Ranking fuzzy numbers plays an very important role in linguistic decision making and some other fuzzy application systems. Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques have been shown to produce non-intuitive results in certain cases. 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 @a-levels of trapezoidal fuzzy numbers. The calculation of the proposed method is far simpler and easier. Finally, some comparative examples are used to illustrate the advantage of the proposed method.

A new approach for ranking of trapezoidal fuzzy numbers

The modeling of extreme values is important to scientists in such  elds as hydrology, civil engineering, environmental science, oceanography and  nance. Stuart Coles’s book on the modeling of extreme values provides an introductory text on the topic. It is a modeling-oriented text with an emphasis on different types of data and analytical approaches. The book is laid out in nine chapters. Following introductory material and discussion of necessary theoretical background are chapters on approaches to extreme values that focus on the different types of data that might be used in an extreme value analysis. These include models for block maximums, threshold models, models for data from stationary and nonstationary processes, and approaches based on point processes. A chapter covers analysis of multivariate extremes, and the  nal chapter brie y covers such topics as Bayesian inference, Markov chains, and spatial extremes. Although this is not a data-driven text, it does contain numerous examples and analyses. These examples are used to illustrate the methodology; I would have preferred to see more motivation and interpretation of the results of the analyses. Datasets and S-PLUS programs for the analyses in the text are available at a website. These are easy to use for those slightly familiar with S-PLUS. The appendix describes the programs and illustrates how to access data and use the programs. It also gives links to sites that provide other software. The text does not include problem sets; these would have been useful, especially if the text is to be used in coursework. The text by Reiss and Thomas (2001) contains more thoroughly analyzed datasets, although it is twice the length and not as streamlined as the text under review. The book is meant for individuals with moderate statistical background. Those with coursework in maximum likelihood methods should have no dif culty reading and comprehending the text. Overall, this is a good text for someone getting started in extreme value methods.

Statistical Quality Control

https://personalpages.manchester.ac.uk/staff/jian-bo.yang/JB%20Yang%20Journal_Papers/WangYangXuChin_centroidsin_FSS.pdf

On the centroids of fuzzy numbers

The concept of an intuitionistic fuzzy number (IFN) is of importance for quantifying an ill-known quantity, and the ranking of IFNs is a very difficult problem. The aim of this paper is to introduce the concept of a triangular IFN (TIFN) as a special case of the IFN and develop a new methodology for ranking TIFNs. Firstly the concepts of TIFNs and cut sets as well as arithmetical operations are introduced. Then the values and ambiguities of the membership function and the non-membership function for a TIFN are defined. A new ranking method is developed on the basis of the concept of a ratio of the value index to the ambiguity index and applied to multiattribute decision making problems in which the ratings of alternatives on attributes are expressed with TIFNs. The validity and applicability of the proposed method, as well as analysis of the comparison with other methods, are illustrated with a real example.

A ratio ranking method of triangular intuitionistic fuzzy numbers and its application to MADM problems

In this article, we propose the reproducing kernel Hilbert space method to obtain the exact and the numerical solutions of fuzzy Fredholm---Volterra integrodifferential equations. The solution meth...

Adaptation of reproducing kernel algorithm for solving fuzzy Fredholm–Volterra integrodifferential equations

Ranking of fuzzy numbers by min distance

Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered.

Mahmood Otadi

Papers

Ranking of fuzzy numbers by min distance

Minimal solution of general dual fuzzy linear systems

Numerical solution of fuzzy polynomials by fuzzy neural network

Numerical solution of a system of fuzzy polynomials by fuzzy neural network

Evaluation of fuzzy regression models by fuzzy neural network