Interval Approximation Of Fuzzy Numbers Research Articles

Fuzzy Data Envelopment Analysis with Ordinal and Interval Data

In this paper, we reformulate the conventional DEA models as an imprecise DEA problem and propose a novel method for evaluating the DMUs when the inputs and outputs are fuzzy and/or ordinal or vary in intervals. For this purpose, we convert all data into interval data. In order to convert each fuzzy number into interval data, we use the nearest weighted interval approximation of fuzzy numbers by applying the weighting function, and we convert each ordinal data into interval one. In this manner, we could convert all data into interval data. The presented models determine the interval efficiencies for DMUs. To rank DMUs based on their associated interval efficiencies, we first apply the Ω-index that is developed for ranking of interval numbers. Then, by introducing an ideal DMU, we rank efficient DMUs to present a complete ranking. Finally, we use one example to illustrate the process and one real application in health care to show the usefulness of the proposed approach. For this evaluation, we consider interval, ordinal, and fuzzy data alongside the precise data to evaluate 38 hospitals selected by OIG. The results reveal the capabilities of the presented method to deal with the imprecise data.

Multiobjective security game with fuzzy payoffs

A multiobjective security game problem with fuzzy payoffs is studied in this paper. The problem is formulated as a bilevel programming problem with fuzzy coefficients. Using the idea of nearest interval approximation of fuzzy numbers, the problem is transformed into a bilevel programming problem with interval coefficients. The Karush-Kuhn-Tucker conditions is applied then to reduce the problem to an interval multiobjective single-level problem. It is shown that the solutions of this problem are obtained by solving a single-objective programming problem. Validity and applicability of the method are illustrated by a practical example.

Solving Fully Fuzzy Multi-objective Linear Programming Problem Using Nearest Interval Approximation of Fuzzy Number and Interval Programming

This paper focuses on Fully Fuzzy Multi-Objective Linear Programming (FFMOLP) problem in which all the coefficients and decision variables are LR flat fuzzy numbers, the more generalized version of fuzzy numbers and all the constraints are fuzzy inequalities. A new algorithm is proposed for solving FFMOLP problem which first converts it into the Multi-Objective Interval Linear Programming (MOILP) problem. Further, taking the help of fuzzy slack variable, fuzzy surplus variables, nearest interval approximation of fuzzy numbers and scalarization technique, MOILP is then converted into the Crisp Linear Programming (CLP) problem. It is shown that the optimal solution of CLP problem is the fuzzy Pareto optimal solution of FFMOLP problem. The main advantage of the proposed algorithm is that it transforms FFMOLP problem into Crisp Linear Programming problem. Moreover, to apply algorithm, only the knowledge of arithmetic operations of LR flat fuzzy numbers, centre and width of the closed intervals are required. At the end, to illustrate the proposed method and its effectiveness over the existing method, numerical examples are solved and compared.

Extending TOPSIS in fuzzy environment by using the nearest weighted interval approximation of fuzzy numbers

TOPSIS is one of most popular methods in the process of selecting a possible course of action from all of the alternatives. In this paper by using the nearest weighted interval approximation of the...

Extending TOPSIS in fuzzy environment by using the nearest weighted interval approximation of fuzzy numbers

TOPSIS is one of most popular methods in the process of selecting a possible course of action from all of the alternatives. In this paper by using the nearest weighted interval approximation of the fuzzy numbers we try to extend TOPSIS in fuzzy environment. This paper proposes four new fuzzy TOPSIS methods. Two numerical examples are given to clarify the main results developed in this paper. In these examples we have applied some non-triangular and non-trapezoidal fuzzy numbers too. These methods are evaluated and compared with some other existing methods. We can say that, this is the main advantages of the proposed methods, because, other fuzzy TOPSIS methods can't solve these kinds of problems.

