Representation Of Fuzzy Numbers Research Articles

Penggabungan Metode Fuzzy Simple Additive Weighting dengan Rank Order Centroid sebagai Pendukung Keputusan Penilaian Kemiskinan di Jawa Timur

The purpose of this study is to determine the results of the combination of Fuzzy Simple Additive Weighting with Centroid Rank Order as a support for poverty assessment decisions in East Java Province. Using a combination of Fuzzy Simple Additive Weighting and Rank Order Centroid is expected to provide better results. Decision support systems can help the government to determine the poverty status of a district or city in poverty reduction. Poverty itself is an important problem in life in many provinces. The problem of poverty triggers social problems that are closely related to the quality of education, crime, hunger, and others, which cause indirect disruption of stability and sustainability. Therefore, a decision support system is needed to make it easier for the government to determine the poorest districts or cities so that the government can aid programs or make strategies to reduce poverty. Fuzzy logic is a method that can be used to overcome uncertainty in decision making. One method in fuzzy logic to overcome uncertainty is to use the Fuzzy Simple Additive Weighting method. In the Fuzzy Simple Additive Weighting method, there is a selection of criteria that will later be weighted based on importance or priority using the Rank Order Centroid method. The criteria used in this study are life expectancy (AHH), literacy rate (AMH), per capita expenditure, and population. The membership function used is the Tringular Fuzzy Number representation. In this study, twenty four rules were given which were obtained from giving different weights to each criterion. So that twenty four of the poorest districts or cities were obtained. Then the final result is the name of the most Regency or City from the twenty four results, namely alternatives twenty seven and twenty eight, namely Sampang Regency and Pamekasan Regency which were entitled to assistance programs from the government.

A multi-objective scheduling method for operational coordination time using improved triangular fuzzy number representation.

In modern warfare, the comprehensiveness of combat domain and the complexity of tasks pose great challenges to operational coordination.To address this challenge, we use the improved triangular fuzzy number to express the combat mission time, first present a new multi-objective operational cooperative time scheduling model that takes the fluctuation of combat coordinative time and the time flexibility between each task into account. The resulting model is essentially a large-scale multi-objective combinatorial optimization problem, intractably complicated to solve optimally. We next propose multi-objective improved Bat algorithm based on angle decomposition (MOIBA/AD) to quickly identify high-quality solutions to the model. Our proposed algorithm improves the decomposition strategy by replacing the planar space with the angle space, which helps greatly reduce the difficulty of processing evolutionary individuals and hence the time complexity of the multi-objective evolutionary algorithm based on decomposition (MOEA/D). Moreover, the population replacement strategy is enhanced utilizing the improved bat algorithm, which helps evolutionary individuals avoid getting trapped in local optima. Computational experiments on multi-objective operational cooperative time scheduling (MOOCTS) problems of different scales demonstrate the superiority of our proposed method over four state-of-the-art multi-objective evolutionary algorithms (MOEAs), including multi-objective bat Algorithm (MOBA), MOEA/D, non-dominated sorting genetic algorithm version II (NSGA-II) and multi-objective particle swarm optimization algorithm (MOPSO). Our proposed method performs better in terms of four performance criteria, producing solutions of higher quality while keeping a better distribution of the Pareto solution set.

A Modified Method for Finding Initial Basic Feasible Solution for Fuzzy Transportation Problems Involving Generalized Trapezoidal Fuzzy Numbers

In this paper, we propose a modified method for finding an initial basic feasible solution(IBFS) for fuzzy transportation problem(FTP) involving generalized trapezoidal fuzzy numbers(GTFNS). Without disturbing the fuzzy nature, using the parametric representation of fuzzy numbers, the optimal solution of the FTPP is obtained. A numerical illustration is given to demonstrate the suitability and efficiency of the proposed procedure and the solution is compared with the existing methods.

