Using trapezoidal intuitionistic fuzzy number to find. We include basic arithmetic operations like addition. 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. Cut of a normal hexagonal fuzzy number a 1, a 2, a 3, a4, a5, a 6 given by the definition i.
Pentagonal fuzzy number, its properties and application in. The screenshot from a pdf i created by printing to adobe pdf, but i can tell also within word that these numbers are blurry. Solutions of fully fuzzy linear systems are described in section 5. It is a fuzzy number represented with three points as follows. An introduction to analytical fuzzy plane geometry. Pdf in this paper we define diamond fuzzy number with the help of triangular fuzzy number. In the hyperstructural domain, a fuzzy number carries two dimensions of uncertainties for its base, lower, and upper values in the accuracy dimension of quantities as well as the degrees of memberships of its values in the confidentiality dimension. Definitionfuzzy number it is a fuzzy set the following conditions. Fuzzy number represents a real number whose boundary is fuzzy. An application of pentagonal fuzzy number matrix in decision making a gnana santhosh kumar 1, s cynthiya margaret indrni 2 1 m.
It is clear that the decision to use some particular definition will in general depend on the problem in question. Intuitionistic fuzzy number and its arithmetic operation with application on system failure g. A study on ranking of trapezoidal intuitionistic fuzzy numbers. Definition fuzzy number it is a fuzzy set the following conditions. A normal triangular intervalvalued fuzzy number a is a triangular intervalvalued fuzzy number happens to 22 aal u and lu1 aa. A fuzzy number is a triangular fuzzy number denoted by a. List number blurry, multilevel list microsoft community.
Fuzzy ifthen rules a fuzzy ifthen rule fuzzy rule fuzzy implication assumes the form of. Moreover, the metric properties of suggested distance measure are investigated. A fuzzy number is thus a special case of a convex, normalized fuzzy set of the real line. These will have a number of rules that transform a number of variables into a fuzzy result, that is, the. A fuzzy number is a fuzzy subset of the real line whose highest membership values are clustered around a given real number called the mean value. There are numerous methods for ranking of simple fuzzy numbers but, we lack of effective methods for ranking of intuitionistic fuzzy numbers ifn. 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. In order to rank trifns, we have defined a ranking function by taking sum of value and. 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. This notion leads to the formal definition of fuzzy numbers as follows. Fuzzy set definition of fuzzy set by merriamwebster.
Fuzzy set definition is a mathematical set with the property that an object can be a member of the set, not a member of the set, or any of a continuum of states of being a partial member of the set. Fuzzy definition and meaning collins english dictionary. 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. 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. Based on both the zadehs definition 26, 27, 28 and the definition given by bede 1. Granular computing is an emerging computing theory and paradigm that deals with the processing of information granules, which are defined as a number of information entities grouped together due to their similarity, physical adjacency, or indistinguishability. A new operation on triangular fuzzy number 527 properties to qualify as a fuzzy number, i.
We know that any crisp numbera is a fuzzy number with this formaa%,0,0. An application of pentagonal fuzzy number matrix in. So, fuzzy set can be obtained as upper envelope of its. It is the process that maps a fuzzy set to a crisp set. Since the boundary of this interval is ambiguous, the interval is also a fuzzy set. A and b represent fuzzy sets x and y are two fuzzy linguistic variables x is a is called antecedent y is b is called consequent. We define nine operations for the addition of these fuzzy numbers and we.
Trapezoidal approximation of a fuzzy number preserving the. In a narrow sense, fuzzy logic is a logical system, which is an extension of multivalued logic. To arrive at the of various types of fuzzy numbers, we start with basic definitions of some wellproduct known fuzzy numbers. Being so in love its beyond euphoria that could be described as hopeless romance, comparable to having butterflies. 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. Joakim lindblad, 20070221 18 fuzzy sets and fuzzy techniques joakim lindblad outline interval numbers arithmetic operations on intervals fuzzy numbers and fuzzy intervals linguistic variables. In most aspects of human reasoning, these granules have an uncertain formation, so the concept of granularity of fuzzy. A fuzzy number a is a fuzzy set on the real line that satisfies the conditions of normality and convexity. Fuzzy definition in the cambridge english dictionary. Fuzzy numbers generalize classical real numbers and roughly speaking a fuzzy number is a fuzzy subset of the real line that has some additional properties. However, in a wider sense fuzzy logic fl is almost synonymous with the theory of fuzzy sets, a theory which relates to classes of objects with unsharp boundaries in which membership is a matter of degree. Fuzzy logic is an approach to computing based on degrees of truth rather than the usual true or false 1 or 0 boolean logic on which the modern computer is based.
Fuzzy number, lr fuzzy number, membership function. Pdf fuzzy numbers and fuzzy arithmetic researchgate. Fuzzy sets and fuzzy techniques lecture 9 fuzzy numbers. A fuzzy set a is called normal if there is at least one point x.
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. 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. An application of fuzzy matrices in medical diagnosis. A note on adjoint of trapezoidal fuzzy number matrices. 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. In order to address the aforementioned challenging problems, an improved theory of fuzzy numbers and fuzzy arithmetic is presented for applications in fuzzy inference systems, cognitive robots, cognitive informatics, cognitive computing, and computational intelligence. R 0, l such that fyx 1 x a and limi fax 0 will be called a z, fuzzy number, or simply a fuzzy number.
