Chen and hwang 10 manuscript received april 15, 20. The main objective of this paper is to introduce an intuitionistic fuzzy transportation problem with hexagonal intuitionistic fuzzy number. Pdf on intuitionistic fuzzy transportation problem using. Complete ranking of intuitionistic fuzzy numbers sciencedirect. Arithmetic operations on symmetric trapezoidal intuitionistic fuzzy numbers r. Apr 17, 2019 the first one starts by laying the groundwork of fuzzy intuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. An ordering method for intuitionistic fuzzy numbers. There are a large number of literatures on intuitionistic fuzzy sets and intuitionistic fuzzy numbers and their applications see 2434. In this appendix, we go through some of the definitions necessary for our use of intuitionistic fuzzy numbers. Let and with be two intuitionistic trapezoidal fuzzy numbers. 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. Intuitionistic fuzzy measures download ebook pdf, epub. Nonlinear triangular intuitionistic fuzzy number and its.
Krassimir atanassov9 1983 as an extension of lotfi zadehs notion of fuzzy set7, which itself. Supplier risk assessment based on trapezoidal intuitionistic. In this paper we introduce hexagonal intuitionistic fuzzy number with its membership and non membershi p functions. However, uncertainty is always considered as a major obstacle for extracting. In last few years, di erent methods for ranking ifns have been introduced79,10,12,23. A new ranking method for intuitionistic fuzzy numbers. A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. Multiple attribute decisionmaking methods based on normal. Abstract in this paper, magnitude of membership function and non membership function of a trapezoidal intuition istic fuzzy number tifn are introduced. Pdf an ordering method for intuitionistic fuzzy numbers. The arithmetic operations on hexagonal intuitionistic fuzzy numbers are performed. Fuzzy number, intuitionistic fuzzy set, trapezoidal fuzzy number 1 introduction. Trapezoidal intuitionistic fuzzy numbers trifns is a special intuitionistic fuzzy set on a real number set.
In this paper we introduce the trapezoidal intuitionistic fuzzy numbers and prove some operation for them. Linear programming problem with intuitionistic fuzzy numbers. This enables us to define a fuzzy rank and a characteristic vagueness factor for each intuitionistic fuzzy number. A study on ranking of trapezoidal intuitionistic fuzzy numbers. Project scheduling method using triangular intuitionistic fuzzy numbers and. There exist a large amount of literature involving the ranking of fuzzy numbers 1,2,10,11,20 and decision. Later it was generalized to intuitionistic fuzzy number by burillo et al. A comparative study on interval arithmetic operations with. 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. To the best of our knowledge very few methods have been proposed in previous studies for comparing intuitionistic fuzzy if numbers. Ban and coroianu presented a method to obtain trapezoidal approximations of intuitionistic fuzzy numbers. 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. In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number nifn. Linear programming problem with triangular intuitionistic fuzzy numbers, proceedings of the national conference on frontiers in applied sciences and computer technology, nit, trichy, tamil nadu, india, pp.
Pdf techniques for ranking simple fuzzy numbers are abundant in nature. Improved possibility degree method for ranking intuitionistic. An approximation method of intuitionistic fuzzy numbers ios. Aggregation operators on triangular intuitionistic fuzzy. Intuitionistic logic can be understood as a weakening of classical logic, meaning that it is more conservative in what it allows a reasoner to infer, while not permitting any new inferences that could not be made under classical logic. International journal of computational intelligence systems. Trifns are useful to deal with illknown quantities in decision data and decision making problems themselves.
But there is no single approach that can be used to solve all kinds of problems because of the partial ordering defined on. A new type of intuitionistic fuzzy arithmetic operations for stifn have been proposed. A new approach 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. Roy2 1 department of mathematics, siliguri institute of technology, p.
