Solution of algebraic and transcendental equations using. We establish relationships between the set of trapezoidal intuitionistic fuzzy numbers and the set of intervalvalued trapezoidal fuzzy numbers and, on the other hand, between the set of triangular intuitionistic fuzzy numbers and the set of triangular fuzzy numbers. An illustrative numerical example is provided to demonstrate the effectiveness of the fuzzy assignment problems. Sep 12, 2017 extended algebraic operations between two triangular fuzzy numbers are wellknown. First of all, well look into interval, the fundamental concept of fuzzy number, and then operation of fuzzy numbers. There exist several approaches to measure similarity of triangular fuzzy. Our ambition for this paper is to be easily understood by the non expert on fuzzy logic reader and. Voskoglou, use of the triangular fuzzy numbers student assessmentfor.
In this paper, some elementary operations on triangular fuzzy numbers are defined. A new operation on triangular fuzzy number for solving. Then we define the parameter corresponding to the beta distribution as follows. From this point of view, we propose using the fuzzy elementary numbers in the process of adopting ethical decisions using the qualitative evaluations via experts. Universal direct analytic models for the minimum of. In the present paper we use the triangular fuzzy numbers tfns as an alternative tool for the same purpose and we compare this approach with the assessment methods of the bivalent and fuzzy logic that we have already used in earlier works. Pdf theory of triangular fuzzy number janani bharatraj. Hungarian method, robust ranking method, triangular numbers.
Here, the kcut set of triangular fuzzy number ta is. Abstractthe order relation of fuzzy number is important in decision making and. Based on these main results of the paper, the methods or procedures elaborated for intervalvalued trapezoidal or triangular. Mar 01, 2017 the purpose of this paper is to study necessary and sufficient conditions of linear operators which are preserved by interval, triangular, symmetric triangular, trapezoidal, or symmetric trapezoidal approximations of fuzzy numbers. A new method for defuzzification and ranking of fuzzy. Summation and multiplication of fuzzy numbers defined as 18. Further, the concepts of regulation and representative of a finite collection of fuzzy triangular numbers are introduced. Kandels definition of a fuzzy measure kandel 5 16 has defined a fuzzy measure as follows. When interval is defined on real number, this interval is said. Existence of interval, triangular, and trapezoidal. The similarity of triangular fuzzy numbers is an important metric for application of it. The canonical representation of multiplication operation.
Grey fuzzy multiple attribute group decisionmaking methods. We convert the data in to triangular fuzzy numbers and then by using topsis for fuzzy numbers the ranking is made. Multiplication operation on fuzzy numbers journal of software. A new method for defuzzification and ranking of fuzzy numbers. Three new methods are proposed, and a notion of preference between alternatives is suggested. Ranking triangle and trapezoidal fuzzy numbers based on the. The mcdm model can be built up based on evidence sourcesto be. For a triangular fuzzy number ax, it can be represented by with membership function given by definition. Pdf trapezoidal triangular intuitionistic fuzzy numbers. A multiattribute decision making for electrician selection. Introduction a fuzzy transportation problem is a transportation problem in which the transportation cost, supply and demand quantities are fuzzy quantities.
A study on triangular type 2 triangular fuzzy matrices. The above definition of a fuzzy number is known as an lr fuzzy number. Fuzzy numbers, increasing function, decreasing function, symmetric triangular fuzzy random variable and arithmetic operations. Operations on triangular fuzzy number to determine the. The results of this paper are linked with those presented in 1,p. The geometric representation of triangular fuzzy number is shown in figure. In 1, we generated the triangular fuzzy numbers on r to r2. Fuzzy set theory applications in production management. The hungarian ones assignment method has been applied to solve the fuzzy assignment problem.
A triangular fuzzy number a is a fuzzy number with piecewise linear membership function. Type2 triangular fuzzy number, alphacut, typereduction, defuzzification 1 introduction type2 fuzzy number t2fn concept was introduced as the extension of type1 fuzzy number t1fn 2,5 concept in dealing the problems of defining the. Comparison of fuzzy multiplication operation on triangular. Linear equations of generalised triangular fuzzy numbers. A new distance and ranking method for triangular fuzzy numbers. 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. In this paper, a new operation on triangular fuzzy numbers. Main results ranking of triangular fuzzy number with distance method let all of fuzzy numbers be either positive or. American journal of applied mathematics and statistics, vol. As a particular case if b c, the trapezoidal fuzzy number reduces to a triangular fuzzy number given by a a,b,d. A representative is defined as a fuzzy triangular number such that the sum of distances between this.
