Investment portfolio evaluation by the fuzzy approach lambovska maya, marchev angel abstract this paper presents a new fuzzy approach for the evaluation of investment portfolio, where the approach is viewed by the authors as a subphase of the management process of. The nasa langley multidisciplinary uncertainty quanti. Because most models, especially those characterizing uncertainty, are imperfect. However, except for some conceptual observations, such a discussion is beyond the scope of this article. Random variables, fuzzy variables can be regarded as special cases of fuzzy random variables. The goal is to present a test procedure to explicitly examine whether an independent variable has a clear functional relationship with the dependent variable in a specific regression model, or whether their relationship is fuzzy. Fuzzy set approaches to classification of rock masses a. Then the probability density function pdf of x is a function fx such that for any two numbers a and b with a. Once the fuzzyrandom extension has been introduced, it is also shown how to obtain some variables linked with central mortality rates such as death probabilities or life expectancies by using fuzzy numbers arithmetic. Fuzzy logic classical logic multivalued logic fuzzy propositions fuzzy quantifiers linguistic hedges interference from conditional fuzzy propositions, conditional and qualified propositions and quantified propositions.
We will describe the analysis of the interpretation, modeling, and impact of fuzzy random variables. An application of fuzzy random variables to control charts. The present appendix is based on the description of fuzzy random variable available in rohmer and baudrit, 2011. Fuzzy random variables are mathematical descriptions for fuzzy stochastic phenomena, and are defined in several ways. The second one, the changesinchanges wald ratio waldcic, generalizes the changesinchanges estimand introduced by athey and imbens 2006 to fuzzy designs. Overview on the development of fuzzy random variables 1. This concept was then developed by several researchers such as puri and ralescu 242, kruse and meyer 9, and liu and liu 188. A linear regression model for fuzzy lr responses and. We propose a new method for solving fuzzy lp flp problems in which the righthand side parameters and the decision variables are represented by fuzzy numbers.
Quality control process based on fuzzy random variables. The aim of this paper is to deal with the resourceconstrained multiple project scheduling problems rcmpsp, which consider the complex hierarchical organization structure and fuzzy random environment in the decision making process. Robust inference in fuzzy regression discontinuity designs yang he november 2, 2017 abstract fuzzy regression discontinuity rd design and instrumental variables iv regression share similar identi cation strategies and numerically yield the same results under certain conditions. Pdf fuzzy probability spaces and their applications in. Chapter 10 fuzzy control and fuzzy expert systems the fuzzy logic controller flc is introduced in this chapter. In this paper we define the concept of a normal fuzzy random variable and we. Some properties concerning the measurability of fuzzy random variable are also discussed. The notion of fuzzy random variable has been introduced to model random mechanisms generating impreciselyvalued data which can be properly described by means of fuzzy sets. Aydin department of earth sciences, james lee science building, the university of hong kong, pokfulam road, hong kong, china received 4 november 2003. Implementation of fuzzy and adaptive neurofuzzy inference. A bilevel multiobjective rcmpsp model with fuzzy random coe cients is presented by taking into account the strategy and process in. Fuzzy artmap neural network compared to linear discriminant analysis. Investment portfolio evaluation by the fuzzy approach.
The stata journal fuzzy di erencesindi erences with stata. The concept of normality for fuzzy random variables. Application to diabetes bernie black nicholas chabraja professor northwestern university, pritzker school of law and kellogg school of. Robustbased random fuzzy meanvariance model using a fuzzy. Abstractthis paper considers a robustbased random fuzzy meanvariance portfolio selection problem using a fuzzy reasoning method, particularly a single input type fuzzy reasoning method. Fuzzy probability analysis of the fatigue resistance of steel structural members under bending.
Random variables and probability distributions random variables suppose that to each point of a sample space we assign a number. Pdf a random fuzzy accelerated degradation model and. Now actuarial science is at the threshold of a new era based on the merging of fuzzy variables and random variables. Conceptualizing future lifetime as a fuzzy random variable. Pdf overview on the development of fuzzy random variables. Kwakernaak 142143 first introduced the notion of fuzzy random variable. Zadeh abstract fuzziness is discussed in the context of multivalued logic, and a corresponding view of fuzzy sets is given.
