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. There are some techniques to solve the fuzzy lp problems. Pdf multiplication operation on trapezoidal fuzzy numbers. A new ranking approach for solving fuzzy transportation problems with trapezoidal fuzzy numbers. Some einstein operational laws on intervalvalued pythagorean trapezoidal fuzzy numbers are defined based on einstein sum and einstein product. Pugh matrix and aggregated by extent analysis using trapezoidal fuzzy number for assessing conceptual designs pages 26 download pdf. Pdf arithmetic operations on trapezoidal fuzzy numbers. Ordering of generalised trapezoidal fuzzy numbers based on area method 787 figure 1. Trapezoidaltriangular intuitionistic fuzzy numbers. Duality in fuzzy linear programming with symmetric.
Solving fully fuzzy linear systems with trapezoidal fuzzy. The tpfns are generalizations of the triangular fuzzy numbers. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the. Addition of two trapezoidal intuitionistic fuzzy numbers jianqiang and zhong, 2009. Finally, we discuss the computational complexity involved in the problem. 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. A study on process variability using cusum and fuzzy control charts ph. Ranking function of the trapezoidal fuzzy number a a, b, c,d. Let a, b and c be real numbers with a fuzzy number tfn a a, b, c is the fn with membership function. If 0 x, then x is said to be a zero symmetric trapezoidal fuzzy number. Pdf this paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized trapezoidal fuzzy. Centroid of trapezoidal fuzzy number based on euler line of centroids consider a generalised trapezoid fuzzy number figure 1. Fuzzy transportation problem of trapezoidal fuzzy numbers.
Operations on intuitionistic trapezoidal fuzzy numbers using. Representation of trapezoidal fuzzy numbers with shape function. New methods for ranking of trapezoidal fuzzy numbers. Triangular fuzzy numbers tfns the simplest form of a fn is probably the triangular fuzzy number tfn. Fuzzy regression model using trapezoidal fuzzy numbers for re. A generalization of trapezoidal fuzzy numbers based on.
Also hexagonal, nonagonal, decagonal fuzzy numbers have been introduced to. In case you find almost surely existing bugs or have recommendations for improving the functions comments are welcome to the above mentioned mail addresses. The fuzzification of the cost of the transportation problem is discussed with the help of a numerical example. Jan 11, 2016 solving fuzzy matrix games defuzzificated by trapezoidal parabolic fuzzy numbers ijsrdvol. For convenience, we denote an intuitionistic fuzzy number by, where. In many applications, ranking of fuzzy numbers is an important component of the decision process. A fuzzy number is called positive negative, denoted by 0 fuzzy linear system with trapezoidal fuzzy.
Based on trapezoidal fuzzy numbers and ifss, liu and zuo 11 proposed a trapezoidal intuitionistic fuzzy number tifn. Approximation of fuzzy numbers by trapezoidal fuzzy numbers. Ranking generalized trapezoidal fuzzy numbers with. New aggregation operator for trapezoidal fuzzy numbers. Let and with be two intuitionistic trapezoidal fuzzy numbers.
Trapezoidal fuzzy numbers for the transportation problem. We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and leftright spread of trapezoidal fuzzy numbers. Approximation of fuzzy numbers by trapezoidal fuzzy. Also some of the interesting arithmetic work on fuzzy numbers can be found in abhinav bansal in 9. To deal imprecise in real life situation, many researchers used triangular and trapezoidal fuzzy number 10 111221. A fuzzy number is called trapezoidal fuzzy number if its membership function is given by see figure 1. If x 0 that is x is not equivalent to0, then it is said to be a nonzero symmetric trapezoidal fuzzy number. 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. A new approach for ranking of trapezoidal fuzzy numbers.
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. Two fuzzy number and,, b p q j g are said to be equal i. Using trapezoidal intuitionistic fuzzy number to find. Solving fuzzy matrix games defuzzificated by trapezoidal parabolic fuzzy numbers ijsrdvol. Solving fuzzy matrix games defuzzificated by trapezoidal. Triangular fuzzy numbers and trapezoidal fuzzy numbers have been widely used to express these two different kinds of concepts. In sum, the rank of two fuzzy numbers a and b based on the incentre of the centroids is given as follows steps. A study on ranking of trapezoidal intuitionistic fuzzy numbers.
