Intuitionistic fuzzy number, triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number. Triangular intuitionistic fuzzy numbers tifns are a special case of intuitionistic fuzzy sets. Calculate the location index number and fuzziness in dex functions for tif number and represent the tifn using this bot h. A new ranking method for triangular intuitionistic fuzzy. Introduction in this paper, we proposed a new network approach that can obtain the triangular intuitionistic fuzzy number. The validity of the proposed method was shown by comparing existing ranking methods in the literature. College for women autonomous, nagapattinam 611001, tamilnadu, india. Uthra 2 1 research scholar, bharathiar university assistant professor, dept. The aim of this paper is to introduce the concept of a triangular ifn tifn as a special case of the ifn and develop a new methodology for ranking tifns. Project scheduling method using triangular intuitionistic. Ranking trapezoidal intuitionistic fuzzy numbers trifns is more difficult due to the fact that the trifns are a generalization of the fuzzy numbers. In this paper, two different algorithms are presented to obtain the critical path in a fuzzy network, where the edge weights are taken as triangular intuitionistic fuzzy numbers and. Arithmetic operations and cut sets over tifns are investigated. Method for solving the transportation problem using triangular intuitionistic fuzzy number.
Recently few methods for ranking ifns has also been introduced 29,33,36,41,49. Intuitionistic fuzzy number, if the following conditions hold, there exists m r suct that m 0. An intuitionistic fuzzy set such that and, where for all, are fuzzy numbers called intuitionistic fuzzy numbers. Intuitionistic fuzzy numbers and its applications in fuzzy.
In the present paper, we generalize the intuitionistic fuzzy if number to intervalvalued intuitionistic fuzzy number by defining interval membership and nonmembership functions instead of fixedvalued function and hence it will present uncertain situation better than if. The aim of this paper is to develop a methodology for solving matrix games with payoffs of triangular intuitionistic fuzzy numbers tifns. A trapezoidal intuitionistic fuzzy number, becomes a triangular intuitionistic fuzzy number by setting b c and hence parameters become a. Pdf the notion of triangular fuzzy number is put forward on the basis of intuitionistic fuzzy sense. Expressions for computing the fuzzy reliability of a series system, parallel system,seriesparallel and parallelseries system following triangular intuitionistic fuzzy numbers have been described. Membership and nonmembership function of triangular intuitionistic fuzzy number is a crisp interval and is defined as eiand. In 2009, fuzzy quantities and relations in multi objective flow problem were analyzed by mehdi ghatee and mehdi hashemi 7. Fuzzy number, intuitionistic fuzzy set, trapezoidal fuzzy number 1 introduction in our daily life moments, we frequently deal with. A solution is also given to demonstrate our proposed approach. A novel arithmetic technique for generalized interval. Triangular intuitionistic fuzzy numbers are used to represent activity times in the project network and we propose an algorithm for finding critical path. Linear programming with triangular intuitionistic fuzzy number. An ifs in is an object having the form, where the and define the degree of membership and degree of nonmembership, respectively, of the element to the set, which is a subset of, for every element of. Under the scenario that criteria weights for alternatives are completely unknown, triangular intuitionistic fuzzy method can not only supplement the insufficiency of the method based on the distance but also endow more information to the estimation and.
A study on ranking of trapezoidal intuitionistic fuzzy numbers. A new generalized intuitionistic fuzzy sets in, is defined as an object of the form. Here two types of intuitionistic fuzzy sets, namely triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number is presented. Under the scenario that criteria weights for alternatives are completely unknown, triangular intuitionistic fuzzy method can not only supplement the insufficiency of the method based on the distance but also endow more. All the arithmetic operations are done by maxmin principle method which is nothing but the application of interval analysis. Definition 2 triangular intuitionistic fuzzy number. Nonlinear arithmetic operation on generalized triangular. Firstly, the score function and the accuracy function of triangular intuitionistic fuzzy number are given, the method for ranking triangular intuitionistic fuzzy numbers are developed. Ahp based on triangular intuitionistic fuzzy number and its.
Ahp based on triangular intuitionistic fuzzy number and. System of differential equation with initial value as triangular intuitionistic fuzzy number and its application is solved by mondal and roy 30. Triangular intuitionistic fuzzy number tifn is a more generalized platform for expressing imprecise, incomplete, and inconsistent information when solving multicriteria decisionmaking problems, as well as for expressing and re. Expressions for computing the fuzzy reliability of a. Ranking of intuitionistic fuzzy numbers by new distance. Intuitionistic fuzzy numbers and its applications in. The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Intuitionistic fuzzy arithmetic, triangular intuitionistic fuzzy number tifn, intuitionistic fuzzy multi. Ranking of intuitionistic fuzzy numbers by new distance measure. The notion of fuzzy numbers was introduced by dubois and prade 3.
