An invariant approach to dynamical fuzzy spaces with a three-index variable

A dynamical fuzzy space might be described by a three-index variable C_{ab}^c, which determines the algebraic relations f_a f_b =C_{ab}^c f_c among the functions f_a on the fuzzy space. A fuzzy analogue of the general coordinate transformation would be given by the general linear transformation on f_a. I study equations for the three-index variable invariant under the general linear transformation, and show that the solutions can be generally constructed from the invariant tensors of Lie groups. As specific examples, I study SO(3) symmetric solutions, and discuss the construction of a scalar field theory on a fuzzy two-sphere within this framework.Comment: Typos corrected, 12 pages, 8 figures, LaTeX, JHEP clas

Supplier selection based on two-phased fuzzy decision making / Fairuz Shohaimay...[et. al.]

Supplier selection depends on human evaluation which is subjective and vague in nature. Fuzzy approach is deemed appropriate to measure these uncertainties in the decision making process, rather than using real or crisp values. Predominant in many studies on fuzzy decision making, fixed triangular or trapezoidal fuzzy numbers with symmetric spread from the literature were incorporated. However, these fuzzy numbers do not explain the actual respondents’ opinions which will affect the overall decision making process. Therefore, fuzzy numbers based on respondents should be developed beforehand to be integrated into the existing fuzzy decision making tool. This paper aims to develop triangular fuzzy numbers based on respondents’ opinions. These fuzzy numbers were adopted into a fuzzy evaluation method used in a supplier selection problem. The ranking results were analyzed using three different groups of fuzzy numbers. It was found that the linguistic terms for all three groups are not symmetric with the largest difference in spread that occurs for G2. There is also a variation in ranking of sub-criterion “Background of Supplier” in G2. Future studies in fuzzy decision making should include fuzzy numbers built based on respondents as they provide more reliable outcomes

Relations on FP-Soft Sets Applied to Decision Making Problems

In this work, we first define relations on the fuzzy parametrized soft sets and study their properties. We also give a decision making method based on these relations. In approximate reasoning, relations on the fuzzy parametrized soft sets have shown to be of a primordial importance. Finally, the method is successfully applied to a problems that contain uncertainties.Comment: soft application

Noncommutative Spherically Symmetric Spaces

We examine some noncommutative spherically symmetric spaces in three space dimensions. A generalization of Snyder's noncommutative (Euclidean) space allows the inclusion of the generator of dilations into the defining algebra of the coordinate and rotation operators. We then construct a spherically symmetric noncommutative Laplacian on this space having the correct limiting spectrum. This is presented via a creation and annihilation operator realization of the algebra, which may lend itself to a truncation of the Hilbert space.Comment: 9 pages, revtex, matches Phys.Rev.D versio