Machine tool selection has been an important issue in the manufacturing industry because improper machine tool selection can have a negative effect on productivity, accuracy, flexibility, and the ...responsive manufacturing capabilities of a company. The current multi-criteria decision making (MCDM) approach of machine tool selection mostly focuses on the subjective perspective. However, as the objective evaluation represents the actual performance of machine tools, both subjective and objective perspectives need to be considered when choosing an appropriate machining tool. Therefore, this study proposes a machine tool selection method based on a novel hybrid MCDM model. Firstly, the presented method employs a comprehensive weight technique integrating subjective weights obtained using fuzzy decision-making trial and evaluation laboratory (FDEMATEL) with objective weights obtained using entropy weighting (EW). Secondly, later defuzzification VIKOR (LDVIKOR) is put forward to rank the optional alternatives. Finally, a case application verifies the effectiveness of the proposed method. The evaluation results indicate that the best and worst selected machine tool of the proposed method keeps high conformance with the actual ranking in real factory. Additionally, sensitivity analysis results of the effect of parameters φ on the decision outcome show that irrespective of the variations in this parameter, the best decision outcome will be not influenced. These indicate that the presented hybrid model has advantages in granting flexibility to the preferences of decision makers.
•This research presents a method to select the optimal machine tool.•A novel hybrid MCDM model is proposed to choose the best alternative.•Sensitivity analysis show advantages concerning the decision-makers’ preference.
This article deals with the new approach of finding the defuzzification / ranking index of various types of fuzzy sets. Traditionally, in most of the articles on fuzzy decision making the ...defuzzification methods are not justified with respect to that of highest aspiration levels. This study highlights an efficient defuzzification (ranking) method which links between the gaps on the defuzzified values obtained using ??? and without ??? of fuzzy numbers. Moreover, for a given problem different membership grades are found by different researchers which are confusing and contradicts the conceptual uniqueness of fuzzy set itself. To resolve these issues, first of all, we have studied a polygonal fuzzy set by means of an interpolating polynomial function. However, in fuzzy set theory we usually seek the highest membership grade for ranking any kind of decision-making problem therefore, maximizing the polynomial function, we get the index value of the proposed fuzzy set. An artificial intelligence (AI) based solution algorithm has also been developed to find the exact defuzzified value. Indeed, considering two numerical examples we have compared these ranking values with some of the existing state of- arts under higher aspiration levels. Finally, some graphical illustrations have also been done to justify the proposed approach.
► The Fuzzy VIKOR method solves fuzzy multicriteria problem. ► A ranking fuzzy merit represents distance of alternatives to the ideal solution.
The fuzzy VIKOR method has been developed to solve ...fuzzy multicriteria problem with conflicting and noncommensurable (different units) criteria. This method solves problem in a fuzzy environment where both criteria and weights could be fuzzy sets. The triangular fuzzy numbers are used to handle imprecise numerical quantities. Fuzzy VIKOR is based on the aggregating fuzzy merit that represents distance of an alternative to the ideal solution. The fuzzy operations and procedures for ranking fuzzy numbers are used in developing the fuzzy VIKOR algorithm. VIKOR (VIsekriterijumska optimizacija i KOmpromisno Resenje) focuses on ranking and selecting from a set of alternatives in the presence of conflicting criteria, and on proposing compromise solution (one or more). It is extended with a trade-offs analysis. A numerical example illustrates an application to water resources planning, utilizing the presented methodology to study the development of a reservoir system for the storage of surface flows of the Mlava River and its tributaries for regional water supply. A comparative analysis of results by fuzzy VIKOR and few different approaches is presented.
The paper describes a new fuzzy filter based on the method of areas’ ratio which allows to reduce noise during filtering signals. To expand the functionality of the method of areas’ ratio two ...computational procedures were developed to eliminate errors inherent in classical defuzzification models, namely a narrow range of defuzzification and insensitivity of a defuzzification model. Presented various computational procedures for the fuzzy filter can change the properties of the output variable resulting. As an example, the proposed mathematical model of the Fuzzy Filter based on the Method of Areas’ Ratio illustrated its distinctive characteristics are shown. Firstly, the Fuzzy Filter based on the Method of Areas’ Ratio model has the property of continuity. Secondly, computational procedures provide an increase in the performance of the fuzzy filter. Using detailed numerically calculated Root Mean Square Error and Mean Absolute Percentage Error evaluated the proposed model of the fuzzy filter with other filters such as Kalman Filter, Fuzzy Kalman Filter, Ensemble Kalman Filter and Fuzzy Extended Kalman Filter, Basic defuzzification distributions, Fuzzy mean, Quality method, Root mean square and New weighted trapezoid median average. One of the main goals of the article was to confirm the hypothesis about the possibility of using a fuzzy filter based on the method of area’s ratio for filtering signals. As well as studies of the sensitivity of the proposed fuzzy filter is based on the Root Mean Square Error and Mean Absolute Percentage Error coefficients. These coefficients were established during the experimental studies and showed that the sensitivity of the fuzzy filter based on the method of area’s ratio is better than other filters.
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•Methods to reduce errors inherent in the classic defuzzifiers models are shown.•The fast procedures of FF-MAR speed up defuzzification process.•The experiment proves the effectiveness proposed of FF-MAR procedures.
Fuzzy sets are an important approach to model uncertainty. Defuzzification maps fuzzy sets to non–fuzzy (crisp) values. Type–2 fuzzy sets model uncertainty in the degree of membership in a fuzzy set. ...Type–2 defuzzification maps type–2 fuzzy sets to non–fuzzy values. Type reduction maps type–2 fuzzy sets to type–1 fuzzy sets, in order to make type–2 defuzzification easier and to implement more efficient type–2 defuzzification algorithms.
