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