Based on einstein operations, we define intervalvalued pythagorean trapezoidal fuzzy aggregation operators. Recently few methods for ranking ifns has also been introduced 29,33,36,41,49. New methods for ranking of trapezoidal fuzzy numbers. Multiplication operation on trapezoidal fuzzy numbers. A trapezoidal fuzzy number is said to be zero trapezoidal fuzzy number if and only if m 0, n 0 and d, e 0 definition 3. Solving fully fuzzy linear systems with trapezoidal fuzzy. In this paper, we have been pointed out the study of fuzzy linear fractional programming flfp problems with trapezoidal fuzzy numbers. Where the objective functions are fuzzy numbers and the constraints are real numbers.
Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the generalized trapezoidal fuzzy numbers into three. Trapezoidal fuzzy numbers for the transportation problem. Approximation of fuzzy numbers by trapezoidal fuzzy numbers. A new approach for trapezoidal approximation of fuzzy. Jan 11, 2016 solving fuzzy matrix games defuzzificated by trapezoidal parabolic fuzzy numbers ijsrdvol. Statistical process control spc is a technique applied towards improving the quality of. In particular, when 2 a 3,the trapezoidal fuzzy number is reduced to a triangular fuzzy number denote d by. Wang and zhang41 defined the trapezoidal intuitionistic fuzzy number trifn and gave ranking method which transformed the ranking of trifns in to ranking of interval numbers. Some einstein operational laws on intervalvalued pythagorean trapezoidal fuzzy numbers are defined based on einstein sum and einstein product. In this paper, several new algebraic mathematics for positive fuzzy numbers of type a. Ranking generalized trapezoidal fuzzy numbers with.
Sukna, siliguri734009 darjeeling, west bengal, india 2 department of mathematics, bengal engineering and science university, shibpur. Strongly to very strongly keywords multicriteria decision making, fahp, trapezoidal fuzzy number, extent analysis i. Based on trapezoidal fuzzy numbers and ifss, liu and zuo 11 proposed a trapezoidal intuitionistic fuzzy number tifn. We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and leftright spread of trapezoidal fuzzy numbers.
In sum, the rank of two fuzzy numbers a and b based on the incentre of the centroids is given as follows steps. Using this notation, the interval 2, 4 is the proper interval 2, 4. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the. Solving fully fuzzy linear systems with trapezoidal fuzzy number matrices by partitioning. Analytic hierarchy process using trapezoidal fuzzy number. Addition of two trapezoidal intuitionistic fuzzy numbers jianqiang and zhong, 2009. Each trapezoidal fuzzy number is characterized by its four values inf0,inf1,sup1,sup0 note. Conceptual design, multicriteria decisionmaking, fuzzified pugh matrix, synthetic extent evaluation, trapezoidal fuzzy number. You can also compute this membership function using a fismf object. Let and with be two intuitionistic trapezoidal fuzzy numbers.
Each trapezoidal fuzzy number is characterized by its four values inf0,inf1,sup1,sup0. Trapezoidal operators of fuzzy numbers approximation have been studied by many authors, because fuzzy numbers have lots of uses in the e. Ordering of generalised trapezoidal fuzzy numbers based on area method 787 figure 1. Two fuzzy number and,, b p q j g are said to be equal i. Approximation of fuzzy numbers by trapezoidal fuzzy. A new ranking approach for solving fuzzy transportation problems with trapezoidal fuzzy numbers. For an arbitrary trapezoidal fuzzy number u x 0, y 0. To prove a similar result in the case of ivtfns and tifns, then in the case of. Intuitionistic fuzzy number and its arithmetic operation with. Solving fuzzy matrix games defuzzificated by trapezoidal. A trapezoidal intuitionistic fuzzy number withparameters, 1 1 2 2,isdenotedas, 1, 2,, 1, 2,inthesetofrealnumbersris. A new approach for ranking of trapezoidal fuzzy numbers. Keywords human a ssessment, fuzzy logic, fuzzy numbers fns, triangular tfns and trapezoidal tpfns fuzzy numbers, center of gravity cog defuzzification technique 1. Definitionfuzzy number n convex fuzzy set n normalized fuzzy set n its membership function is piecewise continuo us n it is defined in the real number.
