A new ranking function of triangular fuzzy numbers for. Ranking generalized lr fuzzy numbers using area, mode. Pdf a ranking method of triangular intuitionistic fuzzy. Abstract ranking of intuitionistic fuzzy numbers is a dif. A new distance measure for trapezoidal fuzzy numbers. We analyze the ranking behaviors of all possible combinations of the decomposition and intersection of two fuzzy numbers through eight extensive test cases. The purpose is to elaborate fast and efficient algorithms dealing with.
Fuzzy transportation problem of triangular numbers with cut. Abstract this paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision. Since then, various procedures to rank fuzzy quantities are proposed by various researchers. Optimization of fuzzy assignment model with triangular. Request pdf a new ranking method for triangular intuitionistic fuzzy numbers a new ranking method based on incircle of intuitionistic fuzzy number for triangular intuitionistic fuzzy number. The purpose is to elaborate fast and efficient algorithms dealing with complicated operations and big data in fuzzy decisionmaking. New similarity of triangular fuzzy number and its application.
In this paper, a fuzzy triangular approximation using. Ranking generalized fuzzy numbers based on centroid and. Licomputersandmathematicswithapplications6020101557 1570 iteasilyfollowsfromeq. Ranking fuzzy numbers based on the areas on the left and the right. In, asady and zendehnam presented a method for ranking fuzzy numbers by distance minimization. Abirami and stephen8 developed a new approach on ranking lr type interval valued fuzzy numbers.
Since their inception in 1965, many authors have proposed different methods for ranking fuzzy numbers. International journal of computational intelligence systems. International journal of fuzzy logic systems ijfls vol. By using the centroid formula of triangle and rectangle we can calculate the ranking as. On the other hand, many fuzzy numbers ranking methods give the same order for fuzzy numbers in any level of managers risk taking. Package fuzzynumbers february 5, 2019 title tools to deal with fuzzy numbers type package description s4 classes and methods to deal with fuzzy numbers. New approach for ranking of trapezoidal fuzzy numbers for an arbitrary trapezoidal fuzzy number u x 0, y 0.
Ranking fuzzy numbers with a distance method using. Rajendran 10 compared fuzzy numbers using ranking function and verdegay 7 and maleki et. Main results ranking of triangular fuzzy number with distance method let all of fuzzy numbers be either positive or negative. Various approaches have been developed for ranking fu zzy numbers. Ranking of pentagonal fuzzy numbers applying incentre of. Pdf a new method for ranking triangular fuzzy numbers. Several methods for ranking fuzzy numbers have been widelydiscussed though most of them have shortcomings. Research article a new method for defuzzification and ranking. Pdf triangular approximations of fuzzy numbers using. This method ranks various types of fuzzy numbers which include normal, generalized trapezoidal, and triangular fuzzy numbers along with. The method of ranking fuzzy numbers was first proposed by jain 7, and there have been various methods. So we insert the risk taking factor rf to order fuzzy numbers and provide a reasonable range of fuzzy numbers comparison through wide levels of this factor.
In this paper we define triangular, trapezoidal, pentagonal, hexagonal and octagonal interval valued fuzzy numbers and develop new ranking technique on those fuzzy numbers which are more efficient. An approach for solving fuzzy transportation problem using. A characterization of a general class of ranking functions. In this work, a new ranking approach of triangular intuitionistic fuzzy numbers tifns is proposed and applied to solve multiattribute decision making madm problems. How different are ranking methods for fuzzy numbers. Many methods have been proposed for ranking of intuitionistic fuzzy numbers. We shall here briefly report table 6 with the spearman rank correlations for randomly generated triangular fuzzy numbers with the support in 0, 1.
