Abstract: The purpose of this paper is to present fuzzy TOPSIS in an entropic fuzzy environment. Due to the ambiguous concepts often represented in decision data, exact values are insufficient to model real-life situations. In this paper, the rating of each alternative is defined in fuzzy linguistic terms, which can be expressed with triangular fuzzy numbers. The weight of each criterion is then derived from the decision matrix using the entropy weighting method. Next, a vertex method is proposed to calculate the distance between two triangular fuzzy numbers. According to the TOPSIS concept, a closeness coefficient is defined to determine the ranking order of all alternatives by simultaneously calculating the distances to both the fuzzy positive-ideal solution (FPIS) and the fuzzy negative-ideal solution (FNIS). Finally, an illustrative example of selecting stealth fighter aircraft is shown at the end of this article to highlight the procedure of the proposed method. Correlation analysis and validation analysis using TOPSIS, WSM, and WPM methods were performed to compare the ranking order of the alternatives.
Abstract: This article presents a multiple criteria evaluation approach to uncertainty, vagueness, and imprecision analysis for ranking alternatives with fuzzy data for decision making using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). The fighter aircraft evaluation and selection decision making problem is modeled in a fuzzy environment with triangular fuzzy numbers. The fuzzy decision information related to the fighter aircraft selection problem is taken into account in ordering the alternatives and selecting the best candidate. The basic fuzzy TOPSIS procedure steps transform fuzzy decision matrices into matrices of alternatives evaluated according to all decision criteria. A practical numerical example illustrates the proposed approach to the fighter aircraft selection problem.
Abstract: This article presents a new approach to uncertainty, vagueness, and imprecision analysis for ranking alternatives with fuzzy data for decision making using the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In the proposed approach, fuzzy decision information related to the aircraft selection problem is taken into account in ranking the alternatives and selecting the best one. The basic procedural step is to transform the fuzzy decision matrices into matrices of alternatives evaluated according to all decision criteria. A numerical example illustrates the proposed approach for the military combat aircraft selection problem.
Abstract: Vendor (supplier) selection is a group decision-making (GDM) process, in which, based on some predetermined criteria, the experts’ preferences are provided in order to rank and choose the most desirable suppliers. In the real business environment, our attitudes or our choices would be made in an uncertain and indecisive situation could not be expressed in a crisp framework. Intuitionistic fuzzy sets (IFSs) could handle such situations in the best way. VIKOR method was developed to solve multi-criteria decision-making (MCDM) problems. This method, which is used to determine the compromised feasible solution with respect to the conflicting criteria, introduces a multi-criteria ranking index based on the particular measure of 'closeness' to the 'ideal solution'. Until now, there has been a little investigation of VIKOR with IFS, therefore we extended the intuitionistic fuzzy (IF) VIKOR to solve vendor selection problem under IF GDM environment. The present study intends to develop an IF VIKOR method in a GDM situation. Therefore, a model is presented to calculate the criterion weights based on entropy measure. Then, the interval-valued intuitionistic fuzzy weighted geometric (IFWG) operator utilized to obtain the total decision matrix. In the next stage, an approach based on the positive idle intuitionistic fuzzy number (PIIFN) and negative idle intuitionistic fuzzy number (NIIFN) was developed. Finally, the application of the proposed method to solve a vendor selection problem illustrated.
Abstract: Analysing the world banking sector, we realize that traditional risk measurement methodologies no longer reflect the actual scenario with uncertainty and leave out events that can change the dynamics of markets. Considering this, regulators and financial institutions began to search more realistic models. The aim is to include external influences and interdependencies between agents, to describe and measure the operationalization of these complex systems and their risks in a more coherent and credible way. Within this context, X-Events are more frequent than assumed and, with uncertainties and constant changes, the concept of antifragility starts to gain great prominence in comparison to others methodologies of risk management. It is very useful to analyse whether a system succumbs (fragile), resists (robust) or gets benefits (antifragile) from disorder and stress. Thus, this work proposes the creation of the Banking Antifragility Index (BAI), which is based on the calculation of a triangular fuzzy number – to "quantify" qualitative criteria linked to antifragility.
Abstract: The relationship between Corporate Social Responsibility (CSR) and financial performance (FP) is a subject of great interest that has not yet been resolved. In this work, we have developed a new and original tool to measure this relation. The tool quantifies the value contributed to companies that are committed to CSR. The theoretical model used is the fuzzy discounted cash flow method. Two assumptions have been considered, the first, the company has implemented the IQNet SR10 certification, and the second, the company has not implemented that certification. For the first one, the growth rate used for the time horizon is the rate maintained by the company after obtaining the IQNet SR10 certificate. For the second one, both, the growth rates company prior to the implementation of the certification, and the evolution of the sector will be taken into account. By using triangular fuzzy numbers, it is possible to deal adequately with each company’s forecasts as well as the information corresponding to the sector. Once the annual growth rate of the sales is obtained, the profit and loss accounts are generated from the annual estimate sales. For the remaining elements of this account, their regression with the nets sales has been considered. The difference between these two valuations, made in a fuzzy environment, allows obtaining the value of the IQNet SR10 certification. Although this study presents an innovative methodology to quantify the relation between CSR and FP, the authors are aware that only one company has been analyzed. This is precisely the main limitation of this study which in turn opens up an interesting line for future research: to broaden the sample of companies.
