Savo G. Glisic

Artificial Intelligence and Quantum Computing for Advanced Wireless Networks


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form and Eq. (4.43), the decision function in terms of the fuzzy model by fuzzy mean defuzzification becomes

      Motivated by the underlying concept of granularity, both the kernel in Eq. (4.60) and the fuzzy membership function in Eq. (4.59) are information granules. The kernel is a similarity measure between the support vector and the non‐support vector in SVR, and fuzzy membership functions associated with fuzzy sets are essentially linguistic granules, which can be viewed as linked collections of fuzzy variables drawn together by the criterion of similarity. Hence, [97–99] regarded kernels as the Gaussian membership function of the t‐norm‐based algebra product

      Constructing interpretable kernels: Besides Gaussian kernel functions such as Eq. (4.61), there are some other common forms of membership functions:

      The triangle membership function:

mu Subscript t Baseline left-parenthesis x comma b comma gamma right-parenthesis equals max left-brace right-brace comma minus minus 1 minus minus bar bar x bar bar b gamma comma 0 comma y greater-than 0 period

      The generalized bell‐shaped membership function:

mu Subscript b Baseline left-parenthesis x comma b comma a right-parenthesis equals StartFraction 1 Over 1 plus left-parenthesis StartFraction x minus b Over a EndFraction right-parenthesis squared EndFraction comma a greater-than 0 mu Subscript italic trace Baseline left-parenthesis x comma b comma a comma c right-parenthesis equals StartLayout Enlarged left-brace 1st Row 1st Column 1 2nd Column b minus a less-than-or-equal-to x less-than-or-equal-to b plus a 2nd Row 1st Column max left-brace right-brace comma minus minus 1 bar bar minus minus bar bar xb minus minus ac comma 0 2nd Column otherwise comma a greater-than 0 comma c greater-than </p>
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