Abstract: Fuzzy sets theory affirmed that the linguistic value for
every contraries relation is complementary. It was stressed in the
intuitionistic fuzzy sets (IFS) that the conditions for contraries
relations, which are the fuzzy values, cannot be greater than one.
However, complementary in two contradict phenomena are not
always true. This paper proposes a new idea condition for conflicting
bifuzzy sets by relaxing the condition of intuitionistic fuzzy sets.
Here, we will critically forward examples using triangular fuzzy
number in formulating a new condition for conflicting bifuzzy sets
(CBFS). Evaluation of positive and negative in conflicting
phenomena were calculated concurrently by relaxing the condition in
IFS. The hypothetical illustration showed the applicability of the new
condition in CBFS for solving non-complement contraries
intuitionistic evaluation. This approach can be applied to any
decision making where conflicting is very much exist.
Abstract: In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.
Abstract: A new deployment of the multiple criteria decision
making (MCDM) techniques: the Simple Additive Weighting
(SAW), and the Technique for Order Preference by Similarity to
Ideal Solution (TOPSIS) for portfolio allocation, is demonstrated in
this paper. Rather than exclusive reference to mean and variance as in
the traditional mean-variance method, the criteria used in this
demonstration are the first four moments of the portfolio distribution.
Each asset is evaluated based on its marginal impacts to portfolio
higher moments that are characterized by trapezoidal fuzzy numbers.
Then centroid-based defuzzification is applied to convert fuzzy
numbers to the crisp numbers by which SAW and TOPSIS can be
deployed. Experimental results suggest the similar efficiency of these
MCDM approaches to selecting dominant assets for an optimal
portfolio under higher moments. The proposed approaches allow
investors flexibly adjust their risk preferences regarding higher
moments via different schemes adapting to various (from
conservative to risky) kinds of investors. The other significant
advantage is that, compared to the mean-variance analysis, the
portfolio weights obtained by SAW and TOPSIS are consistently
well-diversified.
Abstract: The aim of this paper is to adopt a compromise ratio (CR) methodology for fuzzy multi-attribute single-expert decision making proble. In this paper, the rating of each alternative has been described by linguistic terms, which can be expressed as triangular fuzzy numbers. The compromise ratio method for fuzzy multi-attribute single expert decision making has been considered here by taking the ranking index based on the concept that the chosen alternative should be as close as possible to the ideal solution and as far away as possible from the negative-ideal solution simultaneously. From logical point of view, the distance between two triangular fuzzy numbers also is a fuzzy number, not a crisp value. Therefore a fuzzy distance measure, which is itself a fuzzy number, has been used here to calculate the difference between two triangular fuzzy numbers. Now in this paper, with the help of this fuzzy distance measure, it has been shown that the compromise ratio is a fuzzy number and this eases the problem of the decision maker to take the decision. The computation principle and the procedure of the compromise ratio method have been described in detail in this paper. A comparative analysis of the compromise ratio method previously proposed [1] and the newly adopted method have been illustrated with two numerical examples.
Abstract: This paper deals with a portfolio selection problem
based on the possibility theory under the assumption that the returns
of assets are LR-type fuzzy numbers. A possibilistic portfolio model
with transaction costs is proposed, in which the possibilistic mean
value of the return is termed measure of investment return, and the
possibilistic variance of the return is termed measure of investment
risk. Due to considering transaction costs, the existing traditional
optimization algorithms usually fail to find the optimal solution
efficiently and heuristic algorithms can be the best method. Therefore,
a particle swarm optimization is designed to solve the corresponding
optimization problem. At last, a numerical example is given to
illustrate our proposed effective means and approaches.
Abstract: Global competitiveness has recently become the
biggest concern of both manufacturing and service companies.
Electronic commerce, as a key technology enables the firms to reach
all the potential consumers from all over the world. In this study, we
have presented commonly used electronic payment systems, and then
we have shown the evaluation of these systems in respect to different
criteria. The payment systems which are included in this research are
the credit card, the virtual credit card, the electronic money, the
mobile payment, the credit transfer and the debit instruments. We
have realized a systematic comparison of these systems in respect to
three main criteria: Technical, economical and social. We have
conducted a fuzzy multi-criteria decision making procedure to deal
with the multi-attribute nature of the problem. The subjectiveness
and imprecision of the evaluation process are modeled using
triangular fuzzy numbers.
Abstract: A linear system is called a fully fuzzy linear system (FFLS) if quantities in this system are all fuzzy numbers. For the FFLS, we investigate its solution and develop a new approximate method for solving the FFLS. Observing the numerical results, we find that our method is accurate than the iterative Jacobi and Gauss- Seidel methods on approximating the solution of FFLS.
Abstract: Although so far, many methods for ranking fuzzy numbers
have been discussed broadly, most of them contained some shortcomings,
such as requirement of complicated calculations, inconsistency
with human intuition and indiscrimination. The motivation of
this study is to develop a model for ranking fuzzy numbers based
on the lexicographical ordering which provides decision-makers with
a simple and efficient algorithm to generate an ordering founded on
a precedence. The main emphasis here is put on the ease of use
and reliability. The effectiveness of the proposed method is finally
demonstrated by including a comprehensive comparing different
ranking methods with the present one.
Abstract: This paper develops a quality estimation method with
the application of fuzzy hierarchical clustering. Quality estimation is
essential to quality control and quality improvement as a precise
estimation can promote a right decision-making in order to help
better quality control. Normally the quality of finished products in
manufacturing system can be differentiated by quality standards. In
the real life situation, the collected data may be vague which is not
easy to be classified and they are usually represented in term of fuzzy
number. To estimate the quality of product presented by fuzzy
number is not easy. In this research, the trapezoidal fuzzy numbers
are collected in manufacturing process and classify the collected data
into different clusters so as to get the estimation. Since normal
hierarchical clustering methods can only be applied for real numbers,
fuzzy hierarchical clustering is selected to handle this problem based
on quality standards.