A new ranking method based on incircle of intuitionistic fuzzy number for triangular intuitionistic fuzzy number was proposed. Pdf generalized triangular fuzzy numbers in intuitionistic. In this section we recall some basic notions on trapezoidal and triangular intuitionistic fuzzy numbers. Ranking of intuitionistic fuzzy numbers by new distance measure debaroti das1,p. A ratio ranking method of triangular intuitionistic fuzzy. Solving triangular intuitionistic fuzzy matrix game by. Intuitionistic fuzzy numbers and its applications in fuzzy optimization problem.
Solving multiobjective intuitionistic linear programming using triangular intuitionistic fuzzy number. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic. Triangular intuitionistic fuzzy numbers tifns are special ifns and are important for fuzzy multiattribute decision making madm problems, in that. Ranking of intuitionistic fuzzy numbers plays an important role in comparison. A method for multiattribute group decisionmaking with. Network, triangular intuitionistic fuzzy number, intuitionistic fuzzy critical. Ranking of triangular intuitionistic fuzzy numbers tifns is an important problem, which is solved by the value and ambiguity based ranking method developed in this paper. We also present that the arithmetic operation of two or more.
In this paper, two different algorithms are presented to obtain the critical path in a fuzzy network, where the edge weights are taken as triangular intuitionistic fuzzy numbers and triangular fuzzy numbers respectively. Fuzzy number, intuitionistic fuzzy set, trapezoidal fuzzy number 1 introduction. An approximation method of intuitionistic fuzzy numbers ios. Wang and zhang41 defined the trapezoidal intuitionistic fuzzy number trifn and gave. Here comparative judgments are taken in the form of triangular intuitionistic fuzzy number tifn. The definitions and operations of tifn given by nan, li and zhang are stated as follows. Scheduling method using triangular intuitionistic fuzzy. 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. The intuitionistic fuzzy set ifset has not been applied to matrix game problems yet since it was introduced by k. Ivifns have huge amount of application in decision making processes 12,19,22,28.
In the proposed paper we have considered a matrix game with payoff as triangular intuitionistic fuzzy number and a new ranking order has been proposed using value judgement index, available definitions and operations. Pdf a ranking method of triangular intuitionistic fuzzy numbers. This gives rise to fuzzy environment and hence we have fuzzy critical path method. We have introduced intuitionistic fuzzy number and its arithmetic operations based on extension principle of intuitionistic fuzzy sets. Using score function in a matrix game is very rare. An approach for evaluating website quality in hotel. Abstract this paper provides an algorithm for solving a multiobjective intuitionistic fuzzy linear programming problem with data as triangular intuitionistic fuzzy numbers. A lexicographic method for matrix games with payoffs of. First order non homogeneous ordinary differential equation.
A triangular fuzzy number is denoted by 3 tuples, where are real numbers and. A generalized triangular intuitionistic fuzzy geometric. A novel arithmetic technique for generalized intervalvalued. Based on these main results of the paper, the methods or procedures elaborated for intervalvalued trapezoidal or.
A ranking method of triangular intuitionistic fuzzy. Atanassov defined four basic distances between intuitionistic fuzzy sets. Pdf notes on triangular intuitionistic fuzzy numbers. Wang 11 gave the definition of trapezoidal intuitionistic fuzzy number which is an extension of triangular intuitionistic fuzzy number. Pdf ranking of intuitionistic fuzzy number by centroid. Intuitionistic fuzzy number and its arithmetic operation. Introduction internet has become a platform for companies in the travel and tourism industry to bring.
The concept of an intuitionistic fuzzy number ifn is of importance for quantifying an illknown quantity. In this paper we introduce the trapezoidal intuitionistic fuzzy numbers and prove some operation for them. Some arithmetic operations on triangular intuitionistic. Definition generalized intervalvalued triangular intuitionistic fuzzy number givtifn definition generalized intervalvalued trapezoidal intuitionistic fuzzy number givtrifn definition support of a givtifs definition height of a givtifs definition level set of givtifs definition the. Multicriteria decision making based on correlation. Also we introduce the intuitionistic fuzzy optimization problem by application of the membership and nonmembership functions.