If x 0 that is x is not equivalent to0, then it is said to be a nonzero symmetric trapezoidal fuzzy number. This function returns n trapezoidal fuzzy numbers contained in a matrix of dimension n x 4. Pdf multiplication operation on trapezoidal fuzzy numbers. Assessment of human skills using trapezoidal fuzzy numbers. Using trapezoidal intuitionistic fuzzy number to find. Since the boundary of this interval is ambiguous, the interval is also a fuzzy set. A fuzzy number is called positive negative, denoted by 0 fuzzy linear system with trapezoidal fuzzy. Trapezoidal numbers mathematical association of america.
The triangular fuzzy number on the existing importance scale in the literature has been converted into trapezoid numbers by keeping the upper and lower bounds of the fuzzy numbers constant and spreading the. To the best of our knowledge, this is the first work on obtaining the solution of the transportation problem using fuzzy trapezoidal numbers. Also hexagonal, nonagonal, decagonal fuzzy numbers have been introduced to. Fuzzy transportation problem of trapezoidal fuzzy numbers. Mar 31, 2016 however, expression of a fuzzy number is based on the objective observation, therefore a fuzzy number includes subjective concept as well as objective concept. Scientists in many disciplines face the problem of interpretation of com.
Fung and hu, 5, introduced the linear programming with the technique coefficients based on fuzzy numbers. Introduction the social demand of classifying humans according to their qualifications. A new distance measure for trapezoidal fuzzy numbers. The degree of membership and the degree of nonmembership for a tifn are expressed in the form of trapezoidal fuzzy numbers. It is to be noted that if 0 x, then 0 x but the converse need not be true. Many different types of fuzzy numbers are defined in the literature dealing with fuzzy logic and applications. It is true that fuzzy numbers are frequently partial order and cannot be compared like. In section 3, operations including exponentiation, logarithms and n th root of trapezoidal intuitionistic fuzzy number. Fuzzy regression model using trapezoidal fuzzy numbers for re. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Human assessment, fuzzy logic, fuzzy numbers, trapezoidal. This function computes fuzzy membership values using a trapezoidal membership function.
A fuzzy number whose membership functions graph forms a trapezoid with the oxaxis. International journal of computer applications 649. Trapezoidaltriangular intuitionistic fuzzy numbers. New approach for ranking of trapezoidal fuzzy numbers. Operations on intuitionistic trapezoidal fuzzy numbers. Centroid of trapezoidal fuzzy number based on euler line of centroids consider a generalised trapezoid fuzzy number figure 1. A study on process variability using cusum and fuzzy control charts ph. The set of all trapezoidal fuzzy numbers is denoted by ftr. This paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized trapezoidal fuzzy numbers.
This paper propose a method to solve trapezoidal fuzzy number linear programming problem. Roy2 1 department of mathematics, siliguri institute of technology, p. Operations on intuitionistic trapezoidal fuzzy numbers using. This is followed by the solution of transportation problem using fuzzy trapezoidal numbers in section 4.
Jan 10, 2019 the aim of this paper is to investigate information aggregation methods under intervalvalued pythagorean trapezoidal fuzzy environment. Ordering generalized trapezoidal fuzzy numbers with area. Number theory numbers with special forms or properties select rating give trapezoidal numbers 15 give trapezoidal numbers 25 give trapezoidal numbers 35 give trapezoidal numbers 45 give trapezoidal numbers 55. May 02, 2019 this function returns n trapezoidal fuzzy numbers contained in a matrix of dimension n x 4. The fuzzification of the cost of the transportation problem is discussed with the help of a numerical example. Finally, we discuss the computational complexity involved in the problem. In this paper a new efficient method for flfp problem has been proposed, in order to obtain the fuzzy optimal solution with unrestricted variables and parameters. The trapezoidal fuzzy number linear programming 125 programming within the limits of technical coefficients fuzzy and fuzzy right side. In this paper, we consider the fuzzy transportation problem ftp where cost, availability and demand of the. A generalization of trapezoidal fuzzy numbers based on.
Let a, b and c be real numbers with a 0 pages 26 download pdf. Arithmetic operations on trapezoidal fuzzy numbers. Also some of the interesting arithmetic work on fuzzy numbers can be found in abhinav bansal in 9. Profit maximization solid transportation problem with. Ordering generalized trapezoidal fuzzy numbers 557 in this paper a new method is proposed which is based on incentre of centroids to rank fuzzy quantities. For convenience, we denote an intuitionistic fuzzy number by, where. Moreover, the metric properties of suggested distance measure are investigated. A trapezoidal fuzzy number is said to be nonnegative trapezoidal fuzzy number if and only if m dt 0. Pugh matrix and aggregated by extent analysis using trapezoidal fuzzy number for assessing conceptual designs pages 26 download pdf. A fuzzy number is called trapezoidal fuzzy number if its membership function is given by see figure 1. A general form of fuzzy linear fractional programs with. Ranking function of the trapezoidal fuzzy number a a, b, c,d. Lu decomposition method for solving fully fuzzy linear system. We are grateful for jstors cooperation in providing the pdf pages that we are using for classroom capsules.
