| Summary: | In this paper, the matrix game based on triangular intuitionistic fuzzy payoff is put forward. Then, we get a conclusion that the equilibrium solution of this game model is equivalent to the solution of a pair of the primal−dual single objective intuitionistic fuzzy linear optimization problems <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>I</mi> <mi>F</mi> <mi>L</mi> <mi>O</mi> <mi>P</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>I</mi> <mi>F</mi> <mi>L</mi> <mi>O</mi> <mi>D</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. Furthermore, by applying the accuracy function, which is linear, we transform the primal−dual single objective intuitionistic fuzzy linear optimization problems <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>I</mi> <mi>F</mi> <mi>L</mi> <mi>O</mi> <mi>P</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>I</mi> <mi>F</mi> <mi>L</mi> <mi>O</mi> <mi>D</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> into the primal−dual discrete linear optimization problems <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>P</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>D</mi> <mn>1</mn> <mo>)</mo> <mo>.</mo> </mrow> </semantics> </math> </inline-formula> The above primal−dual pair <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>P</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>−<inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>D</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> is symmetric in the sense the dual of <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>D</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> is <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>P</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula>. Thus the primal−dual discrete linear optimization problems <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>P</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> and <inline-formula> <math display="inline"> <semantics> <mrow> <mo>(</mo> <mi>G</mi> <mi>L</mi> <mi>O</mi> <mi>D</mi> <mn>1</mn> <mo>)</mo> </mrow> </semantics> </math> </inline-formula> are called the symmetric primal−dual discrete linear optimization problems. Finally, the technique is illustrated by an example.
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