Aggregation of intuitionistic fuzzy information has been studied by a few authors 23, 31, 32, 34, and aggregation operators are applied in multiattribute group decision making. New operators on triangular intuitionistic fuzzy numbers and their applications in system fault analysis. Possibility degree of intervalvalued intuitionistic fuzzy. Ranking of intuitionistic fuzzy numbers is a difficult task. Pdf complete ranking of intuitionistic fuzzy numbers. Pdf fuzzy number was introduced by dubois and prade 10 to handle imprecise numerical quantities. The present research work is a continuous study of 4. A new prospect projection multicriteria decisionmaking. In section 3, operations including exponentiation, logarithms and n th root of trapezoidal intuitionistic fuzzy number. An intuitionistic fuzzy set a in x is defined as an object of the form where the functions. Ranking of intuitionistic fuzzy numbers by new distance measure. Ranking of intuitionistic fuzzy numbers by new distance. The next covers fuzzy numbers and explains zadehs extension principle.
Intuitionistic fuzzy numbers and its applications in fuzzy. Intuitionistic fuzzy sets were first introduced by atanassov 1, 2 as a generalization of fuzzy sets. Intuitionistic fuzzy sets evolved from nonsatisfication of. The existing shortcomings are overcome by proposing a new possibility degree measure for ifns. The first one starts by laying the groundwork of fuzzyintuitionistic fuzzy sets, fuzzy hedges, and fuzzy relations. In the present paper, we define an improved possibility degree method to rank the different intuitionistic fuzzy numbers ifns. This book aims to be a comprehensive and accurate survey of stateofart research on intuitionistic fuzzy sets theory and could be considered a continuation and extension of the author. Pdf notes on triangular intuitionistic fuzzy numbers researchgate. Multicriteria decisionmaking approach based on atanassovs intuitionistic fuzzy sets with incomplete certain information on weights. In this paper we introduce hexagonal intuitionistic fuzzy number with its membership and non membership functions.
There are a large number of literatures on intuitionistic fuzzy sets and intuitionistic fuzzy numbers and their applications see. Section 2 is preliminaries to intuitionistic fuzzy set and intuitionistic fuzzy numbers needed for consequent sections. Rankingintuitionistic fuzzy numbers international journal. However, we lack effective methods for ranking intuitionistic fuzzy. Intuitionisticfuzzysetspast,presentandfuture krassimirt. Sukna, siliguri734009 darjeeling, west bengal, india 2 department of mathematics, bengal engineering and science university, shibpur. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. We adopt a statistical viewpoint and interpret each intuitionistic fuzzy number as an ensemble of ordinary fuzzy numbers. A ranking method of triangular intuitionistic fuzzy numbers. Software development in intuitionistic fuzzy relational calculus. Power average operators of trapezoidal intuitionistic fuzzy. All the arithmetic operations are done by maxmin principle method which is nothing but the application of interval analysis. The comparison between some intervalvalued intuitionistic fuzzy numbers can not be undertaken because of its limitation.
To achieve it, we first present some shortcomings of the existing possibility degree method and score function of ifns. Pdf a new generalized intuitionistic fuzzy number researchgate. Intuitionistic fuzzy sets from ifigenia, the wiki for. Trifns are useful to deal with illknown quantities in decision. Malathi abstract in this paper, symmetric trapezoidal intuitionistic fuzzy numbers stifns have been introduced and their desirable properties are also studied. Further, several ranking methods have also been proposed to solve the ranking problems of ifns. Pdf the notion of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy sense.
Strategic studies are of high importance in every business administration. Pdf ranking of trapezoidal intuitionistic fuzzy numbers. Addition of two trapezoidal intuitionistic fuzzy numbers jianqiang and zhong, 2009. Some of them, like strengths, weaknesses, opportunities, threats swot, can be used widely. A pentagonal intuitionistic fuzzy number is defined as.
Pdf application of intuitionistic fuzzy numbers in swot. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept. Szmidt and kacpryzk introduced the hamming distance between intuitionistic fuzzy sets and proposed a similarity measure based on the distance. Also we introduce the intuitionistic fuzzy optimization problem by application of the membership and nonmembership functions. Many methods have been proposed for ranking of intuitionistic fuzzy numbers.
