For convenience, we denote an intuitionistic fuzzy number by, where. This is followed by the solution of transportation problem using fuzzy trapezoidal numbers in section 4. Pdf arithmetic operations on trapezoidal fuzzy numbers. Intuitionistic fuzzy number, triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number. Any fuzzy number can be thought of as a function whose domain is a specified set usually the set of real numbers, and whose range is the span of nonnegative real numbers between, and including, 0 and. You can also compute this membership function using a fismf object. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two.
G esan a veeram idal f nd uzzy num new ty fuzzy whic of numare fuzzy arithmetic for symmetric trapezoidal b. Lu decomposition method for solving fully fuzzy linear system. In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this paper a new method is proposed which is based on incentre of centroids to rank fuzzy quantities. Research article using trapezoidal intuitionistic fuzzy number to find optimized path in a network p. Fuzzy regression model using trapezoidal fuzzy numbers for. The calculation of the proposed method is far simpler and easier. 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.
Trapezoidal fuzzy numbers tfns and trfns are extensively used in fuzzy applications owing to their. Ranking generalized trapezoidal fuzzy numbers with. Fuzzy risk analysis based on the similarity measure of. In this method, splitting the generalized trapezoidal fuzzy numbers into three plane figures and then calculating the centroids of each plane figure followed by the incentre of the centroids and then finding the euclidean distance. Intervalvalued intuitionistic trapezoidal fuzzy number. 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 our paper we are developing an inventory model using trapezoidal fuzzy number for holding cost, ordering cost and shortage cost. The degree of membership and the degree of nonmembership for a tifn are expressed in the form of trapezoidal fuzzy numbers. New approach for ranking of trapezoidal fuzzy numbers. We will not consider the triangular number 1to be trapezoidal, since it only has a single layer. Recently few methods for ranking ifns has also been introduced 29,33,36,41,49. Pdf dual trapezoidal fuzzy number and its applications.
On the other hand, many fuzzy numbers ranking methods give the same order for fuzzy numbers in any level of managers risk taking. Assessment of human skills using trapezoidal fuzzy. 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. Statistical process control spc is a technique applied towards improving the quality of. For example grzegorzewski and mrowka proposed in 12 a method to find the nearest with respect to a wellknown metric between fuzzy numbers. So we insert the risk taking factor rf to order fuzzy numbers and provide a reasonable range of fuzzy numbers comparison through wide levels of this factor. In the present paper, an inventory model without shortages has been considered in a fuzzy environment. A study on process variability using cusum and fuzzy control charts ph. Introduction the social demand of classifying humans according to their qualifications. Arithmetic operations on trapezoidal fuzzy numbers. Then, we have the if 0,0,0,0 then is said to be zero trapezoidal fuzzy number.
New aggregation operator for trapezoidal fuzzy numbers. Type2 trapezoidal fuzzy number is placing more vital role in science and engineering. Solution of matrix games with generalised trapezoidal. Intervalvalued intuitionistic trapezoidal fuzzy number and its application junhong li1. In addition, we define the value and the ambiguity of an extended. Operations on intuitionistic trapezoidal fuzzy numbers using. 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. For an arbitrary trapezoidal fuzzy number u x 0, y 0. Research article using trapezoidal intuitionistic fuzzy. Triangular intuitionistic fuzzy numbers and trapezoidal intuitionistic fuzzy numbers are the extensions of if sets in another way, which extends discrete set to continuous set. A generalization of trapezoidal fuzzy numbers based on. 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.
Triangular fuzzy numbers and trapezoidal fuzzy numbers have been widely used to express these two different kinds of concepts. In this paper, we will introduce a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some. Ordering generalized trapezoidal fuzzy numbers hikari. Cut converges to the fuzzy numbers and it will be illustrated by example using dual trapezoidal fuzzy number and some mensuration problems are illustrated with. A new method for trapezoidal fuzzy numbers ranking based. Fuzzy number approximation by trapezoidal fuzzy numbers which preserve expected interval is discussed. This paper is organized as follows, in section 2, the representation of trapezoidal intuitionistic fuzzy numbers and. Rezvani 1015 evaluated the system of fuzzy numbers. It is shown that the adequate approximation operator is chosen with respect both to the global spread of a fuzzy number and the size of possible asymmetry between the. 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. Our goal is to determine the optimal total cost and the optimal order quantity for the proposed inventory model. If a be nonnormal fuzzy number, it will be denoted by.