Yagers ranking method has been used for ranking the fuzzy numbers. Ranking of intuitionistic fuzzy numbers plays an important role in comparison of intuitionistic fuzzy numbers decision making problems. Ranking fuzzy numbers are an important aspect of decision making in a fuzzy environment. The parametric form of a triangular fuzzy number is represented by a a a r a a r. The aim of this work is to present some aggregation operators with triangular intuitionistic fuzzy numbers and study their desirable properties. Firstly, i use a weighted average operator to introduce the risk preference of the decision maker dm, and construct the score and accuracy expected functions of tifn. In many applications, ranking of fuzzy numbers is an important and prerequisite procedure for decision makers. Representation and ranking of fuzzy numbers with heptagonal. Ranking generalized fuzzy numbers using centroid of centroids. Triangular fuzzy numbers one couldwonderwhether different results can be obtained if the fuzzy numbers considered in the studywere triangular.
In this paper, we will introduce a new approach for ranking of trapezoidal fuzzy numbers based on the left and the right spreads at some. An application of linguistic variables in assignment. Introduction a fuzzy transportation problem is a transportation problem in which the transportation cost, supply and demand quantities are fuzzy quantities. The fuzzy assignment problem has been transformed into a crisp one, using linguistic variables and solved by hungarian technique.
A new approach for ranking of trapezoidal fuzzy numbers. 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. A ranking method of triangular intuitionistic fuzzy numbers. Intuitionistic fuzzy number and its arithmetic operation. The advantage of the proposed approach is that it provides the correct ordering of the generalized and normal lr fuzzy numbers and it can rank all types of fuzzy numbers. Based on the above a methodology is adopted in solving the flpp with hexagonal fuzzy numbers. Aggregation operators on triangular intuitionistic fuzzy. A study on ranking of trapezoidal intuitionistic fuzzy numbers. Two ranking methods of single valued triangular neutrosophic. Fuzzy optimal solution to fuzzy transportation problem.
Ranking of octagonal intuitionistic fuzzy numbers g. Indeed, we show that for two arbitrary trapezoidal fuzzy numbers if the distance between centroid points and also the distance between left spreads and right. The valuation method considered was introduced initially by the yager and filev. A revised method for ranking generalized fuzzy numbers. Note on ranking fuzzy triangular numbers facchinetti. Comparison of different fuzzy set ranking methods required for. For a fuzzy number defined by definition 1, garcia and lamata proposed an index associated with the ranking as the convex combination, where is the area of the core of the fuzzy number which is equal to for a triangular fuzzy number defined by and the average value of the plateau in case of a trapezoidal fuzzy number given by, is the. A ranking method of triangular intuitionistic fuzzy. The similarity of triangular fuzzy numbers is an important metric for application of it. The validity of the proposed method was shown by comparing existing ranking methods in the literature.
A new ranking method based on incircle of intuitionistic fuzzy number for triangular intuitionistic fuzzy number was proposed. Here two types of intuitionistic fuzzy sets, namely triangular intuitionistic fuzzy number and trapezoidal intuitionistic fuzzy number is presented. A weighted ranking function for ranking triangular fuzzy numbers. In this paper we have ranked both trapezoidal intuitionistic fuzzy numbers and triangular intuitionistic fuzzy numbers using the centroid concept. Research article the intelligence of octagonal fuzzy number.
The proposed method is much simpler and more efficient than other methods in the literature. In 34 triangular fuzzy number neutrosophic weighted arithmetic averaging operator and triangular fuzzy number neutrosophic weighted geometric averaging operator are defined to aggregate triangular fuzzy number. A new method for trapezoidal fuzzy numbers ranking based. In this paper, a new method of ranking trapezoidal intuitionistic fuzzy numbers has been introduced based on the concept of value and ambiguity at different levels of decision. Fuzzy number, intuitionistic fuzzy set, ranking function, trapezoidal fuzzy number. In this paper we introduce octagonal intuitionistic fuzzy numbers with its membership and nonmembership functions. In this paper, a new form of nonnormal fuzzy number named.
