Intuitionistic fuzzy transportation problem using sign. Intuitionistic fuzzy number and its arithmetic operation with application on system failure g. In this paper we have discussed about the transportation problem and solve some numerical examples of transportation problem in triangular fuzzy number, intuitionistic fuzzy number, triangular intuitionistic fuzzy number by using. Solving multi objective linear programming problems using. The assignment problem ap is a special type of linear programming problem in which the objective is to assign origins to destinations at a minimum cost or maximum pro t in a one to one. Solving hexagonal intuitionistic fuzzy fractional transportation.
International journal of computational intelligence systems. Fuzzy optimal solution to fuzzy transportation problem. Hussain and kumar 27 28 29 and nagoor gani and abbas 24 proposed a method for solving intuitionistic fuzzy transportation problem. Intuitionistic fuzzy methods are proposed to find starting basic feasible. A novel ranking approach to solving fully lrintuitionistic fuzzy. To the extent of our knowledge, there is no method in fuzzy environment to solving the fully lrintuitionistic fuzzy transportation problems lriftps in which all. Senthil kumar method for finding an intuitionistic fuzzy optimal solution for fully intuitionistic fuzzy transportation problem fiftp is extended to solve the mixed and type4 ifstp. The fuzzy numbers and fuzzy values are widely used in engineering applications. E cient algorithms have been established for solving the transportation problem where the cost coe cients. Jan 01, 2016 in general, fuzzy numbers are used to study the transportation problem.
A novel algorithm for solving intuitionistic fuzzy transportation problem via new ranking method shashi aggarwal, chavi gupta received 27 february 2014. Pdf in this research article, we used the triangular intuitionistic fuzzy numbers. The concept of intuitionistic fuzzy sets ifss proposed by atanassov1 in. In section 4, we propose a new algorithm to find the initial fuzzy feasible solution for the given fuzzy transportation problem and obtained the fuzzy optimal solution. In section 3, we introduce the fuzzy transportation problem with triangular fuzzy numbers and related results. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy. Santhi 2 1research scholar, department of mathematics, ngm college, pollachi, india642001 2assistant professor, department of mathematics, ngm college, pollachi, india642001 abstract. Sep 20, 2014 in solving real life transportation problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. In section 6, we give the revised distribution algorithm to solve the intuitionistic fuzzy transportation problem. Jana and roy 11 studied the multi objective intuitionistic fuzzy linear programming problem and applied it to transportation problem. 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 scope. An approach to solve unbalanced intuitionisitic fuzzy. New approach for solving intuitionistic fuzzy multiobjective. Let i ai be the quality of commodity available at origin i.
Novel arithmetic operations on type2 intuitionistic fuzzy and its applications to transportation problem. Pdf a new approach for solving intuitionistic fuzzy. Transportation problem with triangular mixed intutionistic. Solving hexagonal intuitionistic fuzzy fractional transportation problem using ranking and russells method. The main objective of this paper is to i ntroduce an intuitionistic fuzzy transportation pro blem with hexagonal intuitionistic fuzzy. Pdf solving intuitionistic fuzzy transportation problem using zero. Algorithmic approach for solving intuitionistic fuzzy transportation. Due to storage constraints destinations are unable to receive the quantity in excess of their minimum demand. Kumuthavalli2 1department of mathematics, sri ramalinga sowdambigai college of science and commerce, coimbatore641 109, tamil nadu, india, m. Revised distribution method for intuitionistic fuzzy transportation problem 97 in section 4, we explain the method of ranking for tifns with example.
A is a continuous mapping from r to the closed interval 0,1 and. Singh and yadav 37 applied an interesting methodology in solving a tp having uncertainty as well as hesitation in prediction of the transportation costs. Mixed intuitionistic fuzzy bcm is used to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. Linear programming approach for solving balanced and. For the first time, this paper attempts to introduce the mathematical representation of a transportation problem in neutrosophic environment. Optimal solution of an intuitionistic fuzzy transportation problem. Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets, and intuitionistic fuzzy sets to represent uncertain, inconsistent, and incomplete information about a real world problem. It is shown that the proposed ranking method for lrintuitionistic fuzzy numbers satisfies the. Intuitionistic fuzzy number and its arithmetic operation with. Numerical examples are also provided to illustrate the proposed algorithm. In this paper, we investigate transportation problem in which supplies and demands are intuitionistic fuzzy numbers. A new method for solving intuitionistic fuzzy transportation. Both of the methods are used to solve the balanced and unbalanced intuitionistic fuzzy transportation problems.
Pdf on may 1, 2012, nagoor gani and others published solving intuitionistic fuzzy transportation problem using zero suffix algorithm find, read and cite all. Also, we find the optimal solution for intuitionistic fuzzy transportation problem using nanogonal intuitionistic fuzzy number. On intuitionistic fuzzy transportation problem using hexagonal intuitionistic fuzzy numbers a. This article proposes a method for solving intuitionistic fuzzy solid transportation problems ifstps in which only the transportation costs are represented in terms of intuitionistic fuzzy numbers ifns. Transportation problem with nanogonal intuitionistic fuzzy. Pdf a method for solving unbalanced intuitionistic fuzzy. We used real, fuzzy and intuitionistic fuzzy numbers are employed to get the optimal solution. The membership and nonmembership function of ai is of the following form. The degree of satisfaction of the objective function and the constraints is maximized to find the optimal solution. Intuitionistic fuzzy transportation problem in which the transportation costs, supply and demand quantities are intuitionistic fuzzy quantities.