Notes on ifs, volume 20, 2014, number 2, pages 4351. It is obvious that there is an innite number of methods for the approximation of fuzzy numbers with trapezoidal numbers. Triangular fuzzy numbers tfns the simplest form of a fn is probably the triangular fuzzy number tfn. By the properties of the operations which are defined on the linear ranking function, we construct an algorithm to solve the trapezoidal fuzzy number linear programming. A study on ranking of trapezoidal intuitionistic fuzzy numbers. The trapezoidal fuzzy number linear programming hikari. In section 2, the trapezoidal membership function is defined. A generalized model for fuzzy linear programs with. In many applications, ranking of fuzzy numbers is an important component of the decision process. Triangular fuzzy numbers and trapezoidal fuzzy numbers have been widely used to express these two different kinds of concepts.
Research article a new similarity measure of generalized. Pdf this paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized trapezoidal fuzzy. There are some techniques to solve the fuzzy lp problems. Based on einstein operations, we define intervalvalued pythagorean trapezoidal fuzzy aggregation operators, such. In this study, the importance scale given as a triangular fuzzy number is transformed into trapezoidal fuzzy numbers as shown in fig. The proposed method is simple, and can calculate the similarity measure for both real numbers and fuzzy numbers by the. If 0 x, then x is said to be a zero symmetric trapezoidal fuzzy number.
To deal imprecise in real life situation, many researchers used triangular and trapezoidal fuzzy number 10 111221. Principal components analysis for trapezoidal fuzzy numbers. The tpfns are generalizations of the triangular fuzzy numbers. Trapezoidaltriangular intuitionistic fuzzy numbers versus. Representation of trapezoidal fuzzy numbers with shape function. New aggregation operator for trapezoidal fuzzy numbers. We can see that both the methods give the same ranking. Ordering of generalised trapezoidal fuzzy numbers based on. We can also know that it is an ordinary crisp interval figure 2. Solving fuzzy matrix games defuzzificated by trapezoidal parabolic fuzzy numbers ijsrdvol. So, triangular fuzzy numbers are special cases of trapezoidal fuzzy numbers. We say is an intuitionistic fuzzy number throughout this paper, where the function and.
However we do acknowledge that the proposed method has more. In the next section, the general transportation problem with fuzzy trapezoidal numbers is discussed. A ranking function, where is set of all fuzzy numbers defined on set of real numbers and maps each fuzzy number into a real number. To solve this problem, we use trapezoidal fuzzy numbers. In this section we recall some basic notions on trapezoidal and triangular intuitionistic fuzzy numbers. When c is greater than b, the resulting membership function is trapezoidal when b is equal to c, the resulting membership function is equivalent to a triangular membership function with parameters a b d when c is less to b, the resulting membership function is triangular with a maximum value less than 1. D thesis 52 chapter vi construction of fuzzy control charts using trapezoidal fuzzy number 1. Generally a fuzzy interval is represented by two end points a. Let a, b and c be real numbers with a fuzzy number tfn a a, b, c is the fn with membership function. Duality in fuzzy linear programming with symmetric.
Geometric aggregation operators with intervalvalued. The aim of this paper is to investigate information aggregation methods under intervalvalued pythagorean trapezoidal fuzzy environment. In case you find almost surely existing bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses. This paper is organized as follows, in section 2, the representation of trapezoidal intuitionistic fuzzy numbers and. Centre of area of fuzzy number coa of fuzzy number. The previously proposed approximation operators are improved so as to always obtain a. Pdf arithmetic operations on trapezoidal fuzzy numbers. The problem to find the nearest trapezoidal approximation of a fuzzy number with respect to a wellknown metric, which preserves the expected interval of the fuzzy number, is completely solved. Ijca solving fully fuzzy linear systems with trapezoidal. Trapezoidal fuzzy numbers in extent analysis method in fuzzy ahp. The arithmetic operations of interval type2 fuzzy set 15 suppose a1 and a2 are two trapezoidal interval type2 fuzzy numbers. Fuzzy risk analysis based on the similarity measure of. We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of intervalvalued trapezoidal fuzzy numbers and, on the other hand.
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