• Title/Summary/Keyword: interval fuzzy number

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Evaluation criterion for different methods of multiple-attribute group decision making with interval-valued intuitionistic fuzzy information

  • Qiu, Junda;Li, Lei
    • KSII Transactions on Internet and Information Systems (TIIS)
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    • v.12 no.7
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    • pp.3128-3149
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    • 2018
  • A number of effective methods for multiple-attribute group decision making (MAGDM) with interval-valued intuitionistic fuzzy numbers (IVIFNs) have been proposed in recent years. However, the different methods frequently yield different, even sometimes contradictory, results for the same problem. In this paper a novel criterion to determine the advantages and disadvantages of different methods is proposed. First, the decision-making process is divided into three parts: translation of experts' preferences, aggregation of experts' opinions, and comparison of the alternatives. Experts' preferences aggregation is considered the core step, and the quality of the collective matrix is considered the most important evaluation index for the aggregation methods. Then, methods to calculate the similarity measure, correlation, correlation coefficient, and energy of the intuitionistic fuzzy matrices are proposed, which are employed to evaluate the collective matrix. Thus, the optimal method can be selected by comparing the collective matrices when all the methods yield different results. Finally, a novel approach for aggregating experts' preferences with IVIFN is presented. In this approach, experts' preferences are mapped as points into two-dimensional planes, with the plant growth simulation algorithm (PGSA) being employed to calculate the optimal rally points, which are inversely mapped to IVIFNs to establish the collective matrix. In the study, four different methods are used to address one example problem to illustrate the feasibility and effectiveness of the proposed approach.

Fault Tree Analysis Model Based on Trapezoidal Fuzzy Number (사다리꼴퍼지수에 기초한 F.T.A. 모형에 관한 연구)

  • Sin, Mun-Sik;Jo, Nam-Ho
    • Journal of Korean Society for Quality Management
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    • v.20 no.1
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    • pp.118-125
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    • 1992
  • Studies upto date for estimating the reliability by means of one accarate value contain risks of many erroneous options. The objective of this paper is to presents a fault tree analueis model on the basis of the membership functions of trape Zoidal fuzzy number after imposing an interval of Confidence on the residual possibility theory. The results from the model Show that the value of Stability was reliable.

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SOLVING SYSTEMS OF EQUIVALENTIONS

  • BAN A. I.;BICA A. A.
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.97-118
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    • 2006
  • We obtain a property of distributivity in the equivalence form over LR fuzzy intervals. As an application and main result of the paper, we give a determinant method to solve systems of linear equivalentions. The expected value of the obtained solution is equal to the corresponding solution of the classical system of linear equations considering the expected values as data.

T-sum of bell-shaped fuzzy intervals

  • Hong, Dug-Hun
    • 한국데이터정보과학회:학술대회논문집
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    • 2006.11a
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    • pp.81-95
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    • 2006
  • The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.

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LATTICE OF KEYCHAINS

  • MURALI V.
    • Journal of applied mathematics & informatics
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    • v.20 no.1_2
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    • pp.409-420
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    • 2006
  • In this paper we consider the set of all n + 1-tuples of real numbers, not necessarily all distinct, in the decreasing order from the unit interval under the usual ordering of real numbers, always including 1. Such n + 1-tuples inherently arise as the membership values of fuzzy subsets and are called keychains. An natural equivalence relation is introduced on this set and the equivalence classes of keychains are studied here. The number of such keychains is finite and the set of all keychains is a lattice under the coordinate-wise ordering. Thus keychains are subchains of a finite chain of real numbers in the unit interval. We study some of their properties and give some applications to counting fuzzy subsets of finite sets.

Use of uncertain numbers for appraising tensile strength of concrete

  • Tutmez, Bulent;Cengiz, A. Kemal;Sarici, Didem Eren
    • Structural Engineering and Mechanics
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    • v.46 no.4
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    • pp.447-458
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    • 2013
  • Splitting tensile strength (STS) is a respectable mechanical property reflecting ability of the concrete. The STS of concrete is mainly related to compressive strength (CS), water/binder (W/B) ratio and concrete age. In this study, the assessment of STS is made by a novel uncertainty-oriented method which uses least square optimization and then predicts STS of concrete by uncertain (fuzzy) numbers. The approximation method addresses a novel integration of fuzzy set theory and multivariate statistics. The numerical examples showed that the method is applicable with relatively limited data. In addition, the prediction of uncertainty at various levels of possibility can be described. In conclusion, the uncertainty-oriented interval analysis can be suggested an effective tool for appraising the uncertainties in concrete technology.

A note on T-sum of bell-shaped fuzzy intervals

  • Hong, Dug-Hun
    • Journal of the Korean Institute of Intelligent Systems
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    • v.17 no.6
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    • pp.804-806
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    • 2007
  • The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. Recently, Hong [Fuzzy Sets and Systems 158(2007) 739-746] defined a broader class of bell-shaped fuzzy intervals. Then he study t-norms which are consistent with these particular types of fuzzy intervals as applications of a result proved by Mesiar on a strict f-norm based shape preserving additions of LR-fuzzy intervals with unbounded support. In this note, we give a direct proof of the main results of Hong.

New Fuzzy Concepts as a consequence of the encoding with intervals

  • KARBOU, Faitha
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 1998.06a
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    • pp.573-578
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    • 1998
  • In this paper, we propose a new technique of codification. The purpose of this method is to take in consideration the natural language nuances and the fuzziness that characterizes the human reasoning. So, we warranted a means of more flexible encoding that translates as well the linguistic descriptions. Its principle is simple and intuitive. It consists simply in replacing in ambiguous cases, a unique number by an interval. The introduction of the new codification necessitates the elaboration of metric or similarity in order to compare two intervals. This comparison must take in consideration the difference of their size, the remoteness of their center and the width of their intersection. In consequence, we defined three new fuzzy concepts : "fuzzy inclusion degree", "fuzzy resemblance degree," and " fuzzy curve".

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Controllability for the Semilinear Fuzzy Integrodifferential Equations with Nonlocal Conditions and Forcing Term with Memory (기억을 갖는 강제항과 비국소조건을 갖는 준선형 퍼지 적분미분방정식에 대한 제어가능성)

  • Kwun, Young-Chel;Ahn, Young-Chel;Park, Dong-Gun;Kim, Seon-Yu
    • Proceedings of the Korean Institute of Intelligent Systems Conference
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    • 2007.04a
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    • pp.213-216
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    • 2007
  • In this paper. we study the controllability for the semilinear fuzzy integrodifferential equations with nonlocal condition and forcing term with memory in $E_N$ by using the concept of fuzzy number whose values are normal, convex, upper semicontinuous and compactly supported interval in $E_N$.

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Software Reliability Assessment with Fuzzy Least Squares Support Vector Machine Regression

  • Hwang, Chang-Ha;Hong, Dug-Hun;Kim, Jang-Han
    • Journal of the Korean Institute of Intelligent Systems
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    • v.13 no.4
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    • pp.486-490
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    • 2003
  • Software qualify models can predict the risk of faults in the software early enough for cost-effective prevention of problems. This paper introduces a least squares support vector machine (LS-SVM) as a fuzzy regression method for predicting fault ranges in the software under development. This LS-SVM deals with the fuzzy data with crisp inputs and fuzzy output. Predicting the exact number of bugs in software is often not necessary. This LS-SVM can predict the interval that the number of faults of the program at each session falls into with a certain possibility. A case study on software reliability problem is used to illustrate the usefulness of this LS -SVM.