This paper propose a method to solve trapezoidal fuzzy number linear programming problem. Here two types of intuitionistic fuzzy sets, namely triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number is presented. A fuzzy number is a number whose value is influenced by a set of numbers, which can produce many different outcomes. In this video some extension concepts like another definition of fuzzy number. In this paper we define diamond fuzzy number with the help of triangular fuzzy number.
A fuzzy set is empty if and only if its membership function is identically zero on x. Pdf in this article, our main intention is to revisit the existing definition of complementation of fuzzy sets and thereafter various theories. Product type operations between fuzzy numbers and their. This situation occurs mainly in geosciences, since in this case we cannot have two. The set of fuzzy rational numbers and flexible querying apmd. Fns package differs from that in the fuzzynumbers package. 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. We include basic arithmetic operations like addition. Indeed, there is no reason yet to consider such a membership function as a fuzzy number, for in this way one obtains a fuzzy set without any connection with properties which are characteristic of real numbers. A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers. Zhang and le1982 introduced the possibility degree to describe the fuzzy truevalue logic with some operators, and studied some. Arithmetic operations of a particular pentagonal fuzzy number are also addressed.
The total approximate is determined by convex combining of fuzzy number s relative and its area that based on decision. Learning algorithms may require an exponential number of iterations with respect to the number of weights until a solution to a learning task is found. Based on both the zadehs definition 26, 27, 28 and the definition given by bede 1. It is clear that the decision to use some particular definition will in general depend on the problem in question. It is a fuzzy number represented with three points as follows. Possibility degree of intervalvalued intuitionistic fuzzy. This notion leads to the formal definition of fuzzy numbers as follows. Two fuzzy sets a and b are equal, written as a b, if and only if fax fbx for all x in x. Preliminaries this section recalls some basic definitions of fuzzy numbers, triangular fuzzy number and trapezoidal fuzzy number.
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. Since the boundary of this interval is ambiguous, the interval is also a fuzzy set. A new hendecagonal fuzzy number for optimization problems. Pdf in this paper we define diamond fuzzy number with the help of triangular fuzzy number. Intuitionistic fuzzy number and its arithmetic operation. 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. A new operation on triangular fuzzy number 527 properties to qualify as a fuzzy number, i. A quantity whose value is imprecise, in contrast to an ordinary number.
Introduction to fuzzy logic, by franck dernoncourt home page email page 2 of20 a tip at the end of a meal in a restaurant, depending on the quality of service and the quality of the food. We define nine operations for the addition of these fuzzy numbers and we. Remark 1 the cross product is defined for any fuzzy numbers in rurff there exists an unique such that 1,x ux0. The aim of this paper is to define hendecagonal fuzzy number and. A fuzzy number is a convex normalized fuzzy set on the real line r such that there exist at least one x r with 1. An extended multiple criteria decision making method based. The cross product of fuzzy numbers and its applications in. Fuzzy number a fuzzy number is a generalization of a regular, real number. In this paper we emphasize that the definition of positive fuzzy number in. In fact, the cross product is defined for any fuzzy. Pentagonal fuzzy number, its properties and application in. Fuzzy number if a fuzzy set is convex and normalized, and its membership function is defined in r and piecewise continuous, it is called as fuzzy number.
Assessment of human skills using trapezoidal fuzzy. Definition fuzzy 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. A fuzzy number f is a fuzzy set constrained by a membership function. Pdf a nonagonal fuzzy number and its arithmetic operation.
These membership grades are often represented by real numbers ranging from 0,1. We begin with several definitions involving fuzzy sets which are obvious extensions of the corresponding definitions for ordinary sets. An application of fuzzy matrices in medical diagnosis. A study on triangular type 2 triangular fuzzy matrices.
Fuzzy set theoryand its applications, fourth edition. I already said that i would give the part 1 video in description here the video link part 1 video link. In this section, we will define some basic definitions such as fuzzy sets, fuzzy number, triangular fuzzy number and its algebra. 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. In this paper the concept on different type of pentagonal fuzzy number is defined. The said number valued function is extended to its generalized hukuhara difference concept, where it is applied to elucidate the pentagonal fuzzy solutions of the equation. As an abbreviated notation, we can define an lr fuzzy number with the membership function in 1 by 2 where the subscripts l and r specify the reference functions 5. Fuzzy number a fuzzy number a is a fuzzy set on the real line r, must satisfy the following conditions. A fuzzy number is a fuzzy set on the real line that satisfies the conditions of normality and convexity. Fuzzy numbers dictionary definition fuzzy numbers defined.
Arithmetic operations of fuzzy numbers continued session. The fuzzy numbers with ten ordinates exists in literature. To solve this problem, we use trapezoidal fuzzy numbers. International journal of fuzzy logic systems ijfls vol. A new fuzzy number called hendecagonal fuzzy number and its membership function is introduced, which is used to represent the uncertainty with eleven points. We include basic arithmetic operations like addition, subtraction of. 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.
Definition fuzzy number it is a fuzzy set the following conditions. A number word and a linguistic modifier fuzzy number a fuzzy set defined in the set of real number degree 1 of central value membership degree decrease from 1 to 0 on both side in the other word 4 6 8 1 normal fuzzy sets the cuts of fuzzy number are closed intervals the support of every fuzzy number is the open interval. Fuzzy system reliability analysis using triangular fuzzy. Dubois, prade, 1979 a fuzzy number is a fuzzy subset.
It must be noted that the definition of fuzzy number in the calculator. Possibility degree reflects the probability of one fuzzy number is larger than another fuzzy number and can be used to compare two fuzzy numbers. A fuzzy number a is a convex normalized fuzzy set on the real line r such that. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle. Fuzzy number is expressed as a fuzzy set defining a fuzzy interval in the real number. Triangular fuzzy number triangular fuzzy number is. R a fuzzy sub set tx of r is called a fuzzy number if it satisfies some results contained in this chapter were published in the joural of fuzzy mathematics b. Product type operations between fuzzy numbers and their applications in geology 124 probabilistic, since, in many applications the measurements cannot be repeated.
We also present that the arithmetic operation of two or more intuitionistic fuzzy number is again an intuitionistic fuzzy number. The notion of expectation is defined for fuzzy numbers or intervals, viewing them as consonant random sets. An application of pentagonal fuzzy number matrix in decision making a gnana santhosh kumar 1, s cynthiya margaret indrni 2 1 m. It refers to a connected set of possible values, where each possible value has its own weight isbn. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. An lr fuzzy quantity number or interval u has membership function of the form. Moreover, this package has the ability of calculating the membership function of the scalar multiplication of a real number and an lr fuzzy number. Solution of algebraic and transcendental equations using. On some difficulties in the addition of trapezoidal ordered fuzzy.
Other fuzzy cardinalities based on the definition of fgcounts, such as flcounts or fecounts, have been defined by zadeh or wygralak 10,29,32. 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. Let us assume that the membership function of any fuzzy number a% is. Multiplication of fuzzy quantities 239 is called the product of a and b. A note on adjoint of trapezoidal fuzzy number matrices. Lu decomposition method for solving fully fuzzy linear. An application of pentagonal fuzzy number matrix in. Let x be the real line r and let a be a fuzzy set of numbers. A fuzzy number is called positive negative, denoted by 0 fuzzy linear system with trapezoidal fuzzy. Arithmetic of fuzzy numbers and intervalsa new perspective with. So fuzzy number supported by the national natural science foundation of china under grant no. A study on triangular type 2 triangular fuzzy matrices 147 2. To distinguis h the multiplication over real number ans d over n.
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