Here, we give some necessary definitions of fuzzy set theory. A new distance measure for trapezoidal fuzzy numbers. 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. These functions may be used to define a fuzzy number, now with. In section 2, we recall some fundamental results on fuzzy numbers. This manner of approximation leads to great losses of important information and we can call this method, according to 51, type i approximation another version of approximation is the attaching of a real numbers interval to a fuzzy number e. Fuzzy number a fuzzy number a is a fuzzy set on the real line r, must satisfy the following conditions. A study on triangular type 2 triangular fuzzy matrices. We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and leftright spread of trapezoidal fuzzy numbers.
Any fuzzy number can be thought of as a function whose domain is a specified set. Postscript ps files are generated by substituting the call to pdf for the call. 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 new operation on triangular fuzzy number for solving. A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers 36. International journal of fuzzy logic systems ijfls vol.
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. Fuzzy numbers and fuzzy intervals linguistic variables arithmetics on fuzzy numbers lattice of fuzzy numbers interval equations fuzzy equations linear programming fuzzy linear programming interval numbers an interval number, representing an uncertain real number a a1. To serve the purpose, the value and ambiguity index of trifns have been defined. 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. Primarily intended for engineers and researchers in the field of fuzzy arithmetic, the book also offers a valuable source of basic information on fuzzy models and an easytounderstand reference guide to their applications for advanced undergraduate students, operations researchers, modelers and managers alike. Below is an example of the number of my second level in my multilevel list. We include basic arithmetic operations like addition, subtraction of. The numbers on my first, and third level in the list are perfectly clear and vectorized. Sukna, siliguri734009 darjeeling, west bengal, india 2 department of mathematics, bengal engineering and science university, shibpur. In this paper the concept on different type of pentagonal fuzzy number is defined. Each numerical value in the domain is assigned a specific grade of membership. A quantity whose value is imprecise, in contrast to an ordinary number. So fuzzy number supported by the national natural science foundation of china under grant no. A fuzzy set a on the set r of real numbers is said to be a fuzzy number if it.
A read is counted each time someone views a publication summary such as the title, abstract, and list of authors, clicks on a figure, or views or downloads the fulltext. An exposition article pdf available in international journal of intelligent systems and applications 88. Pdf pentagonal fuzzy number iir publications academia. Roy2 1 department of mathematics, siliguri institute of technology, p. A mathematical logic that attempts to solve problems by assigning values to an imprecise spectrum of data in order to arrive at the most accurate conclusion possible. Fuzzy definition is marked by or giving a suggestion of fuzz. When we speak of the table we have the rows and columns clearly marked out so the table by removing the lines can become a matrix with rows and columns. The mapping a is also called the membership function of fuzzy set a 2. Now the fuzzy number 00,0,0% that is not positive in real concept, with duboiss definition is a positive fuzzy number and this is not. Fuzzy distance measure for fuzzy numbers hamid rouhparvar, abdorreza panahi, azam noorafkan zanjani department of mathematics, saveh branch, islamic azad university, saveh, iran. Trapezoidal approximation and examples are in section 3.
A fuzzy number is a number whose value is influenced by a set of numbers, which can produce many different outcomes. In this paper we define diamond fuzzy number with the help of triangular fuzzy number. Fuzzy number is expressed as a fuzzy set defining a fuzzy interval in the real number. 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. A fuzzy set a in r real line is defined to be a set of ordered pairs a. Intuitionistic fuzzy number and its arithmetic operation with. A fuzzy set 1 a on, set of real numbers is called a fuzzy number 2 which satisfies at least the following three properties. In this paper, the usual algebraic operations on real numbers are extended to fuzzy numbers by the use of a fuzzification principle.
A x is called the membership function for the fuzzy set. Triangular fuzzy number triangular fuzzy number is defined as a. Ottovonguericke university of magdeburg faculty of computer science department of knowledge processing and language engineering. Cut approach for fuzzy product and its use in computing.
A fuzzy number is a generalization of a regular, real number in the sense that it does not refer to. Wang 11 gave the definition of trapezoidal intuitionistic fuzzy number which is an extension of triangular intuitionistic fuzzy number. Fuzzy sets type1 and type 2 and their applications presented by prof. Fuzzy numbers generalize classical real numbers and roughly speaking a fuzzy number is a fuzzy subset of the real line that. An lr fuzzy quantity number or interval u has membership function of the form. Fuzzy numbers dictionary definition fuzzy numbers defined. A fuzzy number is a quantity whose value is imprecise, rather than exact as is the case with ordinary singlevalued numbers. The fuzzy number concept is basic for fuzzy analysis and fuzzy differential equations, and a very useful tool in several applications of fuzzy sets and fuzzy logic. A fuzzy number a is a convex normalized fuzzy set on the real line r such that. This open access book offers comprehensive coverage on ordered fuzzy numbers, providing readers with both the basic information and the necessary ex. Usually, a% is a positive nonnegative fuzzy number, if and only if a is positive nonnegative crisp number.
Intuitionistic fuzzy number and its arithmetic operation. A new method for defuzzification and ranking of fuzzy. A study on triangular type 2 triangular fuzzy matrices 147 2. A new operation on triangular fuzzy number for solving fuzzy. 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. In this paper, we provide a formal definition for this restricted triangular intervalvalued fuzzy number. A fuzzy set is a function a on a set x to the unit interval. In this paper a formula of fuzzy distance measure for fuzzy numbers is presented and also the metric properties of the proposed method are studied.1025 1092 1160 1002 986 1202 907 555 792 97 666 538 675 1205 1334 528 1058 1070 1141 197 1601 1401 568 821 1375 1179 505 215 1065 1037 1358 682 1360 601 1120 773 1424 330 1164 765 819 1275 1169 1459 1321 401 995 1398 235 1335 410