A synthetic method for knowledge management performance. By restricting fuzzy number to triangular fuzzy numbers, addition and subtraction become simpler. The similarity of triangular fuzzy numbers is an important metric for application of it. Thus, in this paper, we only consider problem in a closed subspace t f. In application fuzzy set theory fuzzy number plays an important role. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result.
In this paper, some elementary operations on triangular fuzzy numbers tfns are defined. A note on adjoint of trapezoidal fuzzy number matrices. The dual problem of the lp with trapezoidal fuzzy number and some duality results to solve fuzzy linear programming problem was introduced in. Fuzzy number, nonnegative and positive fuzzy numbers. Intuitionistic fuzzy number and its arithmetic operation. Package fuzzynumbers february 5, 2019 title tools to deal with fuzzy numbers type package description s4 classes and methods to deal with fuzzy numbers. Compared with the existing method, our proposed method is more efficient with less complexity. The fuzzy assignment problem has been transformed into a crisp one, using linguistic variables and solved by hungarian technique. Lu decomposition method for a crisp matrix is well known in solving linear system of equations. Tzl 1,1,1,1 then is said to be a unit trapezoidal fuzzy number. Pdf some special types of type2 triangular fuzzy number. The theory of uncertainty measure makes ifs useful. Fuzzy optimal solution to fuzzy transportation problem.
This function computes fuzzy membership values using a triangular membership function. 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. 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. The collective opinions are represented using triangular fuzzy numbers whose construction is based on the possibility distribution of the grading process. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. Fuzzy system reliability analysis using triangular fuzzy.
A quadratic programming with triangular fuzzy numbers. Pdf a triangular fuzzy number analytical hierarchy process. New arithmetic triangular fuzzy number for solving fully. Program beasiswa ini diharapkan dapat memacu minat belajar mahasiswa agar lebih berprestasi. In addition, the proposed method is to apply a practical example to test the application of the model. The triangular fuzzy number can be formally written as follows. Properties of operations on triangular fuzz y number 1. The conventional failure probabilities of basic events are treated as crisp values. Moreover, the fuzzy transportation problem of triangular numbers has been transformed into. Pdf use of the triangular fuzzy numbers for student assessment. Some arithmetic operations on triangular intuitionistic. Mar 27, 2017 fuzzy number a fuzzy number is a generalization of a regular, real number. 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. But the main hurdle in the development of applications is the computational complexity.
The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. Multiplication of triangular fuzzy number among the various shapes of fuzzy number, triangular fuzzy number tfn is the most popular one. 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. In earlier days, there was no mathematical concept to define vagueness. Modified method for solving fully fuzzy linear programming. Fuzzy transportation problem of triangular numbers with. 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. Zadeh, as an extension of fuzzy sets, proposed this concept. The triangular fuzzy number for the number of mammal species 4166, 4629, 5092 is shown by the solid line.
Furthermore, to illustration will given numerical examples of solving fully. The membership function of the tfn introduced by 16 is given in figure 1. Every expert and customer can evaluate km according to preference. The results from addition or subtraction betwe en triangular fuzzy numbers result also triangul. 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. In this paper we have presented exact calculation formulas for addition, subtraction, multiplication and division of two lr fuzzy numbers. 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. Pdf a triangular fuzzy number analytical hierarchy. One of the fuzzy numbers that can be used is a triangular fuzzy number tfn.
These type of numbers are alternately represented as. For the fuzzy transportation problem with fuzzy objective function min z 812. Fault tree analysis based on topsis and triangular fuzzy number. Among the various shapes of fuzzy number, triangular fuzzy number tfn is the most popular one. Sometimes, it is necessary to keep available only left or right triangular fuzzy numbers. The membership function of the left triangular fuzzy number f l may be written as follows gupta and bhattacharjee, 2010. 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. The notation u means that the height of the fuzzy number ut 1,t2 is 1 at the point u. There exist several approaches to measure similarity of triangular fuzzy numbers.