A generalized triangular fuzzy set is a triangular fuzzy set which does not have a maximum value 1. Modified method for solving fully fuzzy linear programming. Note on ranking fuzzy triangular numbers facchinetti. Main results ranking of triangular fuzzy number with distance method let all of fuzzy numbers be either positive or negative. The symmetric triangular fuzzy numbers are converted into crisp values using the proposed ranking. Afuzzy unifying format basedon triangular fuzzy numbers and.
A generalization of generalized triangular fuzzy sets. This paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision. Introduction the history of fuzzy set was started from the year 1965, initially it was discovered independently by l. Hermite interpolation with triangular fuzzy numbers. The generalised fuzzy number reduces to normal fuzzy number if the height wa 1. Let a sl r aa a, and b sl bb b, r be two triangular numbers and x. Divergence, left and right spread, ranking fuzzy numbers.
The motivation of their introduction is explained in 6. N are fuzzy numbers of triangular form, then what is the. The problem is then solved by the usual vam method to get the initial basic feasible solution and modi method to get the optimal solution. Pdf theory of triangular fuzzy number researchgate. Mar 27, 2017 pdf the fuzzy numbers are defined in uncertainty situation and applied in real world problems of science and engineering. One method of finding an intergroup consensus based on. Optimization of fuzzy assignment model with triangular. Keywords weighted trapezoidal approximation, triangular fuzzy number, hilbert space 1 introduction in practice, fuzzy intervals are often used to represent uncertain or incomplete information. Triangular fuzzy numbers are used in many applications such as student assessment 14, collaborative filtering recommendation to measure users similarity 15, etc. Fuzzy transportation problem, triangular fuzzy numbers, optimal solution, roubast ranking method.
The article also provides a framework for interpreting and. Linear programming models and methods of matrix games with. A new distance and ranking method for triangular fuzzy. Interpolation, polynomial, triangular fuzzy numbers ams mathematics subject classification 2010. Comparison of fuzzy multiplication operation on triangular fuzzy. In the numerical example we are deduce that the efficiency of this model. Lin 9 weighted triangular fuzzy numbers to tackle the rate of. Note on ranking fuzzy triangular numbers facchinetti 1998. Stephen dinagar and anbalagan 7 presented new ranking function and arithmetic operations on generalized type2 trapezoidal fuzzy numbers. Among the various shapes of fuzzy numbers, triangular fuzzy number and trapezoidal fuzzy number are the most. A lexicographic method for matrix games with payoffs of.
A normal and convex fuzzy set whose membership function is piecewise continuous is called a fuzzy number. To obtain the crisp real number corresponding to the triangular fuzzy number, we first project on the interval, which will be in the form of. A is a generalized or non normal triangular fuzzy number if 0 w 1. In application fuzzy set theory fuzzy number plays an important role. A new operation on triangular fuzzy number for solving fuzzy. They have certain merits and demerits for each criteria of alternatives, so data. The purpose of this book is to develop a set of effective and efficient linear programming. In an earlier work we have used the triangular fuzzy numbers tfns as an assessment tool of student skills. There exist several approaches to measure similarity of triangular fuzzy numbers. Prade3 in 1978 has defined any of the fuzzy numbers as a fuzzy subset of the real line4,5,6,8.
Arithmetic operations on fuzzy numbers have also been developed, and are based mainly on. Obviously, if then is reduced to, which is a triangular fuzzy number. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. Thus, in this paper, we only consider problem in a closed subspace t f. Pdf the fuzzy numbers are defined in uncertainty situation and applied in real world problems of science and engineering. Let ac1, j1, a1 and bc 2, j2, a2 be two triangular fuzzy numbers which are pythagorean triangles. Abstract in this paper, we use triangular intuitionistic fuzzy numbers to solve mcdm problem. An improved ranking for fuzzy transportation problem using. The arrival and the service rate are fuzzy natures and also analyzed the performance measures of this model both in triangular and trapezoidal fuzzy numbers. Considerations regarding making ethical decisions using. Membership function of triangular fuzzy number the parametric form of a triangular fuzzy number is represented by a a a r a a r.
