Fuzzy linear programming under interval uncertainty based on IFS representation

  • Authors:

  • Dipti Dubey;Suresh Chandra;Aparna Mehra

  • Affiliations:

  • Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India;Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India;Department of Mathematics, Indian Institute of Technology, Hauz Khas, New Delhi 110016, India

  • Venue:
  • Fuzzy Sets and Systems
  • Year:
  • 2012

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Abstract

The equivalence between the interval-valued fuzzy set (IVFS) and the intuitionistic fuzzy set (IFS) is exploited to study linear programming problems involving interval uncertainty modeled using IFS. The non-membership of IFS is constructed with three different viewpoints viz., optimistic, pessimistic, and mixed. These constructions along with their indeterminacy factors result in S-shaped membership functions in the fuzzy counterparts of the intuitionistic fuzzy linear programming models. The solution methodology of Yang et al. [45], and its subsequent generalization by Lin and Chen [33] are used to compute the optimal solutions of the three fuzzy linear programming models.