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