This paper is a first step towards a theoretical foundation of the emerging field of type reduction. Five mathematical properties of type reduction are defined, and two existing type reduction methods (Nie–Tan and uncertainty weight) are examined with respect to our five properties. Furthermore, two new type reduction methods are proposed: consistent linear type reduction and consistent quadratic type reduction. All our five properties are satisfied by consistent quadratic type reduction.
While fuzzy controllers with multiple fuzzy sets and non-uniformly distributed membership functions have the potential to provide better system performance, from the literature, it appears to the ...authors that till now, no one has found exact mathematical models of fuzzy PI/PD controllers with non-uniformly distributed multiple fuzzy sets and Center of Area (CoA) defuzzification. To bridge this gap, in this paper, analytical structures of the general Mamdani type fuzzy PI/PD controllers are presented using unequally distributed multiple fuzzy sets, Minimum (Min) t-norm, Maximum (Max) s-norm, Larsen Product (LP) inference, and CoA defuzzification. For the purpose of comparison, analytical structures of the controllers are also obtained using Center of Sums (CoS) defuzzification. Properties of the newly obtained controllers are analyzed and compared. Since digital computers are often used for simulation, a rough estimate of the computational complexities and memory requirements are provided. To show the applicability of the newly developed controllers, a nonlinear DC series motor and a nonlinear plant with dead-time are considered. The effectiveness of the proposed controllers is finally shown through a detailed system performance comparison.
This paper introduces a new defuzzification technique derived as a generalization of the formula for the calculation of possibilistic mean originally proposed by Carlsson and Fullér in 2001 for fuzzy ...numbers. Unlike the possibilistic mean, the generalized formulation allows also for the defuzzification of subnormal convex fuzzy sets and also for non-convex fuzzy sets (e.g. the outputs of Mamdani- or Larsen-type fuzzy inference). The Luukka–Stoklasa–Collan transformation introduced in 2019 is applied to generalize the possibilistic mean formula. Using this transformation an algorithm for the calculation of the possibilistic-mean-based defuzzification of a general fuzzy set with a continuous membership function on the given interval is proposed. This way the Luukka–Stoklasa Defuzzification (LSD) inspired by the possibilistic mean construction is introduced - a defuzzification that can be calculated also for fuzzy sets in general (subnormal, non-convex), not only for fuzzy numbers. As such LSD is applicable also in fuzzy expert systems and fuzzy control settings where the outputs of the inference systems can be expected to be represented by subnormal and non-convex fuzzy sets. Fast-computation formulas for LSD of piece-wise linear fuzzy sets are also provided. The applicability of LSD in the ranking of fuzzy numbers and its ability to distinguish between fuzzy numbers where other frequently used defuzzification methods do not is shown. Two more case studies are presented where LSD outperforms the chosen frequently used defuzzification methods: a fuzzy expert system for inventory control and a fuzzy cruise controller problem.
Laplace transforms play an essential role in the analysis of classical non-Markovian queueing systems. The problem addressed here is whether the Laplace transform approach is still valid for ...determining the characteristics of such a system in a fuzzy environment. In this paper, fuzzy Laplace transforms are applied to analyze the performance measures of a non-Markovian fuzzy queueing system FM/ FG/1. Starting from the fuzzy Laplace transform of the service time distribution, we define the fuzzy Laplace transform of the distribution of the dwell time of a customer in the system. By applying the properties of the moments of this distribution, the derivative of this fuzzy transform makes it possible to obtain a fuzzy expression of the average duration of stay of a customer in the system. This expression is the fuzzy formula of the same performance measure that can be obtained from its classical formula by the Zadeh extension principle. The fuzzy queue FM/ FE_k /1 is particularly treated in this text as a concrete case through its service time distribution. In addition to the fuzzy arithmetic of L-R type fuzzy numbers, based on the secant approximation, the properties of the moments of a random variable and Little's formula are used to compute the different performance measures of the system. A numerical example was successfully processed to validate this approach. The results obtained show that the modal values of the performance measures of a non-Markovian fuzzy queueing system are equal to the performance measures of the corresponding classical model computable by the Pollaczeck-Khintchine method. The fuzzy Laplace transforms approach is therefore applicable in the analysis of a fuzzy FM/FG/1 queueing system in the same way as the classical M/G/1 model.
Laplace transforms play an essential role in the analysis of classical non-Markovian queueing systems. The problem addressed here is whether the Laplace transform approach is still valid for ...determining the characteristics of such a system in a fuzzy environment. In this paper, fuzzy Laplace transforms are applied to analyze the performance measures of a non-Markovian fuzzy queueing system FM/ FG/1. Starting from the fuzzy Laplace transform of the service time distribution, we define the fuzzy Laplace transform of the distribution of the dwell time of a customer in the system. By applying the properties of the moments of this distribution, the derivative of this fuzzy transform makes it possible to obtain a fuzzy expression of the average duration of stay of a customer in the system. This expression is the fuzzy formula of the same performance measure that can be obtained from its classical formula by the Zadeh extension principle. The fuzzy queue FM/ FE_k /1 is particularly treated in this text as a concrete case through its service time distribution. In addition to the fuzzy arithmetic of L-R type fuzzy numbers, based on the secant approximation, the properties of the moments of a random variable and Little's formula are used to compute the different performance measures of the system. A numerical example was successfully processed to validate this approach. The results obtained show that the modal values of the performance measures of a non-Markovian fuzzy queueing system are equal to the performance measures of the corresponding classical model computable by the Pollaczeck-Khintchine method. The fuzzy Laplace transforms approach is therefore applicable in the analysis of a fuzzy FM/FG/1 queueing system in the same way as the classical M/G/1 model.
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