Generalized triangular intuitionistic fuzzy geometric. We also define the nonlinear intuitionistic fuzzy function which is used for finding the values, ambiguities, and ranking of nonlinear intuitionistic fuzzy. Generalized triangular fuzzy numbers in intuitionistic. Nonlinear triangular intuitionistic fuzzy number and its. The concept of an intuitionistic fuzzy number ifn is of importance for quantifying an illknown quantity, and the ranking of ifns is a very difficult problem. Also arithmetic operations 7,9 were defined for intuitionistic fuzzy numbers. Triangular intuitionistic fuzzy number a triangular intuitionistic fuzzy number tifn i a is an intuitionistic fuzzy set in r with following membership function i a x and nonmembership function i a x 1 1 1 1 1 1 1 1 1 1. The elements of the comparison matrices are transformed into interval valued intuitionistic fuzzy number by using nearest weighted intuitionistic interval approximation nwiia which is introduced in this paper. First order homogeneous ordinary differential equation with initial value as triangular intuitionistic fuzzy number is described by mondal and roy 32. Wang 11 gave the definition of trapezoidal intuitionistic fuzzy number which is an extension of. Linear programming problem with intuitionistic fuzzy numbers. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. Hence, in this paper, we put forward a new model of a matrix game based on triangular intuitionistic fuzzy numbers.
Each numerical value in the domain is assigned a specific grade of membership. A triangular fuzzy number is denoted by 3 tuples, where are real numbers and with membership function defined as. Abstract a new method is proposed for finding the shortest path problem spp with triangular intuitionistic fuzzy numbers tifn, based on bellman dynamic programming algorithm. Mahapatra and roy 14 evaluate system reliability by considering reliability of components as triangular intuitionistic fuzzy number. In this paper we introduce the different arithmetic operations on nonlinear intuitionistic fuzzy number nifn. Aggregation operators on triangular intuitionistic fuzzy. Any fuzzy number can be thought of as a function whose domain is a specified set. A ranking method of triangular intuitionistic fuzzy numbers. Solving multiobjective intuitionistic linear programming. Intuitionistic fuzzy number and its arithmetic operation with. A study on intuitionistic fuzzy multi objective lpp into. Computation of shortest path in a fuzzy network using triangular intuitionistic fuzzy number. Pdf method for solving the transportation problem using.
Arithmetic operations on symmetric trapezoidal intuitionistic. We study a multicriteria fuzzy decisionmaking method based on weighted triangular intuitionistic fuzzy number correlation coefficients. Ranking trapezoidal intuitionistic fuzzy numbers trifns is more difficult due to the fact that the trifns are a. Some arithmetic operations on triangular intuitionistic fuzzy number 367 definition. Pdf notes on triangular intuitionistic fuzzy numbers researchgate.
Pdf ranking of triangular intuitionistic fuzzy numbers tifns is an important problem, which is solved by the value and ambiguity based ranking. Trapezoidaltriangular intuitionistic fuzzy numbers versus. Trapezoidaltriangular intuitionistic fuzzy numbers versus interval. An approach for evaluating website quality in hotel industry. A novel arithmetic technique for generalized intervalvalued triangular intuitionistic fuzzy numbers and its application in decision making. Nonlinear triangular intuitionistic fuzzy number and its application. International journal of pure and applied mathematics special issue. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multiattribute decision making madm problems, in which the attribute values are in the form of tifns and the weight preference information is incomplete. Solution of matrix game with triangular intuitionistic fuzzy. Flow distribution network with triangular intuitionistic. A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. An approximation method of intuitionistic fuzzy numbers. A new concept of score function has been developed to defuzzify the payoff matrix and solution of the matrix.
International journal of computational intelligence systems. It has got many applications 5,6 in information science, decision making problems, medical diagnosis, and system failure and pattern recognition. Ranking of intuitionistic fuzzy number by centroid point. Based on the operational laws, they developed a series of aggregation operators for imtf information. Definition generalized triangular intuitionistic fuzzy number gtifn the membership function of gtifn, where is defined as. There are a large number of literatures on intuitionistic fuzzy sets and intuitionistic fuzzy numbers and their applications see 2434. Solving critical path problem using triangular intuitionistic. Based on these main results of the paper, the methods or procedures elaborated for intervalvalued trapezoidal or triangular fuzzy numbers as input data can be easy transferred to the case of trapezoidal or triangular intuitionistic fuzzy numbers as input data. The comparison of these imprecise numbers needs to develop the ranking methods for intuitionistic fuzzy numbers. Some arithmetic operations on triangular intuitionistic fuzzy. At first triangular intuitionistic fuzzy number and their arithmetic operations are introduced. Abstractthe order relation of fuzzy number is important in decision making and optimization modeling, and ranking fuzzy numbers is difficult in nature.
888 575 1125 585 208 1346 1116 211 326 803 898 621 1372 937 723 391 1421 660 935 679 1042 1113 427 1360 443 1131 284 439 546 139 217 2 637 541 301 422 998 152 119