitionistic Fuzzy Numbers (IFN) measure the degree of uncertainty better than classical fuzzy numbers, while Z-numbers help to highlight the reliability of the judgements. Combining these two fuzzy numbers produces Intuitionistic Z-Numbers (IZN). Both restriction and reliability components are characterized by the membership and non-membership functions, exhibiting a degree of uncertainties that arise due to the lack of information when decision-makers are making preferences. Decision information in the form of IZN needs to be defuzzified during the decision-making process before the final preferences can be determined. This paper proposes an Intuitive Multiple Centroid (IMC) defuzzification of IZN. A novel Multi-Criteria Decision-Making (MCDM) model based on IZN is developed. The proposed MCDM model is implemented in a supplier selection problem for an automobile manufacturing company. An arithmetic averaging operator is used to aggregate the preferences of all decision-makers, and a ranking function based on centroid is used to rank the alternatives. The IZN play the role of representing the uncertainty of decision-makers, which finally determine the ranking of alternatives.
Defuzzification of fuzzy sets is an important aspect of fuzzy processing, as it determines how the fuzziness is dealt with when performing the final step to obtain crisp solutions. In this ...contribution, we consider the possibility of defuzzifying multiple general type-1 fuzzy sets, given that their defuzzified values are bound by a single, known constraint. This stems from an application in spatial data processing, where we obtained a number of fuzzy sets whose defuzzified values should sum up to a crisp and known value. It is possible to defuzzify each fuzzy set individually and rescale the outcomes to meet the constraint. However, considering that the fuzzy set contains information on what constitutes good values, accounting for the constraint in the defuzzification process has the potential to yield better results. We considered this as an optimization problem and investigated appropriate goal functions. The approach and goal functions are discussed with respect to typical properties of defuzzifiers.
Stratification is a feature of the type-reduced set of the general type-2 fuzzy set, from which a new technique for general type-2 defuzzification, Stratic Defuzzification, may be derived. Existing ...defuzzification strategies are summarised. The stratified structure is described, after which the Stratic Defuzzifier is presented and contrasted experimentally for accuracy and efficiency with both the Exhaustive Method of Defuzzification (to benchmark accuracy) and the α-Planes/Karnik–Mendel Iterative Procedure strategy, employing 5, 11, 21, 51 and 101 α-planes. The Stratic Defuzzifier is shown to be much faster than the Exhaustive Defuzzifier. In fact the Stratic Defuzzifier and the α-Planes/Karnik–Mendel Iterative Procedure Method are comparably speedy; the speed of execution correlates with the number of planes participating in the defuzzification process. The accuracy of the Stratic Defuzzifier is shown to be excellent. It is demonstrated to be more accurate than the α-Planes/Karnik–Mendel Iterative Procedure Method in four of six test cases, regardless of the number of α-planes employed. In one test case, it is less accurate than the α-Planes/Karnik–Mendel Iterative Procedure Method, regardless of the number of α-planes employed. In the remaining test case, the α-Planes/Karnik–Mendel Iterative Procedure Method with 11 α-Planes gives the most accurate result, with the Stratic Defuzzifier coming second.
•Minimum triangular norm (t-norm) leads to unrealizable fuzzy PID controllers.•Algebraic Product t-norm leads to realizable fuzzy PID controllers.•Two fuzzy PID controllers are derived using two ...different inference methods, namely, Larsen product and Mamdani minimum.•The mathematical models of the controllers are obtained using Minimum t-norm, Maximum triangular conorm, and Centre of Area (Centre of Gravity) defuzzification.
In this paper, we show that Minimum triangular norm (Min t-norm) always leads to unrealizable fuzzy PID (FPID) controllers. To show this, mathematical models of two FPID controllers are obtained. Two fuzzy sets, Negative (N) and Positive (P), for fuzzification of each of the three input variables (error, change of error, and double change of error), and four fuzzy sets N, Negative Small (NS), Positive Small (PS), and P on the output variable (change of control effort) are considered. Min t-norm, Maximum (Max) s-norm, triangular membership functions, Larsen Product (LP)/ Mamdani Minimum (MM) inference, and Centre of Area (Centre of Gravity) (CoA (CoG)) defuzzification are used for mathematical modeling of the controllers. Then upon thoroughly analyzing the properties of the mathematical models of the controllers, we show that Min t-norm leads to unrealizable FPID controllers.
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