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IF-topologies and IF-automata

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Abstract

The purpose of this work is to indicate that a study of IF-automata (also called, intuitionistic fuzzy automata) can be carried out much on the same lines as the one done for fuzzy automata in Srivastava and Tiwari (Proceedings of 2002 AFSS international conference on fuzzy systems. Lecture notes in artificial intelligence, vol 2275. Springer, Berlin, pp 485–490, 2002). It is also shown that two IF-topologies (also called, intuitionistic fuzzy topologies) can be associated with the state-sets of IF-fuzzy automata whose level topologies have interesting relationships with the topologies introduced by Srivastava and Tiwari (above mentioned) for fuzzy automata.

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Notes

  1. A saturated topology is one which is closed under arbitrary intersections also.

  2. An IF-closure operator \(c:IFS(X)\rightarrow IFS(X)\) on X is being called here saturated if the (usual) requirement \(c(u \vee v) = c(u) \vee c(v)\) is replaced by \(c(\vee u_j) = \vee c(u_j)\), where \(u, v, u_j \in IFS(X),\ j\in J\).

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Acknowledgments

The authors gratefully thank the referee(s) for their observations and suggestions, which have helped them improve the paper.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Centre for Interdisciplinary Mathematical Sciences, Banaras Hindu University, Varanasi, 221 005, India

    Arun K. Srivastava

  2. Department of Applied Mathematics, Indian School of Mines University, Dhanbad, 826 004, India

    S. P. Tiwari

Authors
  1. Arun K. Srivastava
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  2. S. P. Tiwari
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Corresponding author

Correspondence to Arun K. Srivastava.

Additional information

The present paper is a considerably extended version of our paper Intuitionistic fuzzy automata and associated fuzzy topologies (which contained no proofs), in the Proceedings of the Intern. Conf. on Computing: Theory and Applications (ICCTA 2007, 5–7 March 2007, ISI Kolkata, India), IEEE Computer Society, 267–271, 2007.

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Srivastava, A.K., Tiwari, S.P. IF-topologies and IF-automata. Soft Comput 14, 571–578 (2010). https://doi.org/10.1007/s00500-009-0427-z

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