A new approach for generation of generalized basic probability assignment in the evidence theory

The process of information fusion needs to deal with a large number of uncertain information with multi-source, heterogeneity, inaccuracy, unreliability, and incompleteness. In practical engineering applications, Dempster–Shafer evidence theory is widely used in multi-source information fusion owing to its effectiveness in data fusion. Information sources have an important impact on multi-source information fusion in an environment with the characteristics of complex, unstable, uncertain, and incomplete. To address multi-source information fusion problem, this paper considers the situation of uncertain information modeling from the closed-world to the open-world assumption and studies the generation of basic probability assignment with incomplete information. A new method is proposed to generate the generalized basic probability assignment (GBPA) based on the triangular fuzzy number model under the open-world assumption. First, the maximum, minimum, and mean values for the triangular membership function of each attribute in classification problem can be obtained to construct a triangular fuzzy number representation model. Then, by calculating the length of the intersection points between the sample and the triangular fuzzy number model, a GBPA set with an assignment for the empty set can be determined. The proposed method can not only be used in different complex environments simply and flexibly, but also have less information loss in information processing. Finally, a series of comprehensive experiments basing on the UCI data sets is used to verify the rationality and superiority of the proposed method.

Alpha-cut based fuzzy cognitive maps with applications in decision-making

Fuzzy cognitive maps (FCMs) are widely used fuzzy modeling tools for handling causal interdependencies in complex systems. In FCMs, system variables (concepts) and degree of interrelationships are quantified by means of fuzzy sets. However, these fuzzy sets are defuzzified and fuzzy singletons are processed in the inference algorithm. Defuzzification of fuzzy numbers before the FCM inference implies information loss which is an undesired situation. Moreover, the resultant concept values are fuzzy singletons that these crisp numbers do not provide any information about the range of possible outcomes. There is a research gap in the literature regarding fuzzy number representation in FCMs that the both of the inputs and outputs of FCMs being fuzzy sets. This study proposes alpha-cut based computational procedures for simulating FCMs in which concepts and degree of relationships are represented via fuzzy numbers. The proposed model is tested on well-known problems adopted from the literature by using type-1 fuzzy numbers and the results are compared with the extension principle-based approach. Moreover, the proposed model is extended to interval type-2 (IT2) fuzzy sets and computational details regarding IT2 FCMs are given. Because relative importance of criteria is usually modeled via fuzzy sets in multiple-attribute decision making problems, a new FCM-based objective weighting method is proposed in order to demonstrate the usefulness of fuzzy number representation in FCMs. The proposed model is implemented in the real-life third-party logistics service provider selection problem.

Fuzzy String Matching Procedure

Background: There are different methodologies for DNA comparison based on two string algorithms, which are dependent on crisp logical principles, where there is no room for verbal (linguistic) uncertainty. These are successfully applicable procedures in DNA bioinformatics researches even by taking into consideration probabilistic random variability components based on the probability distribution functions of various types. Objective: The main purpose of this paper is to review first briefly all available DNA string matching methodologies that are based on crisp logic and then to suggest a new method based on the fuzzy logic rules and application. Methods: There are different methodologies for DNA comparison based on two string algorithms, which are dependent on crisp logical principles, where there is no room for verbal (linguistic) uncertainty. These are successfully applicable procedures in DNA bioinformatics researchers even by taking into consideration probabilistic random variability components based on the probability distribution functions of various types. Results: Fuzzy number representation of each gene implies some sort of uncertainty or unhealthiness in some or all the genes. Their better identifications can be achieved on the basis of fuzzy numbers with different membership degrees, which imply the unhealthiness or healthiness of the genes and their collective behaviors. Conclusion: After the development of fuzzy number representation of the text string coupled with crisp pattern string their relationships are searched at different shift operations, and hence, the possibility of defaulters are identified in the text string with a certain degree of membership.

A new approach to find optimal solution of fuzzy assignment problem using penalty method for hendecagonal fuzzy number

Fuzzy assignment problem (FAP) is a well-known topic and it is used to solve many real-life problems. In many situations, the parameters are used to characterise the uncertainty either triangular or trapezoidal fuzzy number. But the representation of fuzzy number is not always a triangular or trapezoidal fuzzy number. In this paper, a new generalisation of fuzzy number called hendecagonal fuzzy number (HDFN) is introduced with its arithmetic operations. This research aims to introduce a new penalty approach in order to solve fuzzy assignment problem such that the solution is optimum. The cost of assignment is represented by trapezoidal fuzzy number (TrapFN) and HDFN. The proposed method overcomes the limitations of existing method and HDFN is more optimal than TrapFN.