In measurements, the measurement obtained can suffer from two types of uncertainties. We then have a function defined on the sample space. Pdf fuzzy probability analysis of the fatigue resistance. Combined fuzzy logic and random walker algorithm for pet image tumor delineation motahare soufia, alireza kamaliasla, parham geramifarb, mehrsima abdolic and arman rahmimd,e purpose the random walk rw technique serves as a powerful tool for pet tumor delineation, which typically involves significant noise andor blurring. A random fuzzy accelerated degradation model and statistical analysis article pdf available in ieee transactions on fuzzy systems pp99. Fuzzy sets versus crisp sets additional properties of cuts representations of fuzzy sets. A unified approach to fuzzy random variables are considered by kratschmer2001 kao and hsu2002 discussed a singleperiod inventory model with fuzzy demand. An approach to system reliability analysis with fuzzy random variables zhonglai wang, hongzhong huang. Intervals, fuzzy sets, random variables, probability boxes 3, a. A fuzzy lp model with fuzzy parameters and decision variables 3 ambiguous, uncertain or imprecise data in lp by formalising the inaccuracies inherent in human decisionmaking. Fuzzy random variables are random variables whose values are not real, but fuzzy numbers. Liu 22 defined the fuzzy random failure function of the structure with fuzzy random variables as the basic variables.
Puri redefines the definition of fuzzy random variables and expectations 19. So weve described some examples, some very basic examples of random variables. Original article combined fuzzy logic and random walker. The expected value of a fuzzy variable is a natural generalization of the integral of a set valued function 2. A multiple linear regression model for lr fuzzy random variables. On the otherhand, mean and variance describes a random variable only partially. This work deals with the simulation of fuzzy random variables, which can be used to model various realistic situations, where uncertainty is not only present in form of randomness but also in form. In recent years, many of the fuzzy logic ideas and techniques have been merged into statistics, yielding new methodologies, most notably in the areas of regression and cluster analysis. Modeling future lifetime as a fuzzy random variable. Pmfs and pdfs introduction, probability, expectations.
There are random experiments in which the notion of a classical random variable, as a map sending each elementary event to a real number, does not capture their nature. In addition, the concept of independent and identically distributed fuzzy random. In general, when the relationship between the output and input variables of the system is unknown and cannot be identi. Information sciences 15, 129 1978 1 fuzzy random variabhs. The consideration of this last hypothesis requires developing and solving a fuzzy regression model. Fuzzy set theory and its applications, third edition is a textbook for courses in fuzzy set theory. To illustrate this, we give an example of a simple type of fuzzy random variable. A fuzzy random variable is a variable whose distribution parameters such as mean or standard deviation are fuzzy numbers. Three definitions of fuzzy random variables frvs have been cited in the current literature. Since x and y are independent random variables, their joint probability distribution p, q is the product of p and q. Fuzziness is discussed in the context of multivalued logic, and a corresponding view of fuzzy sets is given. Meanwhile, fuzzy random variables with confidence intervals are applied in the fuzzy multi attribute decision making to enable decision makers to evaluate and find the importance weight 10. Buckley 3, 4 exhibit an approach to fuzzy probability and fuzzy statistics, respectively.
Bivariate and multivariate random variables and distributions variance. Probabilistic aspects of these random elements have been deeply discussed in the literature. Fuzzy logic computing with words 105 ya small medium large fig. Fuzzy random variable frv, which is a random variable with fuzzy values, is adopted to deal with the hybrid uncertainties. Introduction this paper is the first of a series of reports on fuzzy random variables. The nasa langley uq challenge on optimization under. Application to diabetes bernie black nicholas chabraja professor northwestern university, pritzker school of. While the weak identi cation problem is widely recognized in iv. From computing sample variances to computing sample covariances. This paper converts random variables of soil parameters into fuzzy random variables with the fuzzy random processing method of sample mechanics parameters and establishes a fuzzy random limit. In this sense, the fuzzy variable future lifetime and the random variable future lifetime are independent. Capital asset pr icing model is introduced as a future return of each security, and the market portfolio is. This paper presents a new definition of fuzzy random variable, and gives a novel defi.
Puri and others published fuzzy random variables find, read and cite all the research you need on researchgate. It can also be used as an introduction to the subject. Reliability analysis in presence of random variables and. Probability density function is a model and it is defined on continuous random variables. Fuzzy approaches for multiobjective fuzzy random linear. Fuzzy set approaches to classification of rock masses. Because of typographical errors n instead of m, random white spaces, etc. The probability density function, or pdf, of the normal distribution is the. Combining fuzzy cognitive maps and discrete random variables.
Intervals, fuzzy sets, random variables, probability boxes a. A fuzzy random variable frv has been conceptualized as a vague. Pdf random this is the first number produced by the matlab random number. Univariate and multivariate normal distributions, centrallimit theorem, and wishart distributions. A multiple linear regression model for lr fuzzy random.
