The notion of fuzzy set theory has not so far been districted over medical diagnosis. There are some added applications, for example, in image processing, pattern identification, and many medical devices. In this research article, we introduced a new mediative fuzzy ranking technique as the fuzzy extension in decision making. The proposed mediative fuzzy logic-based technique is more relevant and applicable to incomplete and doubtful situations or some contradictions present in the expert knowledge. The value of the contradictory degree for mediative fuzzy sets used in the extension principle is defined. The proposed mediative fuzzy ranking method is easily implemented in the medical field, and the proposed mediative fuzzy extension-based measured technique is useful to medical experts and doctors in many decision-making situations; the entire work is illustrated with numerical examples. We have also given some future aspects of mediative fuzzy extension in the interpretation of type-2 intuitionistic fuzzy sets.

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In this research paper, we proved some general theorems on the absolute convergence transformation of matrix which is expressed in terms of preserving transformation under the very general conditions. This works is motivated by the works of [3],[12] and [14].

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In this research paper, the authors studied some problems related to harmonic summability of double Fourier series on Nörlund summability method. These results constitute substantial extension and generalization of related work of Moricz [<a href="#1">1</a>] and Rhodes <i>et al.</i>, [<a href="#2">2</a>]. We also constructed a new result on \((N,p^{(1)}_b,p^{(2)}_a)\) by regular Nörlund method of summability.