The paper established a hybrid evaluation model based on fuzzy analytic hierarchy process ahp and triangular fuzzy number. Triangular fuzzy number a triangular fuzzy number denoted by m. A study on triangular type 2 triangular fuzzy matrices. In order to address this issue, a new fta method based on the technique for order preference by similarity to an ideal solution and the triangular fuzzy number is presented. The results from addition or subtraction betwe en triangular fuzzy numbers result also triangul ar fuzzy numbers. Multiplication operation on fuzzy numbers shang gao and zaiyue zhang school of computer science and engineering, jiangsu university of science and technology, zhenjiang 212003. Every expert and customer can evaluate km according to preference. Sometimes, it is necessary to keep available only left or right triangular fuzzy numbers. It refers to a connected set of possible values, where each possible value has its own weight isbn. Triangular fuzzy numbers and signed distance of fuzzy sets on r in order to consider the fuzzy system reliability analysis using the triangular fuzzy numbers which were based on statistical data, we need the following definitions. Pdf a triangular fuzzy number analytical hierarchy process.
A new operation on triangular fuzzy number for solving fuzzy linear programming problem a. The fuzzy numbers are defined in uncertainty situation and applied in real world problems of science and engineering. Use of the triangular fuzzy numbers for student assessment. Paper open access triangular fuzzy number in probabilistic. Multiplication of triangular fuzzy number among the various shapes of fuzzy number, triangular fuzzy number tfn is the most popular one. We also denote the set of all triangular fuzzy numbers with fr. Abstract a new method is proposed for finding the shortest path problem spp with triangular intuitionistic fuzzy numbers tifn, based on bellman dynamic programming algorithm. Package fuzzynumbers february 5, 2019 title tools to deal with fuzzy numbers type package description s4 classes and methods to deal with fuzzy numbers. Pdf use of the triangular fuzzy numbers for student. A new distance measure for trapezoidal fuzzy numbers. The theory of uncertainty measure makes ifs useful. Nasseri 2 fuzzy numbers here, we give some necessary definitions of fuzzy set theory. Method for aggregating triangular fuzzy intuitionistic. The similarity of triangular fuzzy numbers is an important metric for application of it.
Cut approach for fuzzy product and its use in computing solutions of fully fuzzy linear systems. There exist several approaches to measure similarity of triangular fuzzy numbers. The conventional failure probabilities of basic events are treated as crisp values. This paper present a new concept arithmetic of triangular fuzzy number, namely by using a board area concept of triangular fuzzy number, so that we will get a form multiplication of fuzzy numbers in some cases. The operators of fuzzy addition and subtraction are closed and the definitions provided in. The triangular fuzzy numbers tfn shape is not closed under multiplication and division. A new operation on triangular fuzzy number 527 properties to qualify as a fuzzy number, i. In this paper we have presented exact calculation formulas for addition, subtraction, multiplication and division of two lr fuzzy numbers. First of all, well look into interval, the fundamental concept of fuzzy number, and then operation of fuzzy numbers. Thus, in this paper, we only consider problem in a closed subspace t f. Here, a triangular fuzzy number is given by definition 2. So an intuitionistic fuzzy number is got based on the triangular.
Fuzzy weights estimation method based on the linguistic. Pdf some similarity measures for triangular fuzzy number. Pdf a triangular fuzzy number analytical hierarchy. Fuzzy optimal solution to fuzzy transportation problem. The results from multiplication or division are n ot triangular fuzzy numbers. The graphical representation of a triangular fuzzy number is shown in figure. You can also compute this membership function using a fismf object. In addition, the proposed method is to apply a practical example to test the application of the model. Computation of shortest path in a fuzzy network using triangular intuitionistic fuzzy number. The triangular intuitionistic fuzzy number this paper extends the intuitionistic fuzzy set and uses the triangular fuzzy number to express the membership degree u x a and the nonmembership degree v x a. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result. A a, b, c this representation is interpreted as membership function figure 6. Intuitionistic fuzzy number and its arithmetic operation. The addition and the scalar multiplication on intuitionistic fuzzy numbers see 4 or 5 become in the particular case of trapezoidal intuitionistic fuzzy numbers as follows.
The shape of a triangular fuzzy number is an important metric. Moreover, the fuzzy transportation problem of triangular numbers has been transformed into. The notation u means that the height of the fuzzy number ut 1,t2 is 1 at the point u. A generalization of generalized triangular fuzzy sets hikari ltd. It is shown that triangular approximation of gaussian membership function in fuzzy control can lead to wrong linguistic classification which may have adverse effects on operational and control decisions. In this paper a procedure for the completion of the. It is a fuzzy number represented with three points as follows. Fuzzy transportation problem of triangular numbers with.
Therefore, a new method siam shapes indifferent area and midpoint to measure the similarity of two triangular fuzzy numbers is proposed, which considers the shapes and midpoints of them. The triangular fuzzy number for the number of mammal species 4166, 4629, 5092 is shown by the solid line. A fuzzy number fn is a special form of fuzzy sets on the set r of real numbers. A study on triangular type 2 triangular fuzzy matrices 147 2.