A solid transportation problem with safety factor under different uncertainty environments

In this paper, we introduce a new concept ‘safety factor’ in a transportation problem. When items are transported from plants to destinations through different conveyances, there are some difficulties/risks to transport the items due to bad road, insurgency, land slide, etc. in some routes. Due to these, a desired total safety factor is being introduced, and depending upon the nature of the safety factor, we develop five models. In this paper, a solid transportation problem (STP) with imprecise unit costs is considered. The sources' availabilities, destinations' demands, and capacities of conveyances are also represented by fuzzy numbers like trapezoidal and triangular numbers. The transportation problem has been formulated with and without a safety factor. To reduce the different models into its crisp equivalent, we introduce different methods as chance-constraint programming, an approach using interval approximation of fuzzy numbers and the application of the expected value model. Generalized reduced gradient technique is used to find the optimal solutions for a set of given numerical data. To illustrate the model, a numerical example has been presented and solved using LINGO.12 software. The effect of safety factors on transported amount is illustrated.

English

  In the present paper, the researchers discuss the problem of parametric interval approximation of fuzzy numbers. It is the interval which fulfills two conditions. In the first, this interval is a continuous interval approximation operator. In the second, the parametric weighted distance between this interval and the approximated number is minimal and continuous. This interval can be used as a crisp set approximation with respect to a fuzzy quantity. These indices can be applied for comparison of fuzzy numbers namely fuzzy correlations in fuzzy environments and expert's systems. Finally, some of their applications are mentioned.   Key words: Fuzzy numbers, defuzzification, interval approximation, correlation.

Multi-objective solid transportation problems with budget constraint in uncertain environment

This paper investigates multi-objective solid transportation problems (MOSTP) under various uncertain environments. The unit transportation penalties/costs are taken as random, fuzzy and hybrid variables respectively, in three different uncertain multi-objective solid transportation models and in each case, the supplies, demands and conveyance capacities are fuzzy. Also, apart from source, demand and capacity constraints, an extra constraint on the total budget at each destination is imposed. Chance-constrained programming technique has been used for the first two models to obtain crisp equivalent forms, whereas expected value model is formulated for the last. We provide an another approach using the interval approximation of fuzzy numbers for the first model to obtain its crisp form and compare numerically two approaches for this model. Fuzzy programming technique and a gradient based optimisation - generalised reduced gradient (GRG) method are applied to beget the optimal solutions. Three numerical examples are provided to illustrate the models and programming.

On The Optimal Index for Comparison fuzzy Quantities Based On Weighted Expected Interval

In the present paper, the researchers discuss the problem of weighted expected interval approximation of fuzzy numbers. This interval can be used as a crisp approximation set with respect to a fuzzy quantity. Then, by using this, the researchers propose a novel approach to ranking fuzzy numbers. The proposed model is studied for a broad class of fuzzy numbers. The calculation of this method is far simpler than the other approaches.

An Approximation Approach for Ranking Fuzzy Numbers Based on Weighted Interval - Value

In the present paper, the researchers discuss the problem of weighted interval approximation of fuzzy numbers. This interval can be used as a crisp set approximation with respect to a fuzzy quantity. Then, by using this, the researchers propose a novel approach to ranking fuzzy numbers. This method can effectively rank various fuzzy numbers, their images and overcome the shortcomings of the previous techniques.

A new algorithm for selecting equip system based on fuzzy operations

In this endeavor, the authors discuss the problem of defuzzification based on parametric interval approximation of fuzzy numbers and then suggest measure about these points of fuzzy numbers. The measure point of each fuzzy number plays an important role in fuzzy sets and systems, specifically in physics, mathematics and statistics. We provide the definition of the measure of fuzzy numbers as well as the definition of measures in probability theory. Some of their applications are mentioned. Key words: Fuzzy number, measure, ranking, parametric interval approximation, evaluating.

Nearest interval approximation of a fuzzy number

The problem of the interval approximation of fuzzy numbers is discussed. A new interval approximation operator, which is the best one with respect to a certain measure of distance between fuzzy numbers, is suggested.