New Mathematics and Natural Computation

Fuzzy spatial models map a substantial degree of preference indifference. It has been shown that different definitions of covering result in different elements in the uncovered set when preference indifference is present. We consider several of the most frequently used definitions of covering relations found in the literature. The first definition that we examine yields an uncovered set, some of the elements of which are not Pareto efficient. Given that there is no reason to expect a set of players comprising a majority to settle for a Pareto deficient outcome, the remainder of the paper considers the ability of alternative definitions to avoid such a result.

We examine the effect of indifference on the existence of a majority rule maximal set. In our setting, it is shown in all but a limited number of cases that the maximal set is empty in an n-dimensional spatial model if and only if the Pareto set contains a union of cycles. The elements that constitute the exception are completely characterized.

The paper suggests Daily Artificial Dispatcher (DAD), as an ambient intelligence that solves the problem for automatic predictive analysis of electric power system (EPS) security and efficiency, using EPS and weather summarized data. DAD is constructed as heading EPS, implementing common sense thinking a day ahead for EPS. DAD is verified, as it is shown that it is an intentional agent, a robot, and an intelligent system. DAD is validated, as it is shown that it is an EPS adequate security and efficiency computation.

The purpose of this paper is to develop a nonlinear programming model and method for solving fuzzy multi-attribute group decision making (FMAGDM) problems with linguistic variables. In this methodology, alternatives are assessed on qualitative attributes using linguistic terms from the designated linguistic term set, which can be expressed with the triangular fuzzy number set designated a priori. Alternatives for decision makers are assessed on the basis of the distances between the ordered weighted averaging (OWA) comprehensive value and the group best alternative which is unknown a priori. The group best alternative is then estimated through solving an auxiliary nonlinear programming model based on the concept that the sum of the distances of alternatives from the group best alternative for the decision makers should be as small as possible. The obtained group best alternative can be expressed using the designated triangular fuzzy numbers, which are corresponding to the designated linguistic terms. A numerical example is examined to demonstrate the difference between the proposed method and the generalized induced OWA operator method.

Traditional mathematics is the language of precision. Statements are either true or false. But, in reality there are few things that are truly simply true or false. Life is full of shades of grey. Capturing these shades of grey has been problematic using traditional mathematics. Mathematics can model the uncertainty itself but rarely incorporates it into the model. However, an emerging area of mathematical inquiry known as the mathematics of uncertainty seeks to overcome some of these problems by integrating the uncertainly, the shades of grey, directly into the model. Fuzzy theory is one of those emerging ideas. This paper is simply an overview of some of the basic mechanics of fuzzy theory and recent economic applications in both micro and macro-economics.

In Ref. 7, the authors use matrix representation-based distances of soft sets to introduce matching function and distance-based similarity measures. We first give counterexamples to show that their Definition 2.7 and Lemma 3.5(3) contain errors, then improve their Lemma 4.4 making it a corollary of our result. The fundamental assumption of Ref. 7 has been shown to be flawed. This motivates us to introduce set operations-based measures. We present a case (Example 6.7) where Majumdar-Samanta similarity measure produces an erroneous result but the measure proposed here decides correctly. Several properties of the new measures have been presented and finally the new similarity measures have been applied to the problem of financial diagnosis of firms.