A note on belief structures and s-approximation spaces

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space

A note on belief structures and s-approximation spaces

We study relations between evidence theory and S-approximation spaces. Both theories have their roots in the analysis of Dempsterchr('39')s multivalued mappings and lower and upper probabilities, and have close relations to rough sets. We show that an S-approximation space, satisfying a monotonicity condition, can induce a natural belief structure which is a fundamental block in evidence theory. We also demonstrate that one can induce a natural belief structure on one set, given a belief structure on another set, if the two sets are related by a partial monotone S-approximation space

Why Philosophers Should Care About Computational Complexity

One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In particular, I argue that computational complexity theory---the field that studies the resources (such as time, space, and randomness) needed to solve computational problems---leads to new perspectives on the nature of mathematical knowledge, the strong AI debate, computationalism, the problem of logical omniscience, Hume's problem of induction, Goodman's grue riddle, the foundations of quantum mechanics, economic rationality, closed timelike curves, and several other topics of philosophical interest. I end by discussing aspects of complexity theory itself that could benefit from philosophical analysis.Comment: 58 pages, to appear in "Computability: G\"odel, Turing, Church, and beyond," MIT Press, 2012. Some minor clarifications and corrections; new references adde

Spacetime Reduction of Large N Flavor Models: A Fundamental Theory of Emergent Local Geometry?

We introduce a novel spacetime reduction procedure for the fields of a supergravity-Yang-Mills theory in generic curved spacetime background, and with large N flavor group, to linearized forms on an infinitesimal patch of local tangent space at a point in the spacetime manifold. Our new prescription for spacetime reduction preserves all of the local symmetries of the continuum field theory Lagrangian in the resulting zero-dimensional matrix Lagrangian, thereby obviating difficulties encountered in previous matrix proposals for emergent spacetime in recovering the full nonlinear symmetries of Einstein gravity. We conjecture that the zero-dimensional matrix model obtained by this prescription for spacetime reduction of the circle-compactified type I-I'-mIIA-IIB-heterotic supergravity-Yang-Mills theory with sixteen supercharges and large N flavor group, and inclusive of the full spectrum of Dpbrane charges, offers a potentially complete framework for nonperturbative string/M theory. We explain the relationship of our conjecture for a fundamental theory of emergent local spacetime geometry to recent investigations of the hidden symmetry algebra of M theory, stressing insights that are to be gained from the algebraic perspective. We conclude with a list of open questions and directions for future work.Comment: 30pgs. v6: Ref [4] added, some terminology corrected in Intro, sections 5,6. Footnote 2 clarifies the relation to hep-th/0201129v1. Acknowledgments adde

Review and prioritization of investment projects in the Waste Management organization of Tabriz Municipality with a Rough Sets Theory approach

Purpose: Prioritization of investment projects is a key step in the process of planning the investment activities of organizations. Choosing the suitable projects has a direct impact on the profitability and other strategic goals of organizations. Factors affecting the prioritization of investment projects are complex and the use of traditional methods alone cannot be useful, so there is a need to use a suitable model for prioritizing projects and investment plans. The purpose of this study is to prioritize projects and investment methods for projects (10 projects) considered by the Waste Management Organization of Tabriz Municipality. Methodology: The method of analysis used is the theory of rough, so that first the important investment projects in the field of waste management were determined using the research background and opinion of experts and the weight and priority of the projects were obtained using the Rough Sets Theory. Then, the priority of appropriate investment methods (out of 6 methods) of each project was obtained using Rough numbers, the opinion of experts and other aspects. Findings: The result of the research has been that construction project of a specialized recycling town, plastic recycling project, and recycled tire recycling project are three priority projects of Tabriz Municipality Waste Management Organization, respectively. Three investment methods, civil partnership agreements, BOT, and BOO can be used for them. Originality/Value: Tabriz Municipality Waste Management is an important and influential organization in the activities of the city, in which the investment methods in its projects are mostly based on common contracts and are performed in the same way for all projects. This research offers new methods for projects and their diversity according to Rough Sets technique