Arithmetic operations and cut sets over tifns are investigated. The purpose is to elaborate fast and efficient algorithms dealing with complicated operations and big data. A new method for ranking triangular fuzzy numbers article pdf available in international journal of uncertainty fuzziness and knowledgebased systems 205. Ranking of intuitionistic fuzzy numbers by new distance. The ranking method studied is based upon the idea of associating with a fuzzy number a scalar value, its valuation, and using this valuation to compare and order fuzzy numbers. The assignment model is the special case of transportation where the number. Moreover, the metric properties of suggested distance measure are investigated.
In addition, if b c, then a is called a normal triangular fuzzy number and is denoted as a a, b, d. A new approach for ranking of intuitionistic fuzzy numbers. They allow for computing any arithmetic operations e. It can be noted that, based on propositions 11 and 12 and remark, the unified index fulfills the consistency property for ranking the fuzzy numbers and their partnered images. In case of intervalued intuitionistic fuzzy numbers ivifns lee 14 proposed a novel method for ranking of. D represents a relation matrix r 0 and it gives an approximate description. A triangular fuzzy number a is a fuzzy number with piecewise linear. Abstract in this paper, we propose a novel approach for ranking triangular intuitionistic fuzzy numbers tifns. A triangular fuzzy number is denoted by 3 tuples, where are real numbers and. This paper deals with the problem of ranking a set of alternatives, represented by triangular fuzzy numbers, in decision. Different ranking methods of fuzzy numbers maybe produce different ranking results, which can bring some difficulties for decision makers. A new distance and ranking method for triangular fuzzy numbers.
Though several methods for ranking of intuitionistic fuzzy numbers are available in literature but each of them has some limitations. However, there is no method which gives a satisfactory result to all situations. In this paper, we present a new method for ranking triangular fuzzy numbers based on their incenter and inradius. Several strategies have been proposed for ranking of fuzzy numbers. Pdf ranking triangular fuzzy numbers using fuzzy set. Thus utilizing the relative preference relation ranks fuzzy numbers easily and quickly, and is able to reserve fuzzy information. Ranking triangle and trapezoidal fuzzy numbers based on the.
Dengfeng li and jie yang china school of economics and management, fuzhou university, no. Representation and ranking of fuzzy numbers 43 remark 3. Note on ranking fuzzy triangular numbers facchinetti 1998. Pdf a ranking method of triangular intuitionistic fuzzy numbers. 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. Pdf ranking of intuitionistic fuzzy number by centroid. Ye26 also proposed a novel accuracy function to rank intervalvalued intuitionistic fuzzy numbers.
The ranking and comparing of fuzzy numbers have important practical uses, such as in risk analysis problems, decisionmaking, optimization, forecasting. More ranking methods can be found in literature as developed by kumar and kaur 20, zhang and yu 20, esmailzadeh and esmailzadeh 20 and papakostas. There exist several approaches to measure similarity of triangular fuzzy numbers. This paper aims to the discussion of properties for ranking fuzzy numbers. Ranking triangular fuzzy numbers using fuzzy set inclusion index. A ranking method of triangular intuitionistic fuzzy numbers and application to decision making. A ratio ranking method of triangular intuitionistic fuzzy. The existing methods of ranking fuzzy numbers and intuitionistic fuzzy number may be extended to svn numbers 10.
