# triangular fuzzy numbers

## Top PDF triangular fuzzy numbers: ### ON FUZZY TRANSPORTATION PROBLEM USING TRIANGULAR FUZZY NUMBERS WITH MODIFIED REVISED SIMPLEX METHOD

In this paper, we present a Modified Revised Simplex Method for minimizing fuzzy transportation problem of a Triangular Fuzzy Numbers. In which the supplies and demands are triangular fuzzy numbers. A parametric approach is used to obtain a fuzzy basic feasible solution with the help of Revised Simplex Method. We get optimal solution of fuzzy transportation problem in which number of constraints equal to number of occupied cells. ### A Quadratic Programming with Triangular Fuzzy Numbers

Quadratic Programming (QP) is a mathematical modeling technique de- signed to optimize the usage of limited resources and has been widely applied to solve real world problems. In conventional quadratic programming model the parameters are known constants. However in many practical situations, it is not reasonable to require that the constraints or the objective function in quadratic programming problems be specified in precise, crisp terms. In such situations, it is desirable to use some type of Fuzzy Quadratic Programming (FQP) problem. In this paper a new approach is proposed to derive the fuzzy objective value of fuzzy quadratic programming problem, where the con- straints coefficients and the right-hand sides are all triangular fuzzy numbers. The proposed method is solved using MATLAB TM toolbox and the numerical ### A New Distance and Ranking Method for Triangular Fuzzy Numbers

Abstract. This study presents an approximate approach for ranking fuzzy triangular numbers based on the distance method of a fuzzy triangular number and its area. The total approximate is determined by convex combining of fuzzy triangular number’s relative and its area that based on decision maker’s optimistic perspectives. The proposed approach is simple in terms of computational efforts and is efficient in ranking a large quantity of fuzzy triangular numbers. By a group of examples in  demonstrate the accuracy and applicability of the proposed approach. Finally we construct a new ranking system for fuzzy triangular number which is very realistic and also matching our intuition as the crisp ranking system on R. ### Optimization of Fuzzy Assignment Model With Triangular Fuzzy Numbers Using Robust Ranking Technique

Robust ranking method has been used for rank- ing the fuzzy numbers. The Hungarian (One’s assignment) method has been applied to solve the fuzzy assignment problem. An illustrative numerical example is provided to demonstrate the effectiveness of the fuzzy assignment prob- lems. ### Generalized Triangular Fuzzy Numbers In Intuitionistic Fuzzy Environment

In general, the theory of IFS is the generalization of fuzzy sets. Therefore it is expected that, IFS could be used to stimulate human decision-making process and any activities requiring human expertise and knowledge which are inevitably imprecise or not totally reliable. In this paper, we have introduced a more general definition of triangular fuzzy number in intuitionistic fuzzy environment such that the degree of satisfaction and rejection are so considered that the sum of both values is always less than one. Basic arithmetic operations and -cut sets are defined for this types of fuzzy numbers. Also a GTIFN is approximated to a nearest interval number by using cut sets. Finally, average ranking index is proposed to find inequality relations between two GTIFNs. This approach is very simple and easy to apply in real life problems. Next, we approximate a GTIFN to a nearest interval number. ### Hermite Interpolation with Triangular Fuzzy Numbers

Abstract. In this paper the polynomial interpolation of triangular fuzzy number is discussed. First general form of the polynomial with fuzzy coefficients is proposed. The hermite interpolation method is studied with triangular fuzzy number an example is provided to illustrate the algorithm. ### A study on adjoint of type 2 triangular fuzzy matrices

(2013) presented some types and properties of type-2 triangular fuzzy matrices. The paper 2 of this paper, we recall the definition of type-2 triangular fuzzy number and some 2 triangular fuzzy numbers. In section-3, we review the definition of type-2 triangular fuzzy matrices (T2TFM) -4, we define adjoint of T2TFMs. In section-5, we derive some more special properties 6, relevant numerical examples are presented. Finally in section ### MULTI LEVEL GROUP KEY MANAGEMENT TECHNIQUE FOR MULTICAST SECURITY IN MANET