Fuzzy numbers play an important role in many applications. One of the fuzzy numbers that can be used is a triangular fuzzy number tfn. Zadeh, as an extension of fuzzy sets, proposed this concept. Trapezoidaltriangular intuitionistic fuzzy numbers versus. Fuzzy system reliability analysis using triangular fuzzy. Type2 fuzzy sets possess a great expressive power and are conceptually quite appealing. Here two types of intuitionistic fuzzy sets, namely triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number is presented. Triangular fuzzy numbers and the ipcc watts up with that. We propose some similarity measures between two triangular fuzzy numbers tfns based on the vector similarity measures in vector space, which can be used to aggregate the decision information with tfns. Tzl 1,1,1,1 then is said to be a unit trapezoidal fuzzy number. The triangular fuzzy number can be formally written as follows. Yagers ranking method has been used for ranking the fuzzy numbers. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. We also define some operations on triangular fuzzy matrices tfms such as trace and triangular fuzzy.
Multicriteria decision making with triangular intuitionistic. T riangular approximation of fuzzy numbers a new approach. Mar 27, 2017 fuzzy number a fuzzy number is a generalization of a regular, real number. For the fuzzy transportation problem with fuzzy objective function min z 812. A triangular number or triangle number counts objects arranged in an equilateral triangle thus triangular numbers are a type of figurate numbers, other examples being square numbers and cube numbers. But if we use the secant approximation the inverse is approximated by the triangular lr fuzzy number. New similarity of triangular fuzzy number and its application. A new operation on triangular fuzzy number for solving. We have introduced intuitionistic fuzzy number and its arithmetic operations based on extension principle of intuitionistic fuzzy sets. Hence more attention is needed to simplify arithmetic computation with fuzzy numbers. The membership function of the left triangular fuzzy number f l may be written as follows gupta and bhattacharjee, 2010. An application of linguistic variables in assignment.
Moreover, we give two different definitions for nonnegative and positive triangular fuzzy numbers to eliminate this shortcoming. Furthermore, to illustration will given numerical examples of solving fully. Among various extensions of fuzzy sets such as ifs, vague set, intervalvalued fuzzy set, triangular intuitionistic fuzzy set etc. Pdf use of the triangular fuzzy numbers for student assessment.
The magnitude of a triangular fuzzy number a synthetically reflects the information on every membership degree, and meaning of this magnitude is visual and natural. Lu decomposition method for a crisp matrix is well known in solving linear system of equations. Abstrak universitas bina darma adalah salah satu perguruan tinggi yang memberikan fasilitas beasiswa untuk mahasiswa yang berprestasi. In this paper, some elementary operations on triangular fuzzy numbers tfns are defined. Research article new similarity of triangular 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. Comparison of fuzzy multiplication operation on triangular fuzzy. This new arithmetic concept will be applied for solve the fully fuzzy linear system using inverse matrix. Pdf theory of triangular fuzzy number janani bharatraj. Type2 fuzzy sets are fuzzy sets whose membership values are fuzzy sets on the interval 0, 1. Magdm with triangular intuitionistic fuzzy numbers tifns and apply it to the trustworthy service selection problem. A triplet m 1, m 2, m 3 is known as triangular fuzzy number, where m 1 represents smallest likely value, m 2 the most probable value, and m 3 the largest possible value of any fuzzy event. Since triangular fuzzy numbers is a special case of trapezoidal fuzzy numbers, hence in this paper we considered fully fuzzy linear system with trapezoidal fuzzy numbers. Some arithmetic operations on triangular intuitionistic fuzzy.
Chapter 5 fuzzy number this chapter describes fuzzy numbers. A quadratic programming with triangular fuzzy numbers. The development of the fuzzy controller demonstrates that. A synthetic method for knowledge management performance. Let a sl r aa a, and b sl bb b, r be two triangular num. The dual problem of the lp with trapezoidal fuzzy number and some duality results to solve fuzzy linear programming problem was introduced in. A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers. A method for constructing triangular fuzzy numbers core. Intuitionistic fuzzy number and its arithmetic operation with. These are variables whose states are fuzzy numbers. In order to address this issue, a new fta method based on the technique for order. Pdf the fuzzy numbers are defined in uncertainty situation and applied in real world problems of science and engineering. A fuzzy logic model, based on triangular fuzzy numbers and on the centre of gravity defuzzification technique is utilized in this work for evaluating the responses of greek secondary education.
Here each fuzzy cost is assumed as triangular or trapezoidal fuzzy number. Let a sl r aa a, and b sl bb b, r be two triangular numbers and x. Probabilistic fuzzy goal programming pfgp the pfgp models is a linear goal programming model where goals are expressed with fuzzy numbers. This function computes fuzzy membership values using a triangular membership function. For any two triangular fuzzy numbers a a,a,a 0 and. The membership function of triangular fuzzy number consists of monotone increasing and decreasing functions which have a maximum value 1. In application fuzzy set theory fuzzy number plays an important role. Mar 27, 20 flood risk evaluation and prediction represents an essential analytic step to coherently link flood control and disaster mitigation. The purpose of this paper is to apply triangular fuzzy number tfns and analytical hierarchy process ahp method to distribute single intangible assets from combined intangible assets. A fuzzy number a is called a triangular fuzzy number tfn if its member ship function a is given by.
