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Resolution of single-variable fuzzy polynomial equations and an upper bound on the number of solutions

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Abstract

In this paper, the single-variable fuzzy polynomial equations are studied. We firstly define two solution types for the equations, called solution and r-cut solution. Then, sufficient and necessary conditions are proposed for existence of the solution and r-cut solution of the equations, respectively. Also, a new algorithm is designed to find all the solutions and r-cut solutions of the equations using algebraic computations. Based on Descartes’ rule of signs, we express and prove a fuzzy version of fundamental theorem of algebra to obtain the number of real roots of a single-variable fuzzy polynomial. Moreover, we present an upper bound on the number of solutions of the equations and show that each single-variable fuzzy polynomial equation has at most two distinct solutions.

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Authors and Affiliations

  1. Department of Basic Sciences, Chabahar Maritime University, Chabahar, Iran

    Hamed Farahani

  2. Department of Computer Engineering and Information Technology, Hamedan University of Technology, Hamedan, Iran

    Mahmoud Paripour

  3. Department of Mathematics, Imam Khomeini International University, Qazvin, Iran

    Saeid Abbasbandy

Authors
  1. Hamed Farahani
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  2. Mahmoud Paripour
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  3. Saeid Abbasbandy
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Correspondence to Mahmoud Paripour.

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Communicated by V. Loia.

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Farahani, H., Paripour, M. & Abbasbandy, S. Resolution of single-variable fuzzy polynomial equations and an upper bound on the number of solutions. Soft Comput 23, 837–845 (2019). https://doi.org/10.1007/s00500-017-2790-5

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