T riangular approximation of fuzzy numbers a new approach. Based on these main results of the paper, the methods or procedures elaborated for intervalvalued trapezoidal or. However, triangular fuzzy number is just a method to solve the problem, and we also need a system to perform and support this method. We also present that the arithmetic operation of two or more intuitionistic fuzzy number is again an intuitionistic fuzzy number. However, in many real applications, it is often difficult to evaluate failure probabilities of basic events from past occurrences. Here, a triangular fuzzy number is given by definition 2. For example, if vl is for the weight and vp is for the index, then the triangular fuzzy number is 0, 0, 0. A fuzzy number fn is a special form of fuzzy sets on the set r of real numbers. In addition, well introduce special kind of fuzzy number such as triangular fuzzy number and trapezoidal fuzzy number. 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 laws of logic, the law of identity, the law of. The development of the fuzzy controller demonstrates that.
Quantitative fuzzy variables the concept of a fuzzy number plays fundamental role in formulating quantitative fuzzy variables. A generalization of generalized triangular fuzzy sets hikari ltd. A new operation on triangular fuzzy number 527 properties to qualify as a fuzzy number, i. Some arithmetic operations on triangular intuitionistic fuzzy. 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. We denote a triangular fuzzy number a rby three real numbers sl, and as a slr,, whose meaning are defined in figure 1. Department of mathematical sciences, school of technological applications, graduate technological educational institute t. Use of the triangular fuzzy numbers for student assessment. Triangular fuzzy number a triangular fuzzy number denoted by m. Type2 fuzzy sets are fuzzy sets whose membership values are fuzzy sets on the interval 0, 1. Cut approach for fuzzy product and its use in computing. Fuzzy number, triangular fuzzy number, cut method, standard approximation method.
Pdf some similarity measures for triangular fuzzy number. A study on triangular type 2 triangular fuzzy matrices 147 2. Triangular fuzzy number tfn in this paper, the goals in the pfgp model are expressed as tfn. The membership function of triangular fuzzy number consists of monotone increasing and decreasing functions which have a maximum value 1. The results from multiplication or division are n ot triangular fuzzy numbers. Triangular fuzzy numbers and the ipcc watts up with that. Application of a triangular fuzzy ahp approach for flood risk. A study on triangular type 2 triangular fuzzy matrices. Pdf the fuzzy numbers are defined in uncertainty situation and applied in real world problems of science and engineering. Mohamed assarudeen pg and research department of mathematics jamal mohamed college autonomous. Summation and multiplication of fuzzy numbers defined as. Probabilistic fuzzy goal programming pfgp the pfgp models is a linear goal programming model where goals are expressed with fuzzy numbers. It comprises flood risk evaluation and prediction to obtain risk factors ranking and comprehensive flood risk prediction, and then.
The fuzzy numbers are defined in uncertainty situation and applied in real world problems of science and engineering. Paper open access triangular fuzzy number in probabilistic. You can also compute this membership function using a fismf object. Fault tree analysis based on topsis and triangular fuzzy. The operators of fuzzy addition and subtraction are closed and the definitions provided in. A method for multiattribute group decisionmaking with. Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on.
Let a sl r aa a, and b sl bb b, r be two triangular numbers and x. Hence more attention is needed to simplify arithmetic computation with fuzzy numbers. 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. We also define some operations on triangular fuzzy matrices tfms such as trace and triangular fuzzy.
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. 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. It is apparent that a triangular fuzzy number is a special trapezoidal fuzzy number with. A new operation on triangular fuzzy number for solving fuzzy. Numerical example shows that the total cost obtained is optimal. Trapezoidaltriangular intuitionistic fuzzy numbers versus.
Pdf theory of triangular fuzzy number researchgate. Let us consider the left and right spreads, and cog point of unknown fuzzy number is given. Mar 27, 20 flood risk evaluation and prediction represents an essential analytic step to coherently link flood control and disaster mitigation. 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. A fuzzy number a is called a triangular fuzzy number tfn if its member ship function a is given by.