Transportation problem with nanogonal intuitionistic fuzzy. Where all are real numbers and its membership function, non membership function x are given by ii. Intuitionistic fuzzy sets have been introduced by krassimir atanassov 1983 as an extension of lotfi zadehs notion of fuzzy set, which itself extends the classical notion of a set. Total ordering for intuitionistic fuzzy numbers lakshmana. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition an element either belongs or does. Some limited methods have been presented concerning the ranking of ivif sets in literature. These values are defined by the integral of the inverse fuzzy membership and non. Ranking of intervalvalued intuitionistic fuzzy ivif numbers is a most popular and elegant work in the area of decisionmaking of several realworld problems. Each theorem of intuitionistic logic is a theorem in classical logic, but not conversely. Modified new operations for interval valued intuitionistic fuzzy numbers ivifns. Intuitionistic fuzzy number and its arithmetic operation with application on system failure g.
Using trapezoidal intuitionistic fuzzy number to find. Ranking intuitionistic fuzzy numbers plays an important role in decision making and. Ranking of intuitionistic fuzzy numbers ieee xplore. Notes on intuitionistic fuzzy sets is an international scientific journal, specialized in the theory and application of intuitionistic fuzzy sets and logics as an interdisciplinary field at the cross point between mathematics and engineering sciences. Some arithmetic operations on triangular intuitionistic fuzzy. But there is no single approach that can be used to solve all kinds of problems because of the partial ordering defined on the collection of intuitionistic fuzzy numbers ifns.
Ranking of fuzzy numbers have started in early seventies in the last century and a complete ranking on the class of. Pdf generalized triangular fuzzy numbers in intuitionistic. When lots of approximation and aggregation methods are given. Intuitionistic fuzzy number and its arithmetic operation with. Ranking of intuitionistic fuzzy number by centroid point. There exist a large amount of literature involving the ranking of fuzzy numbers1,2,10,11,20 and decision. Fuzzy numbers intuitionistic fuzzy descriptor systems. Notes on intuitionistic fuzzy sets from ifigenia, the wiki. The concept of fuzzy numbers and arithmetic operations with these numbers were first introduced and investigated by chang and zadeh 9 and others. Trapezoidaltriangular intuitionistic fuzzy numbers versus. Arithmetic operations on symmetric trapezoidal intuitionistic. This paper is organized as follows, in section 2, the representation of trapezoidal intuitionistic fuzzy numbers and. In this paper we consider the problem of ranking a set of intuitionistic fuzzy numbers. We present a brief overview on intuitionistic fuzzy sets which cuts across some definitions, operations, algebra, modal operators and normalization on intuitionistic fuzzy set.
Apr 10, 2018 in the present paper, we define an improved possibility degree method to rank the different intuitionistic fuzzy numbers ifns. To prove a similar result in the case of ivtfns and tifns, then in the case of. A new method for ranking of intuitionistic fuzzy numbers. Normal intuitionistic fuzzy numbers nifns, which combine the normal fuzzy number nfn with intuitionistic number, can easily express the stochastic fuzzy information existing in real decision making, and poweraverage pa operator can consider the relationships of different. Intuitionistic fuzzy number an intuitionistic fuzzy number i a is i.
Fuzzy numbers intuitionistic fuzzy descriptor systems will be a new research direction, and will become a universal method to solve practical problems. Fuzzy numbers intuitionistic fuzzy descriptor systems can be better used to solve the problems of actual nonlinear control. Operations on intuitionistic trapezoidal fuzzy numbers using. On intuitionistic fuzzy transportation problem using. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic fuzzy. 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. The main objective of this paper is to i ntroduce an intuitionistic fuzzy transportation pro blem with hexagonal intuitionistic fuzzy. Project scheduling method using triangular 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. A hexagonal intuitionistic fuzzy number is specified by. Intuitionistic fuzzy number and its arithmetic operation. A ranking approach for intuitionistic fuzzy numbers and.
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