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