Representation and Ranking of Fuzzy Numbers with Heptagonal Membership Function Using value and Ambiguity Index
نویسنده
چکیده
In many real life problems, the parameters used to characterize the uncertainty or vagueness or impreciseness in information are either triangular or trapezoidal fuzzy numbers. But it is not always possible to restrict the membership function to either triangular or trapezoidal form. In this paper, a new form of non-normal fuzzy number named as Heptagonal fuzzy number is introduced and its arithmetic operations are defined. Further, an attempt has been made to give a new version of definition for value and ambiguity of non-normal fuzzy numbers and based on this new definition a parametric ranking method is proposed for ordering Heptagonal fuzzy numbers. Finally, an application of Heptagonal fuzzy number in fuzzy assignment problem is given and it is proved that the optimal value obtained using Heptagonal Fuzzy number is more optimal than the solution obtained by using Trapezoidal fuzzy numbers. 4310 K. Rathi and S. Balamohan
منابع مشابه
New Generalized Interval Valued Intuitionistic Fuzzy Numbers
The aim of this paper is investigate the notion of a generalized interval valued intuitionistic fuzzy number (GIVIFN), which extends the interval valuedintuitionistic fuzzy number. Firstly, the concept of GIVIFNBs is introduced.Arithmetic operations and cut sets over GIVIFNBBs are investigated. Then the values and ambiguities of the membership degree and the non-membership degree and the value ...
متن کاملA Compromise Ratio Ranking Method of Triangular Intuitionistic Fuzzy Numbers\ and Its Application to MADM Problems
Triangular intuitionistic fuzzy numbers (TIFNs) is a special case of intuitionistic fuzzy (IF) set and the ranking of TIFNs is an important problem. The aim of this paper is to develop a new methodology for ranking TIFNs by using multiattribute decision making methods (MADM). In this methodology, the value and ambiguity indices of TIFNs may be considered as the attributes and the TIFNs in compa...
متن کاملA Difference-index Based Ranking Method of Trapezoidal Intuitionistic Fuzzy Numbers and Application to Multiattribute Decision Making
The order relation of fuzzy number is important in decision making and optimization modeling, and ranking fuzzy numbers is difficult in nature. Ranking trapezoidal intuitionistic fuzzy numbers (TrIFNs) is more difficult due to the fact that the TrIFNs are a generalization of the fuzzy numbers. The aim of this paper is to develop a new methodology for ranking TrIFNs. We define the value-index an...
متن کاملAnother Method for Defuzzification Based On Characterization of Fuzzy Numbers
Here we consider approaches to the ranking of fuzzy numbers based upon the idea of associating with a fuzzy number a scalar value, its signal/noise ratios, where the signal and the noise are defined as the middle-point and the spread of each $gamma$-cut of a fuzzy number, respectively. We use the value of a as the weight of the signal/noise ratio of each $gamma$-cut of a fuzzy number to calcula...
متن کاملRanking method of trapezoidal intuitionistic fuzzy numbers
In this paper, considers the usage of intuitionistic fuzzy numbers in decision making. The values and ambiguities of the membership degree and the non-membership degree for trapezoidal intuitionistic fuzzy number are defined as well as the value-index and ambiguity-index. The proposed ranking method is easily implemented and has a natural interpretation. 2010 AMS Classification: 47S20, 03E72
متن کامل