This function computes fuzzy membership values using a trapezoidal membership function. Assessment of human skills using trapezoidal 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. Since the boundary of this interval is ambiguous, the interval is also a fuzzy set. This paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized trapezoidal fuzzy numbers. Centre of area of fuzzy number coa of fuzzy number. Sukna, siliguri734009 darjeeling, west bengal, india 2 department of mathematics, bengal engineering and science university, shibpur. We can see that both the methods give the same ranking. A new approach for trapezoidal approximation of fuzzy.
It is to be noted that if 0 x, then 0 x but the converse need not be true. New approach for ranking of trapezoidal fuzzy numbers. Ijca solving fully fuzzy linear systems with trapezoidal. The proposed method is simple, and can calculate the similarity measure for both real numbers and fuzzy numbers by the. The trapezoidal fuzzy number linear programming hikari. Solving fully fuzzy linear systems with trapezoidal fuzzy number matrices by partitioning. Based on einstein operations, we define intervalvalued pythagorean trapezoidal fuzzy aggregation operators. Trapezoidal fuzzy numbers in extent analysis method in fuzzy ahp.
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. May 02, 2019 this function returns n trapezoidal fuzzy numbers contained in a matrix of dimension n x 4. D thesis 52 chapter vi construction of fuzzy control charts using trapezoidal fuzzy number 1. A new distance measure for trapezoidal fuzzy numbers. In this section we recall some basic notions on trapezoidal and triangular intuitionistic fuzzy numbers. The rog point r x, r y for a fuzzy number a is provided as 18 a aa. Ordering generalized trapezoidal fuzzy numbers with area, mode, spreads. Based on einstein operations, we define intervalvalued pythagorean trapezoidal fuzzy aggregation operators, such. Geometric aggregation operators with intervalvalued. For an arbitrary trapezoidal fuzzy number u x 0, y 0. A trapezoidal fuzzy number is said to be nonnegative trapezoidal fuzzy number if and only if m dt 0. Many different types of fuzzy numbers are defined in the literature dealing with fuzzy logic and applications. Principal components analysis for trapezoidal fuzzy numbers. In a trapezoidal fuzzy number, first the trapezoid is split into three parts where the first, second and third parts are a triangle, a rectangle and a triangle respectively.
Operations on intuitionistic trapezoidal fuzzy numbers. Profit maximization solid transportation problem with. Notes on ifs, volume 20, 2014, number 2, pages 4351. Scientists in many disciplines face the problem of interpretation of com. In this paper, we consider the fuzzy transportation problem ftp where cost, availability and demand of the. A method for solving fully fuzzy linear system with. To the best of our knowledge, this is the first work on obtaining the solution of the transportation problem using fuzzy trapezoidal numbers. 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 previously proposed approximation operators are improved so as to always obtain a. The aim of this paper is to investigate information aggregation methods under intervalvalued pythagorean trapezoidal fuzzy environment. Jan 10, 2019 the aim of this paper is to investigate information aggregation methods under intervalvalued pythagorean trapezoidal fuzzy environment. However we do acknowledge that the proposed method has more. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. This is followed by the solution of transportation problem using fuzzy trapezoidal numbers in section 4. Strongly to very strongly keywords multicriteria decision making, fahp, trapezoidal fuzzy number, extent analysis i. Let a, b and c be real numbers with a 0 pages 26 download pdf. In section 2, the trapezoidal membership function is defined. 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. In particular, when 2 a 3,the trapezoidal fuzzy number is reduced to a triangular fuzzy number denote d by. Intuitionistic fuzzy number and its arithmetic operation with. Fuzzy risk analysis based on the similarity measure of. A new ranking approach for solving fuzzy transportation.