The results of this paper are linked with those presented in 1,p. Here each fuzzy cost is assumed as triangular or trapezoidal fuzzy number. It is a fuzzy number represented with three points as follows. But if we use the secant approximation the inverse is approximated by the triangular lr fuzzy number. These are variables whose states are fuzzy numbers. The results from addition or subtraction betwe en triangular fuzzy numbers result also triangul ar fuzzy numbers. A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers. Among various extensions of fuzzy sets such as ifs, vague set, intervalvalued fuzzy set, triangular intuitionistic fuzzy set etc. Chapter 5 fuzzy number this chapter describes fuzzy numbers. Fuzzy numbers play an important role in many applications. A method for constructing triangular fuzzy numbers core. In an earlier work we have used the triangular fuzzy numbers tfns as an assessment tool of student skills.
We also present that the arithmetic operation of two or more. Pdf theory of triangular fuzzy number janani bharatraj. New similarity of triangular fuzzy number and its application. Type2 fuzzy sets possess a great expressive power and are conceptually quite appealing. 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.
Intuitionistic fuzzy number and its arithmetic operation with. 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. 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. In this paper a procedure for the completion of the. A new distance measure for trapezoidal fuzzy numbers. 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. Method for aggregating triangular fuzzy intuitionistic. Comparison of fuzzy multiplication operation on triangular.
Fault tree analysis fta is widely used in the failure probability evaluation of a system. So an intuitionistic fuzzy number is got based on the triangular. For any two triangular fuzzy numbers a a,a,a 0 and. The graphical representation of a triangular fuzzy number is shown in figure. Moreover, we give two different definitions for nonnegative and positive triangular fuzzy numbers to eliminate this shortcoming. A new operation on triangular fuzzy number for solving. Comparison of fuzzy multiplication operation on triangular fuzzy.
Some arithmetic operations on triangular intuitionistic fuzzy number 367 definition. A new operation on triangular fuzzy number for solving fuzzy linear programming problem a. This new arithmetic concept will be applied for solve the fully fuzzy linear system using inverse matrix. The triangular fuzzy numbers tfn shape is not closed under multiplication and division. It refers to a connected set of possible values, where each possible value has its own weight isbn. The paper established a hybrid evaluation model based on fuzzy analytic hierarchy process ahp and triangular fuzzy number. Expressions for computing the fuzzy reliability of a series system, parallel system,seriesparallel and parallelseries system following triangular intuitionistic fuzzy numbers have been described. Lu decomposition method for solving fully fuzzy linear. An application of linguistic variables in assignment. Nasseri 2 fuzzy numbers here, we give some necessary definitions of fuzzy set theory.
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. Pdf use of the triangular fuzzy numbers for student. In order to address this issue, a new fta method based on the technique for order. We also denote the set of all triangular fuzzy numbers with fr. A a, b, c this representation is interpreted as membership function figure 6. Cut approach for fuzzy product and its use in computing solutions of fully fuzzy linear systems. Moreover, a new distance measure of tifns is proposed, and the corresponding proofs are given. A methodology for multiple criteria group decisionmaking mcgdm problems with triangular fuzzy information is proposed. We have introduced intuitionistic fuzzy number and its arithmetic operations based on extension principle of intuitionistic fuzzy sets. Fuzzy weights estimation method based on the linguistic. Magdm with triangular intuitionistic fuzzy numbers tifns and apply it to the trustworthy service selection problem.
The upper and lower limits of expected number of species vary with the membership value. First of all, well look into interval, the fundamental concept of fuzzy number, and then operation of fuzzy numbers. Here two types of intuitionistic fuzzy sets, namely triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number is presented. Multiplication operation on fuzzy numbers shang gao and zaiyue zhang school of computer science and engineering, jiangsu university of science and technology, zhenjiang 212003. Computation of shortest path in a fuzzy network using triangular intuitionistic fuzzy number. Research article new similarity of triangular fuzzy number. 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. When the fuzzy numbers represent linguistic concepts, e.
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