Type-2 pentagonal fuzzy numbers and its application to get equivalent proverbs in two different languages

  • Authors

    • Pathinathan T
    • Santhoshkumar S
    2018-06-08
    https://doi.org/10.14419/ijet.v7i2.33.15535
  • Emotion, Indian Language, Proverb, Similarity Measure, Type-2 Fuzzy Set, Type-2 Pentagonal Fuzzy Number.

  • Uncertainties in words or phrases are usually represented by fuzzy sets and the quantification of it is represented by fuzzy number.Type-2 fuzzy set is the generalization made from Zadeh’s fuzzy set which resolve the uncertainty of the membership function of type-1 fuzzy set. In this paper, we introduce a new fuzzy number called Type-2 Pentagonal Fuzzy Number (T2PFN). We study its algebraic properties. We define different type of Type-2 Pentagonal Fuzzy Numbers. Also use it to analyze the complex structural representation and categorization of words used in the proverbs from two Indian Languages (IL) Hindi and Tamil. Proverbs used in communication might have different meanings, emotions and intentions in different cultures and contexts. Getting equivalent proverbs in two different languages is a challenge to the translators. Proverbs are popularly utilized in oral contexts which reflect the lifestyle of the common people representing their culture, tradition, emotion and experience gained from forefathers. We try to grasp the core meaning of a proverb expressed through context defined words. Getting equivalent proverbs in two different languages requires the understanding of the context, meaning in that particular cultural environment and timing used in the conversation. Type-2 fuzzy set is employed to study the similarity relation between the texts of two languages with the help of Matlab toolbox. An illustration is made with an example by analyzing the semantically similar proverbs from the two languages.

     

     

  • References

    1. [1] A. Kaufmann, and A. P. Bonaert, “Introduction to the Theory of Fuzzy Subsets – Vol. 1: Fundamental Theoretical Elements,†IEEE Transaction on Systems, Man, and Cybernetics, Vol. 7, No. 6, (1977), pp.495-496.

      [2] A. Kaufmann, Introduction to the Theory of Fuzzy Subsets, Vol. 1, Academic press, New York, (1975).

      [3] D. Dubois, and H. Prade, “Operations on Fuzzy Numbers,†International Journal of Systems Science, Vol. 9, No. 6, (1978), pp.613-626.

      [4] D. Dubois, and J. Didier, Fuzzy sets and systems: theory and applications, Vol. 144, Academic press, (1980).

      [5] D. Stephen Dinagar, and K. Latha, “Some Types of Type-2 Triangular Fuzzy Matrices,†International Journal of Pure and Applied Mathematics, Vol. 82, No. 1, (2013), pp.21-32.

      [6] G. Klir, B. Yuan, Fuzzy sets and fuzzy logic, Vol. 4, New Jersy: Prentice hall, (1995).

      [7] J. M. Mendel, R. I. Bob John, “Type-2 Fuzzy Sets Made Simple,†IEEE Transactions on Fuzzy Systems, Vol. 10, No. 2, (2002), pp.117-127.

      [8] L. A. Zadeh, “The Concept of a Linguistic Variable and its Application to Approximate Reasoning-I,†Information Science, Vol. 8, (1975), pp.199-249.

      [9] R. Rengarajan, Hindi-Tamil-English parallel proverbs, 1st Ed. An imprint of Sura College of Competition, Chennai, India, (2017).

      [10] T. Pathinathan, K. Ponnivalavan, “Diamond fuzzy numbers,†Journal of Fuzzy set Valued Analysis, Vol. 1, (2014), pp.36-44.

      [11] T. Pathinathan, K. Ponnivalavan, “Pentagonal fuzzy numbers,†International Journal of Computing Algorithm, Vol. 3, 2014, pp.1003-1005.

      [12] T. Pathinathan, K. Ponnivalavan, “Reverse Order Triangular, Trapezoidal and Pentagonal Fuzzy Numbers,†Annals of Pure and Applied Mathematics, Vol. 8, (2014), pp.51-58.

  • Downloads

  • How to Cite

    T, P., & S, S. (2018). Type-2 pentagonal fuzzy numbers and its application to get equivalent proverbs in two different languages. International Journal of Engineering & Technology, 7(2.33), 926-933. https://doi.org/10.14419/ijet.v7i2.33.15535