The aim of fuzzy transportation is to find the leasttransportation cost of some commodities through anetwork when the supply and demand ofnodes and the. Similarity measures of intuitionistic fuzzy transportation. A navel method for solving fuzzy transportation problem. Having started in 1995, notes on intuitionistic fuzzy sets is the first and one of the leading scientific journals, exclusively. The objective of the iftp is to determine the shipping schedule that minimizes the total fuzzy transportation cost. One defines a tp having intuitionistic fuzzy transportation costs but crisp availabilities and demands as an intuitionistic fuzzy balanced transportation problem of type2 ifbtp2.
Research article a new approach for optimization of real. Pdf optimal solution solved by triangular intuitionistic. The notions of intuitionistic fuzzy set ifs and intuitionistic lfuzzy sets ilfs were introduced in 1, 21 and 3, respectively, as a generalization of the notion of. In intuitionistic fuzzy transportation problem, the quantities are reduced into an integer using the ranking method called accuracy function. Solving intuitionistic fuzzy transportation problem using. Pdf the transportation problem in an intuitionistic fuzzy. Description of a classical transportation problem can be given as follows. Introduction the transportation problem is the special type of linear programming problem where special mathematical structure of restrictions is used.
Numerical examples show that an intuitionistic fuzzy ranking method offers an effective tool for handling an intuitionistic fuzzy assignment problem. Santhi 2 1research scholar, department of mathematics, ngm college, pollachi, india642001 2assistant professor, department of mathematics, ngm. To illustrate the applicability and suitability of the proposed ranking method and to deal with ambiguity and imprecision, one of the vital mathematical programming problem viz. This paper develops an approach to solve the unbalanced transportation problem where as all the parameters are not in deterministic numbers but imprecise. Pdf the transportation problem in an intuitionistic.
Application of extended fuzzy programming technique to a. A new method has been proposed to compute initial basic feasible solution for the. Expected value of intuitionistic fuzzy number and its. Triangular intuitionistic fuzzy numbers, intuitionistic fuzzy. A method for solving intuitionistic fuzzy assignment. The arc lengths are considered as uncertain and are characterized by triangular intuitionistic fuzzy numbers. Introduction the theory of fuzzy set introduced by zadeh8 in 1965 has achieved successful applications in various fields. Notes on intuitionistic fuzzy sets from ifigenia, the wiki. Sukna, siliguri734009 darjeeling, west bengal, india 2 department of mathematics, bengal engineering and science university, shibpur. The main objective of this paper is to introduce an intuitionistic fuzzy transportation problem with hexagonal intuitionistic fuzzy. The fully fuzzy transportation problem is a transportation problem in which parameters of cost, supply and demand are fuzzy values.
It is shown that the proposed ranking method for lr intuitionistic fuzzy numbers satisfies the general axioms of ranking functions. In this paper we introduce hexagonal intuitionistic fuzzy number with its membership and non membershi p functions. Intuitionistic fuzzy transportation problem consider a transportation with m origins rows and n destinations columns. E cient algorithms have been established for solving. Pdf on intuitionistic fuzzy transportation problem using. A new method for solving a multiobjective, multiitem intuitionistic fuzzy solid transportation problems for damageable items are proposed using expected value of intuitionistic fuzzy numbers and several special cases have been derived from the proposed model. In this paper a new method is proposed for finding a fuzzy optimal solution of fuzzy transportation problem. Different types of real, fuzzy, and intuitionistic fuzzy numbers.
Chapter 0 introduction some problems in intuitionistic. Roy2 1 department of mathematics, siliguri institute of technology, p. Triangular intuitionistic fuzzy numbers, intuitionistic fuzzy transportation problem, intuitionistic fuzzy zero point method, optimal solution. Here we investigate a more realistic problem, namely intuitionistic fuzzy assignm of assigning the jth job to the ith machine. Intuitionistic fuzzy set, triangular intuitionistic fuzzy number, unbalanced intuition istic fuzzy transportation problem, psk method, optimal solution. This paper presents a solution for fractional transportation problem in an intuitionistic fuzzy environment in which cost are.
Any intuitionistic fuzzy feasible solution to a intuitionistic fuzzy transportation problem containing m. Kaur and kumar solved the fuzzy transportation problem with generalized trapezoidal fuzzy numbers. In this transportation problem, costs are represented by gtrifns. An algorithm is proposed to evaluate the initial basic feasible and optimal solution of intuitionistic fuzzy transportation problem. Though, many researchers worked on transportation problem in fuzzy environment, it was oheigeartaigh 11 who proposed a method to solve the fuzzy transportation problem with triangular fuzzy demand and supply. New approach for solving intuitionistic fuzzy multi. Proposed method 1 is based on linear programming technique and proposed method 2 is based on modified distribution method. Also we consider transportation problem in intuitionistic fuzzy environment. In this article, fully fuzzy transportation problem is extended to fully intuitionistic fuzzy transportation problem. An efficient computational approach for solving type2 intuitionistic fuzzy numbers based transportation problems. We assume that one machine can be assigned exactly one job also each machine can do at most one job. We present a brief overview on intuitionistic fuzzy sets which cuts across some definitions, operations, algebra, modal operators and normalization on intuitionistic fuzzy set.