Fuzzy General Linear Modeling for Functional Magnetic Resonance Imaging Analysis

Functional magnetic resonance imaging (fMRI) is a key neuroimaging technique. The classic fMRI analysis pipeline is based on the assumption that the hemodynamic response (HR) is the same across brain regions, time, and subjects. Although convenient, there is ample evidence that this assumption does not hold, and that these differences result in inaccuracies in brain activity detection. This article presents a new fMRI processing pipeline that captures the intrinsic intra- and intersubject variability of the HR. At the core of this new pipeline is the definition of a fuzzy hemodynamic response function (HRF). The proposed pipeline includes a new fuzzy general linear model (GLM) able to handle the fuzzy HRF, including a practical realization based on the LR representation of fuzzy numbers. This article also describes how to obtain activation maps from the fuzzy GLM, and a methodology to compute the statistical power of the analysis. The method is evaluated in synthetic and real fMRI data and compared with other state-of-the-art techniques. The experiments based on synthetic data show that the fuzzy GLM approach is more robust under uncertainty regarding the true specific shape of the HR. The experiments based on the real data show an increased volume of the activated brain areas, suggesting that the proposed method is able to prevent false negative errors in the boundaries of target brain regions in which HR should be negligible.

Necessary and sufficient conditions for the equality of interactive and non-interactive extensions of continuous functions

In this contribution we find the class of n-dimensional joint possibility distributions with the property that the interactive extension principle coincides with the non-interactive extension principle as long as the interactive operations are determined by continuous functions strictly increasing in each argument. This result completes recent studies by the authors, where the particular case of interactive additions and multiplications versus non-interactive additions and multiplications were investigated. In addition, this time we propose results that also cover the cases when we know the fuzzy numbers only from their membership functions. It means that we eliminated the limitations that appear when we cannot pass from membership function representation to parametric representation of fuzzy numbers. As important new applications, we mention the study on the completely correlated fuzzy numbers. Also of note is that we propose two simple methods to extend bidimensional joint possibility distributions to n-dimensional joint possibility distributions. One method is based on an inductive construction while the other one is based on a pairwise construction.

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Fuzzy portfolio selection problem is a major issue in the financial field and a special case of constrained fuzzy-valued optimization problems (CFOPs). In this respect, the present paper aims to investigate the CFOP with regard to the features of the parametric representation of fuzzy numbers named as convex constraint function (CCF) which is proposed by Chalco-Cano et al. in 2014. Furthermore, relying on this parametric representation, some proper conditions are provided for the existence of solutions to a CFOP. To this end, by the increasing representation of CCF, the main problem is converted to a parametric multiobjective programming problem and some solution concepts from a similar framework in the multiobjective programming are proposed for the CFOP. Eventually to illustrate the proposed results, the fuzzy portfolio selection problem is discussed.

A representation of fuzzy numbers

Each fuzzy number can be written in a unique way as the sum of a symmetric and a skew fuzzy number. These two kinds of fuzzy numbers correspond bijectively to certain functions on the unit interval that are of bounded variation. These bijections give rise to a representation of fuzzy numbers by pairs of functions of bounded variation. As application, mathematical structures on the set of functions of bounded variation are transported to that of fuzzy numbers, making the set of fuzzy numbers into a complete metric space, a commutative semiring, and a commutative residuated lattice.

A representation of fuzzy numbers

A representation of fuzzy numbers

Optimal Solution of Balanced and Unbalanced Fuzzy Transportation Problem Using Hexagonal Fuzzy Numbers

A fuzzy transportation problem (FTP) includes cost, supply and demand of transportation problems. Its numbers are fuzzy numbers. Fuzzy transportation problem works to reduce transportation cost of some commodities through a capacitate network. Present research paper points out a technique with an alpha cut, optimal solution for solving transportation problem. We suggest a technique to find the fuzzy optimal solution on scales of transportation problem and propose a new hexagonal representation of fuzzy numbers. In general, the comparison of balanced fuzzy transportation problem (BFTP) and unbalanced fuzzy transportation problem (UFTP) shows that the optimal transportation cost of UFTP is less than BFTP.

