Fuzzy number

About: Fuzzy number is a research topic. Over the lifetime, 35606 publications have been published within this topic receiving 972544 citations.

Comprehensive analysis of a new fuzzy rule interpolation method

Abstract: The first published result in fuzzy rule interpolation was the /spl alpha/-cut based fuzzy rule interpolation, termed as KH fuzzy rule interpolation, originally devoted for complexity reduction. A modified version of the KH approach has been presented by Yam et al. (1999), which eliminates the subnormality problem while at the same time intending to maintain the advantageous computational properties of the original method. This paper presents a comprehensive analysis of the new method, which includes detailed comparison with the original KH fuzzy rule interpolation method concerning the explicit functions of the methods, preservation of piecewise linearity, and stability. The fuzziness of the conclusion with respect to the fuzziness of the observation is also investigated in comparison with several interpolation techniques. All these comparisons shows that the new method preserves the advantageous properties of the KH method and alleviates its most significant disadvantage, the problem of subnormality.

A new fuzzy additive ratio assessment method (ARAS‐F). Case study: The analysis of fuzzy multiple criteria in order to select the logistic centers location

Abstract: The main approaches which are applied to select the logistic center are the methods of gravity center, analytic hierarchy process, similarity to ideal solution, fuzzy ranking, assessment, etc. Multiple Criteria Decision‐Making (MCDM) combines analytical and inductive knowledge, describing a domain problem, which can be fuzzy and/or incomplete. The fuzzy MCDM (FMCDM) approach can explain the problem more appropriately. The purpose of the paper is to select the most suitable site for logistic centre among a set of alternatives, to help the stakeholders with the performance evaluation in an uncertain environment, where the subjectivity and vagueness of criteria are described by triangular fuzzy numbers. The paper presents a newly‐developed ARAS‐F method to solve different problems in transport, construction, economics, technology and sustainable development.

Fuzzy logic for process safety analysis

Abstract: Fuzzy logic deals with uncertainty and imprecision, and is an efficient tool for solving problems where knowledge uncertainty may occur. Such situations frequently arise in a quantitative fault and event tree analysis in safety and risk assessment of different processes. The lack of detailed data on failure rates, uncertainties in available data, imprecision and vagueness may lead to uncertainty in results, thus producing an underestimated or overestimated process risk level. This paper explores the application of fuzzy sets theory for basic tools used in process safety analysis such as fault and event tree methods which can be further used in the “bow-tie” approach for accident scenario risk assessment. In the traditional fault and event tree analyses, the input variables are treated as exact values and the exact outcome data are received by an appropriate mathematical approach. In the fuzzy method, all variables are replaced by fuzzy numbers in the process of fuzzification and subsequently using fuzzy arithmetic, fuzzy probability of the top event for fault tree, and fuzzy outcome probabilities for event tree are calculated. A single value for each of the outcome event result is obtained with the use of one of the defuzzification methods. A typical case study comprising a fault tree for rupture of the isobutane storage tank and the event tree for its consequences is performed and a comparison between the traditional approach and fuzzy method is made.

Fuzzy Probability and Statistics

Abstract: This book combines material from our previous books FP (Fuzzy Probabilities: New Approach and Applications,Physica-Verlag, 2003) and FS (Fuzzy Statistics, Springer, 2004), plus has about one third new results. From FP we have material on basic fuzzy probability, discrete (fuzzy Poisson,binomial) and continuous (uniform, normal, exponential) fuzzy random variables. From FS we included chapters on fuzzy estimation and fuzzy hypothesis testing related to means, variances, proportions, correlation and regression. New material includes fuzzy estimators for arrival and service rates, and the uniform distribution, with applications in fuzzy queuing theory. Also, new to this book, is three chapters on fuzzy maximum entropy (imprecise side conditions) estimators producing fuzzy distributions and crisp discrete/continuous distributions. Other new results are: (1) two chapters on fuzzy ANOVA (one-way and two-way); (2) random fuzzy numbers with applications to fuzzy Monte Carlo studies; and (3) a fuzzy nonparametric estimator for the median.