In this research, we develop a set of Fuzzy Intention Product Design System. The system is capable of breaking the restrictions of time and space. Through the Fuzzy Analytic Hierarchy Process (FAHP), the triangular fuzzy numbers are put into the Pairwise Comparison Matrix to prevent the fuzzy problems during the process of conducting criteria measurement and judgment. By means of FAHP, the AHP Exact Value will be substituted by the Interval Value. And the experts will make strategic decisions with humanity when evaluating problems and give a weight value to the measure factors. ### Analysis of Priority Queuing Models: L - R Method

Abstract. Priority queuing models have a wide range of application in computer network system. In this paper the performance measures of fuzzy priority queuing model are computed using L- R method. L -R method is convenient and flexible compared to other methods. Numerical illustration is given to check the validity of the proposed method. Keywords: Fuzzy queue, priority discipline performance measure, L-R method and triangular fuzzy numbers. ### A STUDY OF THE APPLICATION OF FUZZY ANALYTICAL HIERARCHICAL PROCESS (FAHP) IN THE RANKING OF INDIAN BANKS

Once the hierarchy is established, the fuzzy pair wise comparison takes place. The experts compare all the criteria on the same level of the hierarchy. A pair wise comparison is performed by using Fuzzy linguistic terms in the scale of 0 – 10 described by the Triangular Fuzzy Numbers in the Table 1.1. In Buckley's method, the element of the negative judgment is treated as an inverse and reversed order of the fuzzy number of the corresponding positive judgment. Thus it requires not only a rigorous manipulation in the construction of reciprocal matrix but also due to transitivity the result becomes inconsistent. Again to reflect pessimistic, most likely and optimistic decision making environment, triangular fuzzy numbers with minimum value, most plausible value & maximum value are considered. ### TITLE -SUPPLIER SELECTION: FUZZY-AHP APPROACH

The conventional AHP method is incapable of handling the uncertainty and vagueness involved in the mapping of one’s preference to an exact number or ratio The major difficulty with classical AHP is its inability in mapping human judgments .In recent years it has been observed the due to confusion in decision makers mind probable deviations should be integrated to the decision making process in Fuzzy-AHP, pair wise comparisons are done using fuzzy linguistic preference scale. For simplicity the reciprocal fuzzy numbers are replaced by individual Triangular Fuzzy Numbers in the pair wise comparison matrix. ### Modified critical path method to solve networking problems under an intuitionistic fuzzy environment

A project is combination of interrelated activities which must be executed in a certain order before the entire task can be completed. An activity in a project is usually viewed as a job requiring time and resources for its completion. The Critical Path Method (CPM) plays a vital role in planning, scheduling and controlling the complex projects consisting of number of work contents. The successful implementation of CPM requires the availability of clear determined parameters (time duration, cost etc) for each activity. But in reality, due to uncertainty of information as well as the variation of management scenario, it is often difficult to obtain the exact activity time estimates. Under such situations it is highly impossible to formulate the mathematical model through the classical traditional methods. Therefore the fuzzy set theory proposed by Zadeh  can play a significant role in this kind of problems to handle the ambiguity about the time duration of deeds in a project network. Atanassov ,  extended the fuzzy sets to the theory intuitionistic fuzzy sets in which both the degree of belonging and degree of non-belonging are considered. Several authors such as Takahashi et al , Sophia Porchelvi and Sudha  to  Error! Reference source not found. , Kiran Yadav et al  and Nagoor Gani et al  have studied fuzzy Critical Path Method in Intuitionistic Fuzzy Environment. Sophia Porchelvi and Sudha have studied Intuitionistic Fuzzy Critical Path in a Network using a new ranking method. De. P.K and Amita Bhinchar ,  discussed fuzzy critical path analysis by a ranking method. Jayagowri and Geetharamani  obtained intuitionistic fuzzy critical path by using metric distance ranking method. Elizabeth and Sujatha  presented two different algorithms to obtain the critical path in a fuzzy network problem involving triangular intuitionistic fuzzy numbers and triangular fuzzy numbers. ### Applications Of Fuzzy Number Mathematics

In this paper decagonal Fuzzy number has been newly introduced and the alpha cut operations of arithmetic function principles using addition, subtraction multiplication and division has been fully modified with some conditions and has been explained with numerical examples. In a particular case of the growth rate in bacteria which consists of ten points is difficult to solve using trapezoidal or triangular fuzzy numbers, therefore decagonal fuzzy numbers plays a vital role in solving the problem. It also helps us to solve many optimization problems in future which has ten parameters as in the above case. ### Solution Of Fuzzy Game Problem Using Triangular Fuzzy Number