Approximations of fuzzy numbers by trapezoidal fuzzy. In a trapezoidal fuzzy number, first the trapezoid is split. Ax a therefore, for preserving of these points we consider. It is obvious that there is an innite number of methods for the approximation of fuzzy numbers with trapezoidal numbers. A fuzzy number is called positive negative, denoted by 0 tpfn. This paper propose a method to solve trapezoidal fuzzy number linear programming problem. Addition of two trapezoidal intuitionistic fuzzy numbers jianqiang and zhong, 2009.
Representation of trapezoidal fuzzy numbers with shape function. Trapezoidal approximation of a fuzzy number preserving the. An extended trapezoidal fuzzy number may not be a fuzzy number, but the distance between two extended trapezoidal fuzzy numbers is similarly defined as in or. A trapezoidal fuzzy number is said to be nonnegative trapezoidal fuzzy number if and only if m dt 0. Ranking generalized trapezoidal fuzzy numbers with euclidean distance by the incentre of centroids. Cosine similarity measure based multiattribute decision.
Also some of the interesting arithmetic work on fuzzy numbers can be found in abhinav bansal in 9. Trapezoidaltriangular intuitionistic fuzzy numbers versus. However, expression of a fuzzy number is based on the objective observation, therefore a fuzzy number includes subjective concept as well as objective concept. Here arithmetic mean operation of fuzzy numbers is used for. A fuzzy number whose membership functions graph forms a trapezoid with the oxaxis. New aggregation operator for trapezoidal fuzzy numbers based. We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name modal interval trapezoidal fuzzy numbers. In the next section, the general transportation problem with fuzzy trapezoidal numbers is discussed. The arithmetic operations of interval type2 fuzzy set 15 suppose a1 and a2 are two trapezoidal interval type2 fuzzy numbers.
Arithmetic operations on trapezoidal fuzzy numbers ispacs. It is to be noted that if 0 x, then 0 x but the converse need not be true. A study on ranking of trapezoidal intuitionistic fuzzy numbers. Pdf multiplication operation on trapezoidal fuzzy numbers. In section 2, the trapezoidal membership function is defined. A new approach for ranking of trapezoidal fuzzy numbers. Let and with be two intuitionistic trapezoidal fuzzy numbers. Section 4 is confined to define the cosine similarity measure between two trapezoidal fuzzy neutrosophic numbers and its properties. Algorithms for trapezoidal approximations of 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. Moreover, rezvani proposed a new method for ranking in perimeters of two generalized trapezoidal. Fuzzy inventory model without shortage using trapezoidal. We say is an intuitionistic fuzzy number throughout this paper, where the function and. This present study focus on the generalization normal type2 trapezoidal fuzzy number, for that initially we derived left and right generalization of trapezoidal fuzzy number, symmetric and non. Duality in fuzzy linear programming with symmetric. Geetharamani 2 department of mathematics, sudharsan engineering college, pudukkottai, tamil nadu, india department of mathematics, anna. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the. An extended trapezoidal fuzzy number is an order pair of polynomial functions of degree less than or equal to 1. Profit maximization solid transportation problem with. The previously proposed approximation operator is improved so as to always produce a well formed trapezoidal fuzzy number.
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. Lu decomposition method for solving fully fuzzy linear. New methods for ranking of trapezoidal fuzzy numbers. In 1976 and 1977, jain 1, 2 proposed a method using the concept of maximizing set to order the fuzzy numbers. Approximations of fuzzy numbers by trapezoidal fuzzy numbers. Assessment of human skills using trapezoidal fuzzy numbers.
A note on adjoint of trapezoidal fuzzy number matrices. In this paper, several new algebraic mathematics for positive fuzzy numbers of type a. Pdf in this paper, a methods for solving multiplication operation of two trapezoidal fuzzy numbers are given. Two fuzzy number and,, b p q j g are said to be equal i. 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. Triangular fuzzy number is a subset of trapezoidal fuzzy number. A fuzzy number is called trapezoidal fuzzy number if its membership function is given by see figure 1.