By restricting fuzzy number to triangular fuzzy numbers, addition and subtraction become simpler. Just like fuzzy logic is an extension of boolean logic which uses absolute truth and falsehood only, and nothing in between, fuzzy numbers are an extension of real numbers. Comparison of fuzzy multiplication operation on triangular. Pdf some special types of type2 triangular fuzzy number. Center for the mathematics of uncertainty an introduction to the mathematics of uncertainty including set theory, logic, probability, fuzzy sets, rough sets, and evidence theory. But the main hurdle in the development of applications is the computational complexity. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on. Cut approach for fuzzy product and its use in computing.
Program beasiswa ini diharapkan dapat memacu minat belajar mahasiswa agar lebih berprestasi. We denote a triangular fuzzy number a rby three real numbers sl, and as a slr,, whose meaning are defined in figure 1. We also present that the arithmetic operation of two or more intuitionistic fuzzy number is again an intuitionistic fuzzy number. A methodology for multiple criteria group decisionmaking mcgdm problems with triangular fuzzy information is proposed. We also present that the arithmetic operation of two or more. A new operation on triangular fuzzy number for solving fuzzy. Summation and multiplication of fuzzy numbers defined as. A method for multiattribute group decisionmaking with.
In earlier days, there was no mathematical concept to define vagueness. However, in many real applications, it is often difficult to evaluate failure probabilities of basic events from past occurrences. At first triangular intuitionistic fuzzy number and their arithmetic operations are introduced. Lu decomposition method for solving fully fuzzy linear. Quantitative fuzzy variables the concept of a fuzzy number plays fundamental role in formulating quantitative fuzzy variables. Application of a triangular fuzzy ahp approach for flood risk. It is apparent that a triangular fuzzy number is a special trapezoidal fuzzy number with. The membership function of the tfn introduced by 16 is given in figure 1. A note on adjoint of trapezoidal fuzzy number matrices. Numerical example shows that the total cost obtained is optimal. Expressions for computing the fuzzy reliability of a series system, parallel system,seriesparallel and parallelseries system following triangular intuitionistic fuzzy numbers have been described. The n th triangular number is the number of dots in the triangular arrangement with n dots on a side, and is equal to the sum of the n natural numbers from 1 to n. Moreover, by the application of ranking fuzzy number the fuzzy assignment problem has been transformed into crisp assignment problem and then obtained the optimal solution using asm method. The laws of logic, the law of identity, the law of.
Fault tree analysis based on topsis and triangular fuzzy. Fuzzy number, nonnegative and positive fuzzy numbers. Moreover, a new distance measure of tifns is proposed, and the corresponding proofs are given. In an earlier work we have used the triangular fuzzy numbers tfns as an assessment tool of student skills. Pdf theory of triangular fuzzy number researchgate.
The results from addition or subtraction betwe en triangular fuzzy numbers result also triangul. Mohamed assarudeen pg and research department of mathematics jamal mohamed college autonomous. Properties of operations on triangular fuzz y number 1. When the fuzzy numbers represent linguistic concepts, e. These type of numbers are alternately represented as. For example, if vl is for the weight and vp is for the index, then the triangular fuzzy number is 0, 0, 0.
Among the various shapes of fuzzy number, triangular fuzzy number tfn is the most popular one. The collective opinions are represented using triangular fuzzy numbers whose construction is based on the possibility distribution of the grading process. Triangular fuzzy number tfn in this paper, the goals in the pfgp model are expressed as tfn. Compared with the existing method, our proposed method is more efficient with less complexity. The results of this paper are linked with those presented in 1,p. New arithmetic triangular fuzzy number for solving fully. Based on these main results of the paper, the methods or procedures elaborated for intervalvalued trapezoidal or. It comprises flood risk evaluation and prediction to obtain risk factors ranking and comprehensive flood risk prediction, and then. Fault tree analysis fta is widely used in the failure probability evaluation of a system. Let us consider the left and right spreads, and cog point of unknown fuzzy number is given. Some arithmetic operations on triangular intuitionistic.
Department of mathematical sciences, school of technological applications, graduate technological educational institute t. In addition, well introduce special kind of fuzzy number such as triangular fuzzy number and trapezoidal fuzzy number. Triangular intuitionistic fuzzy number a triangular intuitionistic fuzzy number tifn i a is an intuitionistic fuzzy set in r with following membership function i a x and nonmembership function i a x 1 1 1 1 1 1 1 1 1 1. Fuzzy number, triangular fuzzy number, cut method, standard approximation method. The fuzzy assignment problem has been transformed into a crisp one, using linguistic variables and solved by hungarian technique. Fault tree analysis based on topsis and triangular fuzzy number.
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