One of the most important aspects of fuzzy systems is that they are easily understandable and interpretable. This property, however, does not come for free but poses some essential constraints on the parameters of a fuzzy system (like the linguistic terms), which are sometimes overlooked when learning fuzzy system automatically from data. In this paper, an objective function-based approach to l...

In this article we study a fundamental statistical problem: how to optimally pick the objective to be minimized in a parametric regression when we have information about the error distribution. The classical answer to the problem we posed at the beginning, maximum likelihood, was given by Fisher (5) in the specific case of multinomial models and then at succeeding levels of generality by Cramér...

The Field-wise Objective Function is an important concept in eldwise wind retrieval. A discussion on the purpose of the eld-wise objective function is presented. Several variations of the eld-wise objective function are compared. The gradient vectors and Hessian matrices are derived for each variation. 1 An Overview of Field-wise Objective Functions An objective function is an error metric, pro...

Assumptions about sell-side analysts’ objective function are critical to empirical researchers’ understanding of their incentives and the resulting behavior. This paper provides empirical evidence about the objective function underlying analysts’ choice of forecasts. In contrast to approaches used in previous papers which rely exclusively on statistical properties of forecasts, I compare theore...

In this paper, a new objective function to tune the PID/PI-PD controller is proposed by modifying the integral error squared (ISE) criterion. A new entrant to the family of evolutionary algorithms namely bacterial foraging is used to find the controller parameters by minimizing the objective function. The controller gives a smooth process output with almost zero percent overshoot as desired in ...

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In this paper we analyze several new methods for solving optimization problems with the objective function formed as a sum of two convex terms: one is smooth and given by a black-box oracle, and another is general but simple and its structure is known. Despite to the bad properties of the sum, such problems, both in convex and nonconvex cases, can be solved with efficiency typical for the good ...

Many different algorithms and objective functions for topographic mappings have been proposed. We show that several of these approaches can be seen as particular cases of a more general objective function. Consideration of a very simple mapping problem reveals large differences in the form of the map that each particular case favors. These differences have important consequences for the practic...

We ascertain the modularity-like objective function whose optimization is equivalent to the maximum likelihood in annotated networks. We demonstrate that the modularity-like objective function is a linear combination of modularity and conditional entropy. In contrast with statistical inference methods, in our method, the influence of the metadata is adjustable; when its influence is strong enou...