Abstract: This paper suggests ranking alternatives under fuzzy
MCDM (multiple criteria decision making) via an centroid based
ranking approach, where criteria are classified to benefit qualitative,
benefit quantitative and cost quantitative ones. The ratings of
alternatives versus qualitative criteria and the importance weights of
all criteria are assessed in linguistic values represented by fuzzy
numbers. The membership function for the final fuzzy evaluation
value of each alternative can be developed through α-cuts and
interval arithmetic of fuzzy numbers. The distance between the
original point and the relative centroid is applied to defuzzify the
final fuzzy evaluation values in order to rank alternatives. Finally a
numerical example demonstrates the computation procedure of the
proposed model.
Abstract: Many firms implemented various initiatives such as outsourced manufacturing which could make a supply chain (SC) more vulnerable to various types of disruptions. So managing risk has become a critical component of SC management. Different types of SC vulnerability management methodologies have been proposed for managing SC risk, most offer only point-based solutions that deal with a limited set of risks. This research aims to reinforce SC risk management by proposing an integrated approach. SC risks are identified and a risk index classification structure is created. Then we develop a SC risk assessment approach based on the analytic network process (ANP) and the VIKOR methods under the fuzzy environment where the vagueness and subjectivity are handled with linguistic terms parameterized by triangular fuzzy numbers. By using FANP, risks weights are calculated and then inserted to the FVIKOR to rank the SC members and find the most risky partner.
Abstract: Using neural network we try to model the unknown function f for given input-output data pairs. The connection strength of each neuron is updated through learning. Repeated simulations of crisp neural network produce different values of weight factors that are directly affected by the change of different parameters. We propose the idea that for each neuron in the network, we can obtain quasi-fuzzy weight sets (QFWS) using repeated simulation of the crisp neural network. Such type of fuzzy weight functions may be applied where we have multivariate crisp input that needs to be adjusted after iterative learning, like claim amount distribution analysis. As real data is subjected to noise and uncertainty, therefore, QFWS may be helpful in the simplification of such complex problems. Secondly, these QFWS provide good initial solution for training of fuzzy neural networks with reduced computational complexity.
Abstract: This paper investigates the solutions of two-point fuzzy boundary value problems as the form x = f(t, x(t)), x(0) = A and x(l) = B, where A and B are fuzzy numbers. There are four different solutions for the problems when the lateral type of H-derivative is employed to solve the problems. As f(t, x) is a monotone function of x, these four solutions are reduced to two different solutions. As f(t, x(t)) = λx(t) or f(t, x(t)) = -λx(t), solutions and several comparison results are presented to indicate advantages of each solution.
Abstract: Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. A convenient method for solving these problems is based on using of auxiliary problem. In this paper a new method for solving fuzzy variable linear programming problems directly using linear ranking functions is proposed. This method uses simplex tableau which is used for solving linear programming problems in crisp environment before.
Abstract: We consider different types of aggregation operators
such as the heavy ordered weighted averaging (HOWA) operator and
the fuzzy ordered weighted averaging (FOWA) operator. We
introduce a new extension of the OWA operator called the fuzzy
heavy ordered weighted averaging (FHOWA) operator. The main
characteristic of this aggregation operator is that it deals with
uncertain information represented in the form of fuzzy numbers (FN)
in the HOWA operator. We develop the basic concepts of this
operator and study some of its properties. We also develop a wide
range of families of FHOWA operators such as the fuzzy push up
allocation, the fuzzy push down allocation, the fuzzy median
allocation and the fuzzy uniform allocation.
Abstract: In this paper the concept of strongly (λM)p - Ces'aro
summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.
Abstract: In this paper, a method for deriving a group priority vector in the Fuzzy Analytic Network Process (FANP) is proposed. By introducing importance weights of multiple decision makers (DMs) based on their experiences, the Fuzzy Preferences Programming Method (FPP) is extended to a fuzzy group prioritization problem in the FANP. Additionally, fuzzy pair-wise comparison judgments are presented rather than exact numerical assessments in order to model the uncertainty and imprecision in the DMs- judgments and then transform the fuzzy group prioritization problem into a fuzzy non-linear programming optimization problem which maximize the group satisfaction. Unlike the known fuzzy prioritization techniques, the new method proposed in this paper can easily derive crisp weights from incomplete and inconsistency fuzzy set of comparison judgments and does not require additional aggregation producers. Detailed numerical examples are used to illustrate the implement of our approach and compare with the latest fuzzy prioritization method.
Abstract: In this paper the concept of strongly (λM)p - Ces'aro
summability of a sequence of fuzzy numbers and strongly λM- statistically convergent sequences of fuzzy numbers is introduced.
Abstract: In this paper a new definition of adjacency matrix in
the simple graphs is presented that is called fuzzy adjacency matrix,
so that elements of it are in the form of 0 and
n N
n
1 , ∈
that are
in the interval [0, 1], and then some charactristics of this matrix are
presented with the related examples . This form matrix has complete
of information of a graph.
Abstract: A preconditioned Jacobi (PJ) method is provided for solving fuzzy linear systems whose coefficient matrices are crisp Mmatrices and the right-hand side columns are arbitrary fuzzy number vectors. The iterative algorithm is given for the preconditioned Jacobi method. The convergence is analyzed with convergence theorems. Numerical examples are given to illustrate the procedure and show the effectiveness and efficiency of the method.