Pdf ranking of triangular intuitionistic fuzzy numbers tifns is an important problem, which is solved by the value and ambiguity based ranking. A trapezoidal intuitionistic fuzzy number with parameters is denoted as in the set of real numbers is an intuitionistic fuzzy number whose membership function and nonmembership function are given as if and in a trapezoidal intuitionistic fuzzy number, we have the triangular intuitionistic fuzzy numbers as special case of the trapezoidal intuitionistic fuzzy numbers. A new method for fuzzy critical path analysis in project. A new ranking method for triangular intuitionistic fuzzy numbers. But it is not always possible to restrict the membership function to either triangular or trapezoidal form. We also present that the arithmetic operation of two or more intuitionistic fuzzy number is again an intuitionistic fuzzy number. The objective of this paper is to introduce a new ranking function of triangular fuzzy numbers for solving fuzzy linear programming problems in objective function and find the optimal solution of it by big m method. 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. Jianqiang and zhong used both the score function and accuracy function to ranking trifns. Fd 2 of all triangular fuzzy number matrix over the set sand are determined from expert medical documentation. Ifn as an ensemble of ordinary fuzzy numbers and introduced a ranking method. Keywords triangular fuzzy number, fuzzy linear programming, interval arithmetic. Fully fuzzy critical path problem, ranking function, triangular fuzzy number msc 2010 no. A new method for trapezoidal fuzzy numbers ranking based on.
Each of these techniques have been shown to produce nonintuitive results in certain cases. So trifns play an important role in decision making and optimization modeling 24. A numerical example is given to illustrate the proposed method. Finally we construct a new ranking system for fuzzy triangular number which is very realistic and also matching our intuition as the crisp ranking. Optimization of fuzzy assignment model with triangular fuzzy numbers using robust ranking technique. A new ranking method for triangular intuitionistic fuzzy.
Hungarian method, robust ranking method, triangular numbers. Without less of generality, assume that all of the m are positive. In this paper, an original ranking operator is introduced for triangular fuzzy numbers. An approach of axiomatic type is followed providing the definition of two g.
Ranking method of trapezoidal intuitionistic fuzzy numbers. A fuzzy number is a convex normalized fuzzy set on the real line r such that there exist at least one x r with 1. The proposed method is much simpler and more efficient than other methods in. Li 29 defined the value index and the ambiguity index of triangular intuitionistic fuzzy numbers and developed a ratio ranking. Fuzzy transportation problem of triangular numbers with. The second stage proposes an extended ranking approach for generalized fuzzy numbers integrating the concepts of centroid point, rank index value, height of a fuzzy number, and the degree of the decision makers optimism.
Menaka assistant professor, department of mathematics, sri shakthi institute of engineering and technology, coimbatore, india abstract. We propose a new distance measure for the space of all trapezoidal fuzzy numbers using centroid point and leftright spread of trapezoidal fuzzy numbers. A novel approach for ranking triangular intuitionistic fuzzy. By defining a ranking to the hexagonal fuzzy numbers, it is possible to compare them and using this we convert the fuzzy valued transportation problem to a crisp valued transportation problem, which then can be solved using the matrix minima method. Abbasbandy and hajjari 1 proposed a new ranking method based on the left and the right spreads at some levels of fuzzy numbers. Ranking fuzzy numbers in many applications, ranking of fuzzy number s is an important component of the decision process. Firstly, in 1976, jain, 1976, jain, 1977 proposed a method for ranking of fuzzy numbers, then a large of variety of methods have been developed to rank fuzzy numbers. Ranking triangular fuzzy numbers using fuzzy set inclusion. Ranking of intuitionistic fuzzy numbers by new distance measure. Fuzzy transportation problem, triangular fuzzy numbers, optimal solution, roubast ranking method. Since fuzzy numbers do not form a na tural linear order, like real numbers, a key issue in operationalzing fuzzy set theory is how to compare fuzzy numbers. An approach for ranking of fuzzy numbers sciencedirect.
Wan and li 15 focused on multiattribute decision making madm problems in which the attribute values are expressed. Decomposition and intersection of two fuzzy numbers for fuzzy. A new ranking method for intuitionistic fuzzy numbers. Solving a interval fuzzy linear programming problem using. Most of the methods proposed so far are nondiscriminating and counterintuitive. Trapezoidaltriangular intuitionistic fuzzy numbers versus. To this purpose, we convert each tifn to two related triangular fuzzy numbers tfns based on the their membership functions and. It demonstrates some provable fundamental characteristics and ordering behaviors of their corresponding ranking functions.
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