Generalization and ranking of fuzzy numbers by relative preference relation

We define $$2n+1$$ 2 n + 1 and 2n fuzzy numbers, which generalize triangular and trapezoidal fuzzy numbers, respectively. Then, we extend the fuzzy preference relation and relative preference relation to rank $$2n+1$$ 2 n + 1 and 2n fuzzy numbers. When the data is representable in terms of $$2n+1$$ 2 n + 1 fuzzy number, we generalize the FMCDM (fuzzy multi-criteria decision making) model constructed with TOPSIS and relative preference relation. Lastly, we give an example from telecommunications to present the proposed FMCDM model and validate the results obtained.

Implementation of Modified Best Candidate Method in Fuzzy Assignment Problem

To meet the demands of every customer by supplying the products at the limited time by maximizing the profit is a dream for many companies. By choosing the best candidate among the other candidates and effectively reaching the optimal solution with a new modified approach using Best Candidate Method in Fuzzy assignment problems. In this paper the author solve Fuzzy assignment problem in which Triangular and Trapezoidal fuzzy numbers are used. Robust Ranking Technique is used for the ranking of fuzzy numbers.

Fuzzy system F-CalcRank for calculating functions of fuzzy arguments and ranking of fuzzy numbers

Assessing functions of fuzzy arguments and ranking of fuzzy quantities are two key steps in fuzzy modeling and Fuzzy Multicriteria Decision Analysis (FMCDA). Approximate calculations along with the use of centroid index as a defuzzification based ranking methods are a generally accepted approach to applications in the fuzzy environment. This paper presents a novel fuzzy system, F-CalcRank, which is integration of two coupled fuzzy systems: F-Calc (Fuzzy Calculator) and F-Ranking (Fuzzy Ranking). F-Calc allows assessing functions of fuzzy numbers with the use of different approaches: approximate calculations, standard fuzzy arithmetic, and transformation methods. The input values to F-Calc are fuzzy numbers with the following membership functions: triangular and trapezoidal, Gaussian, bell shape, sigmoid, and piece-wise linear continuous or upper semicontinuous membership functions of any complexity, as well as fuzzy linguistic terms of a given term set. F-Ranking system is intended for ranking of a given set of fuzzy numbers, including those, which are inputs and/or outputs of the F-Calc system. F-Ranking includes six ranking methods: three defuzzification based and three pairwise comparison ones. The structure of F-CalcRank as well as input and output information and the user interfaces of both F-Calc and F-Ranking systems, which can also be used independently, are presented. Examples of computing functions of fuzzy arguments and ranking of fuzzy numbers using implemented methods as well as exploring a real case study in agro-ecology with the use of a math model in fuzzy environment are considered. These examples stress the features and novelty of F-CalcRank system as well as presented applied research. The computer modules created within F-CalcRank are a basis for different FMCDA models developed by the authors. F-CalcRank system is intended for university education, research and various applications in engineering and technology.

A noval ranking approach based on incircle of triangular intuitionistic fuzzy numbers

Since proposed by Zadeh in 1965, ordinary fuzzy sets help us to model uncertainty and developed many types such as type 2 fuzzy, intuitionistic fuzzy, hesitant fuzzy etc. Intuitionistic fuzzy sets include both membership and non-membership functions for their each element. Ranking of a number is to identify a relationship of scalar quantity between these numbers. Ranking of fuzzy numbers play an important role in modeling problems such as fuzzy decision making, fuzzy linear programming problems. In this study, a new ranking method for triangular intuitionistic fuzzy numbers is proposed. The method based on the incircle of the membership function and non-membership function of TIFN uses lexicographical order to rank intuitionistic fuzzy numbers. Two examples are provided to illustrate the applicability of the method. Also, a comparative study is performed to demonstrate the validity of the proposed method. The results indicate that proposed method is consistent with other methods in the literature. Also, the method overcomes the problems such as numbers being very small or close to each other.

Solving Game Problems Involving Heptagonal and Hendecagonal Fuzzy Payoffs

The main aim of this paper is to deal with a two person zero sum game involving fuzzy payoff matrix comprising of heptagonal and hendecagonal fuzzy numbers. Ranking of fuzzy numbers is a hard task. Many methods have been proposed to rank different fuzzy numbers such as triangular, trapezoidal, hexagonal, octagonal etc. In this paper, a matrix game is considered whose payoffs are heptagonal and hendecagonal fuzzy numbers and ranking method is used to solve the matrix game. By using this proposed approach the fuzzy game problem is converted into crisp problem and then solved by applying the usual game problem techniques. The validity of proposed method is illustrated with the help of two different practical examples; one where the two companies are venturing into online restaurant business and the other where the two political parties with conflicting interests during elections are competing with each other.

Ranking of Fuzzy Numbers by using Scaling Method

In this paper, we presented for the first time a multidimensional scaling approach to find the scaling as well as the ranking of triangular fuzzy numbers. Each fuzzy number was represented by a row in a matrix, and then found the configuration points (scale points) which represent the fuzzy numbers in . Since these points are not uniquely determined, then we presented different techniques to reconfigure the points to compare them with other methods. The results showed the ability of ranking fuzzy numbers