Method with horizontal fuzzy numbers for solving real fuzzy linear systems

Landowski, Marek

doi:10.1007/s00500-018-3290-y

Cited by 21 publications

(11 citation statements)

References 25 publications

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“…The MF-arithmetic theoretical foundations are linked with the horizontal fuzzy numbers (HFN) [10]. The HFN with linear or/and nonlinear left and right borders can be defined based on the FN parametric definition.…”

Section: Multidimensional Fuzzy Arithmeticmentioning

confidence: 99%

Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

2020

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To answer the question stated in the title, we present and compare two approaches: first, a standard approach for solving dual fuzzy nonlinear systems (DFN-systems) based on Newton’s method, which uses 2D FN representation and second, the new approach, based on multidimensional fuzzy arithmetic (MF-arithmetic). We use a numerical example to explain how the proposed MF-arithmetic solves the DFN-system. To analyze results from the standard and the new approaches, we introduce an imprecision measure. We discuss the reasons why imprecision varies between both methods. The imprecision of the standard approach results (roots) is significant, which means that many possible values are excluded.

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Section: Multidimensional Fuzzy Arithmeticmentioning

confidence: 99%

Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

2020

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“…Piegat et al primarily elaborated on their proposed approach called RDM fuzzy interval arithmetic enjoying horizontal membership functions in solving some problems of fuzzy mathematics, see [3]- [5]. The successful applications of RDM fuzzy interval arithmetic in comparison with other approaches such as standard interval arithmetic have been proved by Piegat and Landowski in [6]- [9]. Then, Mazandarani et al by introducing a new framework of fuzzy calculus proved the effective applicability of horizontal membership functions and RDM fuzzy interval arithmetic in fuzzy dynamical systems, see [10]- [12] for more details.…”

Section: Introductionmentioning

confidence: 99%

Fractional Fuzzy Inference System: The New Generation of Fuzzy Inference Systems

Mazandarani

2020

IEEE Access

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This paper presents a new machinery of compositional rule of inference called fractional fuzzy inference system (FFIS). An FFIS is a fuzzy inference system (FIS) in which consequent parts of a rule base consist of a new type of membership functions called fractional membership functions. Fractional membership functions are characterized using fractional indices. There are two types of fractional indices. Each type can be either constant or dynamic. An FFIS intelligently considers not only the truth degrees of information included in membership functions, but also the volume of the information in the process of making a conclusion. In other words, the volume of information extracted from a membership function depends on the truth degree of information. Concretely, the higher the truth degree, the larger the volume of information that is involved in the process of making a conclusion. It is shown that typical FISs, e.g. Mamdani's or Larsen's FISs, are special cases of FFISs. Specifically, as the fractional indices approach one, the FFIS approaches a typical FIS. In addition, using two theorems proved in this paper, it is demonstrated that, independent of the problem in question, a typical FIS never leads to results which are more satisfactory than those obtained by the FFIS corresponding to the typical FIS provided that a particular set of fractional indices is taken into account. Put another way, it seems sound to expect that applying FFIS always leads to more satisfactory results than applying its corresponding FIS. It is also shown that FFIS grants a special dynamic to FIS which can be also customized according to a new concept called reaction trajectories map (RTM). Particularly, the RTM enables decision makers to select an FFIS more suitable for their purpose. Some more concepts such as the left and right orders of an FFIS and the fracture index are also introduced in this paper.

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“…In this context, a new concept of multidimensional Relative Distance Measure Interval Arithmetic (RDM-IA) has been developed by Landowski (2012, 2013); Landowski (2015Landowski ( , 2016. The authors (Tomaszewska and Piegat 2015;Piegat and Pluciński 2015;Landowski 2015, 2017;Landowski 2017Landowski , 2019 have demonstrated that the solution obtained from the proposed access is more fruitful than the effect received by employing the standard fuzzy interval arithmetic. There are so many gaps in between the result obtained by the Standard Interval Mathematics (SIA) and the multidimensional Relative Distance Measure Interval Arithmetic (RDM-IA) follows (Landowski 2019):…”

Section: Introductionmentioning

confidence: 99%

Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach

Khatua

Kar

2020

Comp. Appl. Math.

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This paper deals with a single period fuzzy production inventory model with the assortment items in a finite time horizon. Here, we tried to implement the preservation technology for decreasing the deterioration rate and control the preservation cost of the deteriorated products. In harmony with the real-life uncertain production inventory system, the decision variables and some of the parameters of the proposed model are assumed to be fuzzy variables. So a fuzzy dynamical system has been developed and solved for controlling the system. The optimality of the objective function in fuzzy optimal control has been derived and we have introduced a new approach, the granular differentiability for defuzzifying the system. Then the defuzzified optimal control problem is solved by using Pontryagin's maximum principle. Here, we have used the Runge-Kutta forward-backward method of fourth-order through MATLAB software. The proposed model is illustrated through a numerical example to determine the optimality conditions and the results are shown both in tabular form and graphically.

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Method with horizontal fuzzy numbers for solving real fuzzy linear systems

Cited by 21 publications

References 25 publications

Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

Which Alternative for Solving Dual Fuzzy Nonlinear Equations Is More Precise?

Fractional Fuzzy Inference System: The New Generation of Fuzzy Inference Systems

Control the preservation cost of a fuzzy production inventory model of assortment items by using the granular differentiability approach

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