Abstract: Transportation Problem (TP) is based on supply and demand of commodities transported from one source to the different destinations. Usual methods for finding solution of TPs are North-West Corner Rule, Least Cost Method Vogel’s Approximation Method etc. The transportation costs tend to vary at each time. We can use fuzzy numbers which would give solution according to this situation. In this study the Best Candidate Method (BCM) is applied. For ranking Centroid Ranking Technique (CRT) and Robust Ranking Technique have been adopted to transform the fuzzy TP and the above methods are applied to EDWARDS Vacuum Company, Crawley, in West Sussex in the United Kingdom. A Comparative study is also given. We see that the transportation cost can be minimized by the application of CRT under BCM.
Abstract: In this paper, a method is proposed for solving Fuzzy Multi-Objective Linear Programming problems (FMOLPP) with fuzzy right hand side and fuzzy decision variables. To illustrate the proposed method, it is applied to the problem of selecting suppliers for an automotive parts producer company in Iran in order to find the number of optimal orders allocated to each supplier considering the conflicting objectives. Finally, the obtained results are discussed.
Abstract: This work proposed a multi-objective mathematical programming approach to select the appropriate supply network elements. The multi-item multi-objective production-distribution inventory model is formulated with possible constraints under fuzzy environment. The unit cost has taken under fuzzy environment. The inventory model and warehouse location model has combined to formulate the production-distribution inventory model. Warehouse location is important in supply chain network. Particularly, if a company maintains more selling stores it cannot maintain individual secondary warehouse near to each selling store. Hence, maintaining the optimum number of secondary warehouses is important. Hence, the combined mathematical model is formulated to reduce the total expenditure of the organization by arranging the network of minimum number of secondary warehouses. Numerical example has been taken to illustrate the proposed model.
Abstract: Evolution strategy (ES) is a well-known instance of evolutionary algorithms, and there have been many studies on ES. In this paper, the author proposes an extended ES for solving fuzzy-valued optimization problems. In the proposed ES, genotype values are not real numbers but fuzzy numbers. Evolutionary processes in the ES are extended so that it can handle genotype instances with fuzzy numbers. In this study, the proposed method is experimentally applied to the evolution of neural networks with fuzzy weights and biases. Results reveal that fuzzy neural networks evolved using the proposed ES with fuzzy genotype values can model hidden target fuzzy functions even though no training data are explicitly provided. Next, the proposed method is evaluated in terms of variations in specifying fuzzy numbers as genotype values. One of the mostly adopted fuzzy numbers is a symmetric triangular one that can be specified by its lower and upper bounds (LU) or its center and width (CW). Experimental results revealed that the LU model contributed better to the fuzzy ES than the CW model, which indicates that the LU model should be adopted in future applications of the proposed method.
Abstract: Reliability allocation is quite important during early
design and development stages for a system to apportion its specified
reliability goal to subsystems. This paper improves the reliability
fuzzy allocation method, and gives concrete processes on determining
the factor and sub-factor sets, weight sets, judgment set, and
multi-stage fuzzy evaluation. To determine the weight of factor and
sub-factor sets, the modified trapezoidal numbers are proposed to
reduce errors caused by subjective factors. To decrease the fuzziness
in fuzzy division, an approximation method based on linear
programming is employed. To compute the explicit values of fuzzy
numbers, centroid method of defuzzification is considered. An
example is provided to illustrate the application of the proposed
reliability allocation method based on fuzzy arithmetic.
Abstract: The applicability of Net Present Value (NPV) in an
investment project is becoming more and more popular in the field
of engineering economics. The classical NPV methodology involves
only the precise and accurate data of the investment project. In the
present communication, we give a new mathematical model for NPV
which uses the concept of intuitionistic fuzzy set theory. The proposed
model is based on triangular intuitionistic fuzzy number, which may
be known as Intuitionistic Fuzzy Net Present Value (IFNPV). The
model has been applied to an example and the results are presented.
