The Axiomatization Definition of the Pseudo Measure of Fuzziness and the Pseudo Measure of Fuzziness of a Cosine Function

The paper puts forward the axiomatization definition of pseudo measure of fuzziness by means of antithesis. It also constructs and proves the pseudo measure of fuzziness of a cosine function, giving the relationship between measure of fuzziness and pseudo measure of fuzziness. A proximity is also constructed through the relationship between measure of fuzziness, pseudo measure of fuzziness and measure of proximity, and a kind of mathematical models of optimization problems are formed through measure of proximity.