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. It is easy to see that the definition of an tifn is a generalization of that of the triangular fuzzy number. Since, the shape of the triangular fuzzy number is usually in triangle it is called so. The operators of fuzzy addition and subtraction are closed and the definitions provided in. We calculated zadehs maxmin composition operator for two generalized triangular fuzzy sets4. Optimization of fuzzy assignment model with triangular fuzzy. A fuzzy unifying format based on triangular fuzzy numbers and intuitionistic fuzzy numbers doi. Introduction in some problem, people have to deal with massive imprecise data usually represented them as triangular fuzzy numbers. Such concepts may essentially characterize states of fuzzy variables. The triangular fuzzy numbers tfn shape is not closed under multiplication and division. In this section, we introduce the addition operation on triangular fuzzy numbers associated with the lr inverse function arithmetic principle.
This book deals with the limited twoplayer zerosum game in which the returns in each situation are expressed in fuzzy numbers. Next, we determine the number of triangular fuzzy numbers satisfying the equation c 3 j 3 a 3, where c, j, a are natural numbers. Approximations by interval, triangular and trapezoidal fuzzy. Expressions for determining the fuzzy reliability of a following series of triangular fuzzy numbers intuitionnistic system have been described. The value of b corresponds with the mode or core and a,d with the support. Approximations by interval, triangular and trapezoidal. Digital and fuzzy arithmetic operations triangular intuitionistic are introduced. Decomposition and intersection of two fuzzy numbers for. In addition, well introduce special kind of fuzzy number such as triangular fuzzy number and trapezoidal fuzzy number. Linear programming with triangular intuitionistic fuzzy number. A a b d w the value of b corresponds with the mode or core and a, d with the support. Fuzzy risk analysis based on a new approach of ranking fuzzy.
A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. For example, a and b are triangular fuzzy number a a 1, a 2, a 3, b b 1, b 2, b 3. Scalene triangular fuzzy numbers and its advances and applications in mathematical sciences, volume 19, issue 11, september 2020 1209 4 9. A fuzzy number is a quantity whose values are imprecise, rather than exact as is the case with singlevalued numbers. Fr o r where fris a set of fuzzy number defined on set of real numbers, which maps each fuzzy number into the real. Membership function, triangular and trapezoidal fuzzy numbers, cuts, dsw algorithm, interval analysis. Pdf triangular approximations of fuzzy numbers using. A new approach for triangular intuitionistic fuzzy number in. An interesting problem is to approximate general fuzzy intervals by interval, triangular, and trapezoidal fuzzy numbers, so as to simplify calcu. We also denote the set of all triangular fuzzy numbers with fr. A fuzzy number on r is said to be a triangular fuzzy number if its membership function has the following conditions. A quadratic programming with triangular fuzzy numbers.
We replace these values for their corresponding in 3 which results in a convenient assignment problem in the linear. Fuzzy transportation problem of triangular numbers with. Here, a triangular fuzzy number is given by definition 2. New similarity of triangular fuzzy number and its application. Triangular fuzzy number 3, an extension on fuzzy number, gives better result as compared to fuzzy number. Moreover the generalised fuzzy number reduces to generalised triangular fuzzy number if a3 a4 and a triangular fuzzy number if wa 1. A study on multi server fuzzy queuing model in triangular. In standard fuzzy arithmetic operations we have some problem in subtraction and division operations. Use of the triangular fuzzy numbers for student assessment. Reliability evaluation using triangular intuitionistic fuzzy.
Afuzzy unifying format basedon triangular fuzzy numbers. We denote a triangular fuzzy number a rby three real numbers sl, and as a slr,, whose meaning are defined in figure 1. The operations of two fuzzy numbers a, a and b,b defined in def inition 2. If w1, then aa,b,d is a normalized triangular fuzzy number ais a generalized or nonnormal triangular fuzzy number if 0 feb 01, 2009. The result of these operators is a polynomial membership function and the triangular shape only approximates the actual result. One particular lr type fuzzy number is known as the triangular fuzzy number since its membership function has a triangular form as shown in figure 1. Here, we present four theorems involving normal type2 triangular fuzzy number nt2tfn. A method for constructing triangular fuzzy numbers core.
Chapter 5 fuzzy number this chapter describes fuzzy numbers. A new approach for triangular intuitionistic fuzzy number. Pdf use of the triangular fuzzy numbers for student. Intuitionistic fuzzy numbers and application to multiattribute decision making dengfeng li and jie yang china school of economics and management, fuzhou university, no. If w 1, then, a a b d is a normalized triangular fuzzy number. Method for solving unbalanced assignment problems using. Rank, mode, divergence and spread on generalized triangular. Pdf use of the triangular fuzzy numbers for student assessment. A fuzzy number is a generalization of a regular, real number in the sense that it does not refer to one single value but rather to a connected set of possible values, where each possible value has its own weight between 0 and 1.
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