New aggregation operator for trapezoidal fuzzy numbers based. In the next section, the general transportation problem with fuzzy trapezoidal numbers is discussed. Fung and hu, 5, introduced the linear programming with the technique coefficients based on fuzzy numbers. 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. We are grateful for jstors cooperation in providing the pdf pages that we are using for classroom capsules. Type2 trapezoidal fuzzy number is placing more vital role in science and engineering. Using this notation, the interval 2, 4 is the proper interval 2, 4.
It is true that fuzzy numbers are frequently partial order and cannot be compared like. The arithmetic operations of interval type2 fuzzy set 15 suppose a1 and a2 are two trapezoidal interval type2 fuzzy numbers. Each trapezoidal fuzzy number is characterized by its four values inf0,inf1,sup1,sup0 note. Analytic hierarchy process using trapezoidal fuzzy number. Research article a new similarity measure of generalized. 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.
This function returns n trapezoidal fuzzy numbers contained in a matrix of dimension n x 4. This paper is organized as follows, in section 2, the representation of trapezoidal intuitionistic fuzzy numbers and. Generally a fuzzy interval is represented by two end points a. We say is an intuitionistic fuzzy number throughout this paper, where the function and. Trapezoidaltriangular intuitionistic fuzzy numbers versus. The set of all trapezoidal fuzzy numbers is denoted by ftr. Intuitionistic fuzzy number and its arithmetic operation with application on system failure g. A general form of fuzzy linear fractional programs with. Ordering generalized trapezoidal fuzzy numbers with area. In section 3, operations including exponentiation, logarithms and n th root of trapezoidal intuitionistic fuzzy number. The trapezoidal fuzzy number linear programming 125 programming within the limits of technical coefficients fuzzy and fuzzy right side. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the generalized trapezoidal fuzzy numbers into three. We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of intervalvalued trapezoidal fuzzy numbers and, on the other hand. Conceptual design, multicriteria decisionmaking, fuzzified pugh matrix, synthetic extent evaluation, trapezoidal fuzzy number.
It is obvious that there is an innite number of methods for the approximation of fuzzy numbers with trapezoidal numbers. Lu decomposition method for solving fully fuzzy linear system. Ordering of generalised trapezoidal fuzzy numbers based on. The degree of membership and the degree of nonmembership for a tifn are expressed in the form of trapezoidal fuzzy numbers. In this paper, we have been pointed out the study of fuzzy linear fractional programming flfp problems with trapezoidal fuzzy numbers. The aim of this work is to construct quantified trapezoidal fuzzy numbers as an extension of trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the. Human assessment, fuzzy logic, fuzzy numbers, trapezoidal.
Recently few methods for ranking ifns has also been introduced 29,33,36,41,49. Arithmetic operations on trapezoidal fuzzy numbers. A generalized model for fuzzy linear programs with. Multiplication operation on trapezoidal fuzzy numbers. Statistical process control spc is a technique applied towards improving the quality of. So, triangular fuzzy numbers are special cases of trapezoidal fuzzy numbers. A trapezoidal intuitionistic fuzzy number withparameters, 1 1 2 2,isdenotedas, 1, 2,, 1, 2,inthesetofrealnumbersris. In this paper, several new algebraic mathematics for positive fuzzy numbers of type a. This paper propose a method to solve trapezoidal fuzzy number linear programming problem. Where the objective functions are fuzzy numbers and the constraints are real numbers. Trapezoidal numbers mathematical association of america.
Trapezoidal operators of fuzzy numbers approximation have been studied by many authors, because fuzzy numbers have lots of uses in the e. International journal of computer applications 649. To prove a similar result in the case of ivtfns and tifns, then in the case of. 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. Each trapezoidal fuzzy number is characterized by its four values inf0,inf1,sup1,sup0. You can also compute this membership function using a fismf object.
Introduction the social demand of classifying humans according to their qualifications. Roy2 1 department of mathematics, siliguri institute of technology, p. 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. We can also know that it is an ordinary crisp interval figure 2. 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.
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