An intuitionistic fuzzy number c is a special intuitionistic fuzzy set on the set of real numbers, where the membership function. Arithmetic operations of proposed ifn are evaluated. The existing shortcomings are overcome by proposing a new possibility degree measure for ifns. In the present paper, we define an improved possibility degree method to rank the different intuitionistic fuzzy numbers ifns. Trapezoidal intuitionistic fuzzy number now, the centroid point has been determined by using g l. Later it was generalized to intuitionistic fuzzy number by burillo et al. It has got many applications 5,6 in information science, decision making problems, medical diagnosis, and system failure and pattern recognition. It has been applied to solve many real world problems. Afterwards, a novel theory, named intuitionistic fuzzy set theory, was suggested by atanassov 1986. A ranking method of triangular intuitionistic fuzzy. Most of the methods proposed so far are nondiscriminating and counterintuitive.
Using trapezoidal intuitionistic fuzzy number to find. Cosine similarity measure between hybrid intuitionistic. Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof. Ranking intuitionistic fuzzy numbers plays an important role in decision making and. In particular, systems of intuitionistic logic do not include the law of the excluded middle and double negation elimination, which are fundamental inference rules in. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers.
The membership and non membership functions of are in the following form x where, are functions from r 0,1. Intuitionistic fuzzy number and its arithmetic operation with. Also we introduce the intuitionistic fuzzy optimization problem by application of the membership and nonmembership functions. Ivifns have huge amount of application in decision making processes 12,19,22,28. Intuitionistic fuzzy number and its arithmetic operation. Nehi, and maleki 2005 proposed intuitionistic trapezoidal fuzzy numbers which are the extension of intuitionistic triangular fuzzy numbers. Wang 11 gave the definition of trapezoidal intuitionistic fuzzy number which is an extension of triangular intuitionistic fuzzy number. However, we lack effective methods for ranking intuitionistic fuzzy.
Intuitionistic fuzzy twosided matching model and its. A new method for ranking of intuitionistic fuzzy numbers. Many methods have been proposed for ranking of intuitionistic fuzzy numbers. He is best known for introducing the concepts of generalized nets and intuitionistic fuzzy sets, which are extensions of the concepts of petri nets and fuzzy sets, respectively. Ranking of intuitionistic fuzzy number by centroid point. Intervalvalued intuitionistic trapezoidal fuzzy number and its application junhong li1. Fuzzy numbers intuitionistic fuzzy descriptor systems will be a new research direction, and will become a universal method to solve practical problems. We say, is an intuitionistic fuzzy number throughout this paper, where the function. These values are defined by the integral of the inverse fuzzy membership and non.
Possibility degree of intervalvalued intuitionistic fuzzy. Here intuitionistic fuzzy number ifn is presented according to the approach of presentation of fuzzy number. Roy2 1 department of mathematics, siliguri institute of technology, p. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation. A value and ambiguitybased ranking method of trapezoidal. Ranking of intuitionistic fuzzy numbers is a difficult task. In this paper i will introduce the trapezoidal intuitionistic fuzzy numbers if numbers and will prove some operations for them. Power average operators of trapezoidal intuitionistic. Also i am going to propose a new ordering method for if numbers in which i will consider two characteristic values of membership and nonmembership functions for an if number. Some arithmetic operations on triangular intuitionistic. Pdf a new generalized intuitionistic fuzzy number researchgate. Let and with be two intuitionistic trapezoidal fuzzy numbers. Power average operators of trapezoidal intuitionistic fuzzy numbers and application to multiattribute group decision making. Linguistic variables are used for system input and output, and are represented by words such as.
Operations on intuitionistic trapezoidal fuzzy numbers. Ranking of fuzzy numbers have started in early seventies in the last century and a complete ranking on the class of. Sukna, siliguri734009 darjeeling, west bengal, india 2 department of mathematics, bengal engineering and science university, shibpur. An intuitionistic fuzzybased dematel to rank risks of. Ranking fuzzy numbers with a distance method using. Addition of two trapezoidal intuitionistic fuzzy numbers jianqiang and zhong, 2009. Triangular intuitionistic fuzzy number tifn and trapezoidal intuitionistic fuzzy number trifn are defined, and their arithmetic operations based on intuitoinistic. Various methods have been developed to solve multiattribute decisionmaking madm problems with fuzzy numbers 3. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. Further developments of ifs theory, including intuitionistic fuzzy geometry, intuitionistic fuzzy. There are a large number of literatures on intuitionistic fuzzy sets and intuitionistic fuzzy numbers and their applications see. Szmidt and kacpryzk introduced the hamming distance between intuitionistic fuzzy sets and proposed a similarity measure based on the distance. Possibility degree method for ranking intuitionistic fuzzy. As a generalization of the concept of fuzzy set, intuitionistic fuzzy sets were introduced by atanassov.
Intuitionistic fuzzy twosided matching model and its application to personnelposition matching problems. The concept of fuzzy numbers, introduced by dubois and prade 1, has received a great deal of attention due to its capability of representing fuzzy opinions 2. In last few years, di erent methods for ranking ifns have been introduced79,10,12,23. Intuitionistic fuzzy number and its arithmetic operation with application on system failure g. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept.
Ranking of intuitionistic fuzzy numbers by new distance. Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. Fuzzy number intuitionistic fuzzy arithmetic aggregation. Xu 2007 proposed score function and accuracy function to rank interval valued intuitionistic fuzzy numbers. Section 2 presents basic concept of intuitionistic fuzzy sets and intuitionistic fuzzy number. Intuitionisticfuzzysetspast,presentandfuture krassimirt. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number.