Fuzzy Game has been applied in many fields such as Operations Research, Control Theory and Management Sciences etc. In this paper, we consider some operations of triangular fuzzy numbers and a solution of Fuzzy Game Problem with triangular fuzzy numbers. The Solution of such Fuzzy games with pure strategies by minimax-maximin principle is discussed. ### Abstract— Achieving an accomplished e-commerce

Abstract— Achieving an accomplished e-commerce depends on high quality websites which are preferred by prospective customers. Assessing e-commerce website quality can be considered as a multicriteria decision making problem because of its complex structure including qualitative and quantitative factors. In this study, we propose a new methodology based on fuzzy analytic hierarchy process. The proposed methodology enables multiple decision makers on evaluation and uses triangular fuzzy scale that includes both positive and negative fuzzy numbers. The methodology includes simple mathematical calculations, and it yields triangular fuzzy numbers of alternatives’ weights. At the last step, obtained alternatives’ weights are ranked by integral values method. In the empirical study, three e-commerce websites, which are the most famous in Turkey, are evaluated by the methodology. The findings of this study shows that proposed methodology can tackle the e-commerce website quality assessing, effectively. ### G-Numbers: Importance-Necessity Concept in Uncertain Environment

In this research, the linguistic variables such as triangular fuzzy numbers are used for the concepts of importance and necessity, and a new approach is proposed to enhance the decision maker’s ability to reduce ambiguity in decision issues. The results can illustrate the impact of taking into account the concept of necessity in the decision-making process. Notably, G-numbers can be a combination of various planning and decision-making issues. ### MULTI CRITERIA DECISION MAKING MODEL

Ranking of fuzzy numbers plays a very significant role in linguistic multi-criteria decision making problems. Several fuzzy ranking methods have been proposed since 1976. The linguistic terms are represented quantitatively using fuzzy sets and then fuzzy optimal alternative is calculated which gives the relative merit of each alternative. S. Abbasbandy and T.Hajjari  in 2009 proposed a new method based on the left and right spreads at some – levels and defined magnitude of fuzzy numbers. Ranking is done based on this magnitude. S. Abbasbandy and B. Asady  in 2006 proposed sign distance method by considering a fuzzy origin and then calculating distance with respect to the origin. If and is the origin, then distance is defined as ### A Comparative Study of Some Optimization Methods with the Best Candidate Method for Fuzzy Transportation Problem

In this work , the fuzzy transportation problems using interval valued triangular fuzzy numbers have been discussed the initial basic feasible solution of the same transportation problem is obtained by different methods such as North West Corner rule , North East Corner rule , Least cost Method and Best Candidate Method. ### A New Approach to find Total Float time and Critical Path in a fuzzy Project Network

The purpose of the critical path method (CPM) is to identify the critical activities in the critical path of an activity network. In the real world for many projects we have to use human judgment for estimating the duration of activities. However, the unknowns or vagueness about the time duration for activities in network planning, has led to the development of fuzzy CPM. A way to deal with this imprecise data is to employ the concept of fuzziness, where the vague activity times can be represented by fuzzy sets. In this paper a new method based on fuzzy theory is developed to solve the project scheduling problem under fuzzy environment. Assuming that the duration of activities are triangular fuzzy numbers, in this method we compute total float time of each activity and fuzzy critical path without computing forward and backward pass calculations. Through a numerical example, calculation steps in this method and the results are illustrated. Compare with other fuzzy critical method the proposed method is simple, fast and effective to find total float time of each activity and fuzzy critical path in a fuzzy project network. ### Transportation Problem with Triangular Mixed Intutionistic Fuzzy Numbers Solved By BCM

Abstract. In this paper, we formulate a transportation problem in which sources, destinations and costs are different types of fuzzy numbers. We used real, fuzzy and intuitionistic fuzzy numbers are employed to get the optimal solution. Mixed intuitionistic fuzzy BCM is used to find the optimal solution in terms of triangular intuitionistic fuzzy numbers. The method is illustrated by a numerical examples.