Abstract: Multi-component data envelopment analysis (MC-DEA) is a popular technique for measuring aggregate performance of the decision making units (DMUs) along with their components. However, the conventional MC-DEA is limited to crisp input and output data which may not always be available in exact form. In real life problems, data may be imprecise or fuzzy. Therefore, in this paper, we propose (i) a fuzzy MC-DEA (FMC-DEA) model in which shared and undesirable fuzzy resources are incorporated, (ii) the proposed FMC-DEA model is transformed into a pair of crisp models using α cut approach, (iii) fuzzy aggregate performance of a DMU and fuzzy efficiencies of components are defined to be fuzzy numbers, and (iv) a numerical example is illustrated to validate the proposed approach.
Abstract: In recent years, many researchers are involved in the
field of fuzzy theory. However, there are still a lot of issues to be
resolved. Especially on topics related to controller design such as the
field of robot, artificial intelligence, and nonlinear systems etc.
Besides fuzzy theory, algorithms in swarm intelligence are also a
popular field for the researchers. In this paper, a concept of utilizing
one of the swarm intelligence method, which is called Bacterial-GA
Foraging, to find the stabilized common P matrix for the fuzzy
controller system is proposed. An example is given in in the paper, as
well.
Abstract: This paper presents a regression model for interval type-2 fuzzy sets based on the least squares estimation technique. Unknown coefficients are assumed to be triangular fuzzy numbers. The basic idea is to determine aggregation intervals for type-1 fuzzy sets, membership functions of whose are low membership function and upper membership function of interval type-2 fuzzy set. These aggregation intervals were called weighted intervals. Low and upper membership functions of input and output interval type-2 fuzzy sets for developed regression models are considered as piecewise linear functions.
Abstract: In the present paper, we analyze the vague reliability of k-out-of-n : G system (particularly, series and parallel system) with independent and non-identically distributed components, where the reliability of the components are unknown. The reliability of each component has been estimated using statistical confidence interval approach. Then we converted these statistical confidence interval into triangular intuitionistic fuzzy numbers. Based on these triangular intuitionistic fuzzy numbers, the reliability of the k-out-of-n : G system has been calculated. Further, in order to implement the proposed methodology and to analyze the results of k-out-of-n : G system, a numerical example has been provided.
Abstract: In this paper, motivated by the ideas of dependent weighted aggregation operators, we develop some new hesitant fuzzy dependent weighted aggregation operators to aggregate the input arguments taking the form of hesitant fuzzy numbers rather than exact numbers, or intervals. In fact, we propose three hesitant fuzzy dependent weighted averaging(HFDWA) operators, and three hesitant fuzzy dependent weighted geometric(HFDWG) operators based on different weight vectors, and the most prominent characteristic of these operators is that the associated weights only depend on the aggregated hesitant fuzzy numbers and can relieve the influence of unfair hesitant fuzzy numbers on the aggregated results by assigning low weights to those “false” and “biased” ones. Some examples are given to illustrated the efficiency of the proposed operators.
Abstract: According to fuzzy arithmetic, dual fuzzy polynomials cannot be replaced by fuzzy polynomials. Hence, the concept of ranking method is used to find real roots of dual fuzzy polynomial equations. Therefore, in this study we want to propose an interval type-2 dual fuzzy polynomial equation (IT2 DFPE). Then, the concept of ranking method also is used to find real roots of IT2 DFPE (if exists). We transform IT2 DFPE to system of crisp IT2 DFPE. This transformation performed with ranking method of fuzzy numbers based on three parameters namely value, ambiguity and fuzziness. At the end, we illustrate our approach by two numerical examples.
Abstract: The author proposes an extension of genetic algorithm (GA) for solving fuzzy-valued optimization problems. In the proposed GA, values in the genotypes are not real numbers but fuzzy numbers. Evolutionary processes in GA are extended so that GA can handle genotype instances with fuzzy numbers. The proposed method is applied to evolving neural networks with fuzzy weights and biases. Experimental results showed that fuzzy neural networks evolved by the fuzzy GA could model hidden target fuzzy functions well despite the fact that no training data was explicitly provided.
Abstract: The optimal control is one of the possible controllers
for a dynamic system, having a linear quadratic regulator and using
the Pontryagin-s principle or the dynamic programming method .
Stochastic disturbances may affect the coefficients (multiplicative
disturbances) or the equations (additive disturbances), provided that
the shocks are not too great . Nevertheless, this approach encounters
difficulties when uncertainties are very important or when the probability
calculus is of no help with very imprecise data. The fuzzy
logic contributes to a pragmatic solution of such a problem since it
operates on fuzzy numbers. A fuzzy controller acts as an artificial
decision maker that operates in a closed-loop system in real time.
This contribution seeks to explore the tracking problem and control
of dynamic macroeconomic models using a fuzzy learning algorithm.
A two inputs - single output (TISO) fuzzy model is applied to the
linear fluctuation model of Phillips and to the nonlinear growth model
of Goodwin.