Ranking of triangular intuitionistic fuzzy numbers mdpi. Ranking of intuitionistic fuzzy numbers ieee xplore. It is obvious that any fuzzy number u can be represented as an intuitionisticfuzzy number by,1. A trapezoidal intuitionistic fuzzy number withparameters, 1 1 2 2,isdenotedas, 1, 2,, 1, 2,inthesetofrealnumbersris. The problems of containing incomplete informations can be modelled more accurately using intuitionistic fuzzy sets than fuzzy sets. Intervalvalued intuitionistic trapezoidal fuzzy number. Ranking method of trapezoidal intuitionistic fuzzy numbers. A new prospect projection multicriteria decisionmaking. The intuitionistic fuzzy set is the generalization of the fuzzy set, and the intuitionistic fuzzy number is the particular case of intuitionistic fuzzy set in this paper. Intuitionistic fuzzy linear system ifls, intuitionistic fuzzy number ifn, trapezoidal intuitionistic fuzzy number trifn, strong and weak solutions. Pdf method for solving the transportation problem using. Research article using trapezoidal intuitionistic fuzzy. Intuitionistic fuzzy number ifn 46 is a special case of. Arithmetic operations and cut sets on intuitionistic fuzzy number the arithmetic operations on intuitionistic fuzzy number.
Trapezoidal intuitionistic fuzzy numbers trifns are special cases of ifss defined on the set of real numbers, which may deal with more illknown quantities. A ranking function, where is set of all fuzzy numbers defined on set of real numbers and maps each fuzzy number into a real number. Fuzzy numbers intuitionistic fuzzy descriptor systems. An approximation method of intuitionistic fuzzy numbers. Arithmetic operations and cut sets over trifns are investigated.
Since the fuzzy set theory was introduced by zadeh, fuzzy set theory has been used widely in various fields. Abstract ranking of intuitionistic fuzzy numbers is a dif. Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. Forconvenience,wedenotean intuitionistic fuzzy number by. A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. Solving multiobjective intuitionistic linear programming. Trapezoidaltriangular intuitionistic fuzzy numbers versus.
A method for multiattribute group decisionmaking with. Systems of linear equations have so many applications in various fields of mathematical, physical and engineering sciences such as traffic flow, circuit analysis. Mitchell 9 considered the problem of ranking a set of intuitionistic fuzzy numbers to define a. A new approach for ranking of intuitionistic fuzzy numbers. Considering the risk attitude of the decision maker, we transform intervalvalued intuitionistic fuzzy numbers into real numbers via a prospect value function and consequently derive the prospect decision matrices. Introduction internet has become a platform for companies in the travel and tourism industry to bring. Intuitionistic fuzzy number, if the following conditions hold, there exists m r suct that m 0. Complete ranking of intuitionistic fuzzy numbers sciencedirect.
Fuzzy numbers intuitionistic fuzzy descriptor systems can be better used to solve the problems of actual nonlinear control. Also arithmetic operations 7,9 were defined for intuitionistic fuzzy numbers. Pdf the notion of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy sense. The aim of this paper is to develop a method for ranking trapezoidal intuitionistic fuzzy numbers trifns in the process of decision making in the intuitionistic fuzzy environment. Linsome induced aggregating operators with fuzzy number intuitionistic fuzzy. On the front of ranking intuitionistic fuzzy numbers, some work has been reported in the literature. To achieve it, we first present some shortcomings of the existing possibility degree method and score function of ifns. International journal of computational intelligence systems.
In section 3, operations including exponentiation, logarithms and n th root of trapezoidal intuitionistic fuzzy number. Intuitionistic fuzzy sets,triangular intuitionistic fuzzy number,membership and nonmembership,value,ambiguity and score value. An approach for evaluating website quality in hotel. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. Zadeh 11 and the theory of intuitionistic fuzzy set introduced by atanassov 710. Pdf ranking of trapezoidal intuitionistic fuzzy numbers. A study on ranking of trapezoidal intuitionistic fuzzy numbers. Abstract in this paper, magnitude of membership function and nonmembership function of a trapezoidal intuition istic fuzzy number tifn are introduced. Pdf notes on triangular intuitionistic fuzzy numbers researchgate. Method for solving the transportation problem using triangular intuitionistic fuzzy number. Pdf ranking of intuitionistic fuzzy number by centroid. Intuitionistic fuzzy number, triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number. Generalized triangular fuzzy numbers in intuitionistic.
In many applications, ranking of intervalvalued intuitionistic fuzzy sets plays a vital role in decisionmaking, data analysis, artificial intelligence and socioeconomic system. Pdf techniques for ranking simple fuzzy numbers are abundant in nature. Linear programming is one of the most important operations research techniques. Intervalvalued intuitionistic fuzzy number uses membership degree and nonmember ship degree to express a decisionmakers hesitation, which make decisionmaker express hisher opinion in uncertainty decisionmaking environment easily.
To prove a similar result in the case of ivtfns and tifns, then in the case of. An application of fuzzy optimization techniques to linear. U x j, then the intervalvalued intuitionistic fuzzy set is reduced to intuitionistic fuzzy set. A new ranking method for intuitionistic fuzzy numbers. A ranking approach for intuitionistic fuzzy numbers and. However, there is no method which gives a satisfactory result to all situations. The main motivation of fuzzy numbers intuitionistic fuzzy sets is to unify the interval fuzzy number intuitionistic fuzzy sets into the traditional intuitionistic fuzzy sets in the form, so the real motivation of fuzzy numbers intuitionistic fuzzy descriptor systems is to unify type2 fuzzy descriptor systems into the traditional intuitionistic fuzzy descriptor systems in the form.
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