Fuzzy number approximation by trapezoidal fuzzy numbers which preserves the expected interval is discussed. Arithmetic operations on symmetric trapezoidal intuitionistic. New methods for ranking of trapezoidal fuzzy numbers 1161 principle. 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. Based on these main results of the paper, the methods or procedures elaborated for intervalvalued trapezoidal or triangular fuzzy numbers as. Intervalvalued intuitionistic trapezoidal fuzzy number and. Pdf ranking generalized trapezoidal fuzzy numbers with. Moreover, the metric properties of suggested distance measure are investigated. It has got many applications 5,6 in information science, decision making problems, medical diagnosis, and system failure and pattern recognition. If you like, and especially if you have decided that zero is a triangular number, they can be considered to be the zerosized triangle subtracted from a triangle with base at least 2. Trapezoidal operators of fuzzy numbers approximation have been studied by many authors, because fuzzy numbers have lots of uses in the e. A new distance measure for trapezoidal fuzzy numbers.
Fuzzy regression model using trapezoidal fuzzy numbers for re. Wang 11 gave the definition of trapezoidal intuitionistic fuzzy number which is an extension of triangular intuitionistic fuzzy number. A new method for trapezoidal fuzzy numbers ranking based on. The proposed methods will be very helpful in developing fuzzy multi criteria decision making models. Signed distance between the fuzzy sets and is defined as.
Trapezoidal approximations of fuzzy numbers request pdf trapezoidal approximation of fuzzy numbers, but the result of approximation is not always a fuzzy number, sometimes it is not a fuzzy set. The proposed method is simple, and can calculate the similarity measure for both real numbers and fuzzy numbers by the. An inventory model with allowable shortage using trapezoidal. New algorithms for calculating the proper approximations are proposed. This function computes fuzzy membership values using a trapezoidal membership function. Geetharamani 2 department of mathematics, sudharsan engineering college, pudukkottai, tamil nadu, india department of mathematics, anna university chennai, bit campus, tamil nadu, india. If x 0 that is x is not equivalent to0, then it is said to be a nonzero symmetric trapezoidal fuzzy number. Keywords human a ssessment, fuzzy logic, fuzzy numbers fns, triangular tfns and trapezoidal tpfns fuzzy numbers, center of gravity cog defuzzification technique 1. By ranking of fuzzy numbers, we can rank alternatives and find the best one from them. This paper describes a ranking method for ordering fuzzy numbers based on area, mode, spreads and weights of generalized trapezoidal fuzzy numbers. To prove a similar result in the case of ivtfns and tifns, then in the case of. If 0 x, then x is said to be a zero symmetric trapezoidal fuzzy number.
This paper proposes a method on the incentre of centroids and uses of euclidean distance to ranking generalized fuzzy numbers. In section 3, operations including exponentiation, logarithms and n th root of trapezoidal intuitionistic fuzzy number. If n 1, we simply write a a, b, c, d, which is known as a normal trapezoidal. Pdf in this paper, several new algebraic mathematics for positive fuzzy numbers of type a, a, a, a are devised and do not need the.
Section 5 is devoted to present the cosine similarity measure based multiattribute decision making with trapezoidal fuzzy. A method for solving fully fuzzy linear system with. Ftr l au, the set of all trapezoidal fuzzy numbers. To solve this problem, we use trapezoidal fuzzy numbers. The previously proposed approximation operators are improved so as to always obtain a trapezoidal fuzzy number. Soft set theory in medical diagnosis using trapezoidal. The tpfns are generalizations of the triangular fuzzy numbers. Trapezoidaltriangular intuitionistic fuzzy numbers versus interval. The area used in this method is obtained from the generalized trapezoidal fuzzy number, first by splitting the generalized trapezoidal fuzzy numbers into three. A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers. D thesis 52 chapter vi construction of fuzzy control charts using trapezoidal fuzzy number 1. Using trapezoidal intuitionistic fuzzy number to find. Also arithmetic operations 7,9 were defined for intuitionistic fuzzy numbers.
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