The expected value of intuitionistic fuzzy number using credibility measures has been developed here. Intuitionistic fuzzy two stage multiobjective transportation. Neutrosophic sets have been introduced as a generalization of crisp sets, fuzzy sets and intuitionistic fuzzy sets to represent uncertain, inconsistent and incomplete information about a real world problem. On intuitionistic fuzzy transportation problem using. In this paper, a new ranking method for generalized trapezoidal intuitionistic fuzzy number gtrifn is introduced to overcome the. One of the methods uses intuitionistic fuzzy programming technique together with the three different membership functionslinear, exponential and hyperbolic and the other method uses crisp linear. Algorithmic approach for solving intuitionistic fuzzy. In this paper we introduce hexagonal intuitionistic fuzzy number with its membership and non membership functions.
Nagoor gani and others published a new method on solving intuitionistic fuzzy transportation problem find, read and. A novel algorithm for solving intuitionistic fuzzy. In this article, two methods are presented, proposed method 1 and proposed method 2. To deal with uncertainty and hesitation many authors have suggested the intuitionistic fuzzy representation for the data. Proposed method 1 is based on linear programming technique and proposed. In this paper, a novel ranking function is proposed to finding an optimal solution of fully lr intuitionistic fuzzy transportation problem by using the distance minimizer of two lrifns. A novel approach for solving fully intuitionistic fuzzy.
On fully intuitionistic fuzzy multiobjective transportation problems using different membership functions, annals of operations research, 2019, pp. A novel approach for solving fully intuitionistic fuzzy transportation problem a novel approach for solving fully intuitionistic fuzzy transportation problem 20160101 00. Solving intuitionistic fuzzy solid transportation problem. In this paper, a novel ranking function is proposed to finding an optimal solution of fully lrintuitionistic fuzzy transportation problem by using the distance minimizer of two lrifns. Hence, the fuzzy and intuitionistic fuzzy transportation problem were formulated and solved by many researchers. A novel ranking approach to solving fully lrintuitionistic. In section 5, we define a intuitionistic fuzzy transportation problem. The notions of intuitionistic fuzzy set ifs and intuitionistic l fuzzy sets ilfs were introduced in 1, 21 and 3, respectively, as a generalization of the notion of fuzzy set fs. In this work intuitionistic trapezoidal fuzzy numbers itfns are employed to represent the transportation cost. A method for solving intuitionistic fuzzy assignment problem.
At the end, using north west corner method we are to calculate the feasible solution of the them and then continue to use the rest of the transportation simplex method in order to achieve the optimal solution. Revised distribution method for intuitionistic fuzzy. Intuitionistic fuzzy number, intuitionistic fuzzy transportation problem 1. An efficient computational approach for solving type2. In the reduced iftp, identify the row and column difference considering the least two numbers of the respective row and column. In conventional transportation problem tp, supplies, demands and costs are always certain. A fuzzy transportation problem is a transportation problem in which the transportation costs, supply and demand are fuzzy quantities. We formulate the transportation problem in which costs, supplies and demands all are triangular intuitionistic fuzzy numbers. In solving real life transportation problem, we often face the state of uncertainty as well as hesitation due to various uncontrollable factors. Nagoor gani and others published a new method on solving intuitionistic fuzzy transportation problem find, read and cite all the research you need on researchgate. Intuitionistic fuzzy transportation problem 59 of ai ii. The real life transportation problems tp face a lot of problems due to uncertainties and lack of precise data. Linear programming approach for solving balanced and unbalanced intuitionistic fuzzy transportation problems.
Fuzzytransportation problem, intuionistic fuzzy number, optimal solution. In this paper, we formulate a transportation problem in which costs are triangular intuitionistic fuzzy numbers. Intuitionisticfuzzysetspast,presentandfuture krassimirt. A new approach for optimization of real life transportation. Optimal solution for intuitionistic fuzzy transportation. Similarity measures of intuitionistic fuzzy transportation problem m.
Revised 17 april 2014 accepted 16 may 2014 abstract. Introduction a transportation problem is one of the earliest and most important applications of linear programming problem. The present paper focuses on the two methods for solving intuitionistic fuzzy tp. Algorithm for solving intuitionistic fuzzy transportation. Intuitionistic fuzzy set, fuzzy set, modal operator necessity, possibility, topological operator interior, closure. Solid transportation problem stp is formulated in intuitionistic fuzzy environment. Fully fuzzy transportation problem 43 solving the multipleobjective problem. A method for solving unbalanced intuitionistic fuzzy transportation.
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