We use the pxx form when we need to make the identity of the rv clear. In this paper, we construct a new method for discrete and continuous random variables with fuzzy parameters which is completely different from those mentioned above. Their actual age, x say, is an ordinary random variable on the positive real line. Combining fuzzy cognitive maps and discrete random variables piotr szwed agh university of science and technology email. Fuzzy random variable has been defined in several ways in literature. The foregoing merged fuzzy variables with random variables, and was a natural segue into a discussion of fuzzy random variables frvs, that is, random variables whose values are fuzzy numbers, and their implementation. Fuzzy approaches for multiobjective fuzzy random linear programming problems through a probability maximization model hitoshi yano and kota matsui abstractin this paper, two kinds of fuzzy approaches are proposed for not only multiobjective stochastic linear programming problems, but also multiobjective fuzzy random linear. What links here related changes upload file special pages permanent link page. While a parameter may be known to be aleatory, su cient data may not be available to adequately model it as a single random variable.
Then, some essential statistical features of the proposed fuzzy random variables including fuzzy cumulative distribution function, fuzzy expectation, exact variance and imprecise probability of an. Comparing to the reliability membership function for measuring the safety in case of mixed uncertainties, the proposed indices are more intuitive and easier to. For mixed uncertainties of random variables and fuzzy variables in engineering, three indices, that is, interval reliability index, mean reliability index, and numerical reliability index, are proposed to measure safety of structure. This function is called a random variableor stochastic variable or more precisely a random function stochastic function. On various definitions of the variance of a fuzzy random variable. Merging through fuzzy matching of variables in r 2.
This leads to fuzzy random variables in the bugajskigudder sense. Pdf this paper deals with a concept which connects probability and fuzzy set theories. Hingeloss markov random fields and probabilistic soft logic. Theory and applications of fuzzy random variables ieee xplore. The main difculty is to dene the more appropriate pdf to a. This article addresses the fuzziness in regression models. Fuzzy random variables are introduced as random variables whose values are not real but fuzzy numbers, and subsequently redefined as a particular kind of fuzzy set. Dec 03, 2019 pdf and cdf define a random variable completely. This scenario is an example of the puri and ralescu 1986 view of fuzzy random variables, where the fuzzy variable, a fuzzy subset of the future lifetime scale, is associated with the randomly chosen new retiree.
If two random variables x and y have the same pdf, then they will have the same cdf and therefore their mean and variance will be same. The main difculty is to dene the more appropriate pdf to a random uncertainty. A minimax distribution free procedure for mixed inventory models invoving variable lead time with fuzzy lost sales are analyzed by ouyang and chang2002. Note that, once the basis for the linguistic average future lifetime is established, the foregoing fuzzy variables are defined perceived without regard for the actual distribution of t x. Run casecontrol matching open the casecontrol matching dialog box from the menu bar data casecontrol matching use the arrow button to move the variables you would like to match on from the variables box to the variables to match on box i. In this paper, two types of fuzzy probability spaces will be introduced and their applications in methods of decision making under risk especially in the decision matrix method will be. The family of lr fuzzy random variables is considered and an appro. Robust inference in fuzzy regression discontinuity designs.
Probabilistic inventory model with fuzzy cost components and. The probability function of a discrete random variable x is the function px satisfying px prx x for all values x in the range of x. Definitions and theorems huibert kwakernaak department of applied mathematics, twente university of technology, enschede, the netherlands communicated by l. Bilevel optimization of resourceconstrained multiple. A multiple linear regression model for lr fuzzy random variables maria brigida ferraro. Readings in fuzzy sets for intelligent systems, 265271, 1993. Fuzzy random variables also referred to often as random fuzzy sets were introduced. In the literature, fuzzy random variables can be interpreted in different ways. A new evaluation approach integrating information axiom and the theory.
Examples will be given of scenarios modeled by fuzzy. The fuzzy incontrol region based on fuzzy random variables fuzzy random variables frvs provide a vehicle for us to model situations in the presence of both types of uncertainty. Information sciences 15, 129 1978 fuzzy random variables. Research design for causal inference highlevel overview w. Both of these models are explored in the rest of this article, but, for this conceptualization, we focus on models where the data is crisp and the relationship of the variables is fuzzy. This paper presents a new definition of fuzzy random variable, and gives a novel definition of scalar expected value operator for fuzzy random variables. A fuzzy linear programming model with fuzzy parameters and. After introducing the architecture of the flc, we study its components step by step and suggest a design procedure of the flc. Examples and generalizations martin papco abstract. The purpose of this study was to investigate risk assessment applications of fuzzy logic raafl.
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