| Summary: | This manuscript contains several new notions including intuitionistic fuzzy <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula> metric space, intuitionistic fuzzy quasi-<inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula>-metric space, intuitionistic fuzzy pseudo-<inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi>S</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula>-metric space, intuitionistic fuzzy quasi-<inline-formula><math display="inline"><semantics><mrow><mi>N</mi></mrow></semantics></math></inline-formula>-metric space and intuitionistic fuzzy pseudo <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula> fuzzy metric space. We prove decomposition theorem and fixed-point results in the setting of intuitionistic fuzzy pseudo <inline-formula><math display="inline"><semantics><mrow><msub><mrow><mi>N</mi></mrow><mrow><mi>b</mi></mrow></msub></mrow></semantics></math></inline-formula> fuzzy metric space. Further, we provide several non-trivial examples to show the validity of introduced notions and results. At the end, we solve an integral equation, system of linear equations and nonlinear fractional differential equations as applications.
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