Two-step method for multiple criteria investment decision making: mutual funds selection using FuzzME software

The paper presents a decision support method for financial investment decision making - an area where uncertainty is inherent. Investment decision support requires understandable tools able to deal with imprecision and provide easily interpretable outputs to the decision makers. We therefore propose a two-step decision support model that employs two different mathematical approaches. The first step represents investment strategy recommendation and is realised on the base of Mamdani's inference using linguistic fuzzy rules. The second step involves a preselection of mutual funds in accordance with the investment strategy proposed in the first step and provides decision support for mutual funds selection based on multiple criteria (fuzzy OWA aggregation is used). The output is presented to the investor as a picture (graphical representation of fuzzy numbers) with linguistic labels and real number representations (defuzzified values) of the fuzzy outputs. A numerical example of mutual funds selection using FuzzME software is presented.

A New Point of View for Fuzzy Numbers and Their Defuzzification

In this paper we develop a new graphical representation of fuzzy numbers, which we then employ to propose a geometrical approach to their defuzzification. The calculations involved in the proposed method and the resultant representation use Moore's semiplane for intervals and therefore are far simpler than those involved in other approaches. We start by representing triangular and trapezoidal fuzzy numbers in Moore's semiplane. Then we extend this work to any fuzzy number. Although this extension has to be undertaken in [Formula: see text], it preserves all the properties we study for trapezoidal and triangular fuzzy numbers in Moore's semiplane.

The middle-parametric representation of fuzzy numbers and applications to fuzzy interpolation

In this paper we introduce the middle-parametric representation of a fuzzy number presenting some of the advantages in the use of this representation. A special attention is focused on the subset of symmetric fuzzy numbers presenting the special properties of their arithmetic. The approach on symmetric fuzzy numbers is sustained by the applications of these kinds of fuzzy numbers in fuzzy linear programming and by the presence of the symmetric Gaussian type fuzzy numbers in the theory of errors. As potential applications of the middle-parametric representation, some fuzzy interpolation problems are considered. • The middle-parametric representation of fuzzy numbers is introduced. • The structure of symmetric fuzzy numbers is investigated. • Applications of middle-parametric representation in fuzzy interpolation are included.

An Analytical Approach to Evaluating Nonmonotonic Functions of Fuzzy Numbers

This paper presents a novel analytical approach to evaluating continuous, nonmonotonic functions of independent fuzzy numbers. The approach is based on a parametricα-cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models.

Generalized fuzzy differentiability with LU-parametric representation

In the present paper, we use a new generalization of the Hukuhara difference and derivative for fuzzy-valued functions, and we study several properties of the new concepts in the setting of the LU-parametric representation of fuzzy numbers, assessed both from theoretical and computational points of view.

Multivalued representation and new algebraic structures for fuzzy numbers

In this paper we introduce a new representation of fuzzy numbers (called the multivalued representation) and a new multiplication on the set F of fuzzy numbers. Introducing a Dorroh type product between fuzzy numbers, we construct some semiring structures on the set F. Two important particular cases of the general Dorroh type product are the cross product, introduced in [Ban, A. I. and Bede, B., Properties of the cross product of fuzzy numbers, Journal of Fuzzy Mathematics, 14 (2006), 513–531] and the Dorroh product, introduced in this paper. An equivalence relation, compatible with the addition and the Dorroh product, is also given.

An Extended Analytical Approach to Evaluating Monotonic Functions of Fuzzy Numbers

This paper presents an extended analytical approach to evaluating continuous, monotonic functions of independent fuzzy numbers. The approach is based on a parametricα-cut representation of fuzzy numbers and allows for the inclusion of parameter uncertainties into mathematical models.