Feasible algorithms for approximate reasoning using fuzzy logic

Deductive reasoning with classical logic is hampered when imprecision is present in the variables, although human reasoning can cope quite adequately with vague concepts. A new approach to reasoning which allows imprecise conclusions to be drawn consistently from imprecise premises was introduced by Baldwin [2]. This method is economical in calculation as it avoids the high dimensionality that fuzzy set representations often involve.This paper briefly reviews the method from an operational viewpoint, isolating the individual processes that are used in the method. A feasible algorithm for computing each process is then presented.It is assumed that the reader is familiar with the concept of, and operations on, fuzzy sets introduced by Zadeh [14].     

A critical assessment of truth functional modification and its use in approximate reasoning

We examine the inconsistencies in the current notion of fuzzy truth values and show how these have arisen from an attempt to equate two separate concepts. We argue that any approximate reasoning system based on truth functional modification is redundnat and inefficient.     

Real-time moving object segmentation in H.264 compressed domain based on approximate reasoning

This paper presents a real-time segmentation algorithm to obtain moving objects from the H.264 compressed domain. The proposed segmentation works with very little information and is based on two features of the H.264 compressed video: motion vectors associated to the macroblocks and decision modes. The algorithm uses fuzzy logic and allows to describe position, velocity and size of the detected regions in a comprehensive way, so the proposed approach works with low level information but manages highly comprehensive linguistic concepts. The performance of the algorithm is improved using dynamic design of fuzzy sets that avoids merge and split problems. Experimental results for several traffic scenes demonstrate the real-time performance and the encouraging results in diverse situations.     

Approximate reasoning and finite state machines to the detection of actions in video sequences

In this paper a novel approach for recognizing actions in video sequences is presented, where the information obtained from the segmentation and tracking algorithms is used as input data. First of all, the fuzzification of input data is done and this process allows to successfully manage the uncertainty inherent to the information obtained from low-level and medium-level vision tasks, to unify the information obtained from different vision algorithms into a homogeneous representation and to aggregate the characteristics of the analyzed scenario and the objects in motion. Another contribution is the novelty of representing actions by means of an automaton and the generation of input symbols for the finite automaton depending on the comparison process between objects and actions, i.e., the main reasoning process is based on the operation of automata with capability to manage fuzzy representations of all video data. The experiments on several real traffic video sequences demonstrate encouraging results, especially when no training algorithms to obtain predefined actions to be identified are required.     

An acceleration property of theE-algorithm for alternate sequences

We prove a convergence acceleration result by theE-algorithm for sequences whose error has an asymptotic expansion on the scale of comparison for which a determinantal relation holds. This result is generalized to the vector case. Moreover we prove a result which contains an acceleration property for columns and diagonals of theE array. This result is applied to some alternating series.     

A finite characterization ofK-matrices in dimensions less than four

The class of realn × n matricesM, known asK-matrices, for which the linear complementarity problemw – Mz = q, w 0, z 0, w ^T z =0 has a solution wheneverw – Mz =q, w 0, z 0 has a solution is characterized for dimensionsn <4. The characterization is finite and practical. Several necessary conditions, sufficient conditions, and counterexamples pertaining toK-matrices are also given. A finite characterization of completelyK-matrices (K-matrices all of whose principal submatrices are alsoK-matrices) is proved for dimensions <4.Partially supported by NSF Grant MCS-8207217.Research partially supported by NSF Grant No. ECS-8401081.     

Characterizations of spaces in the unit ball of

Let B denote the unit ball of . For 0<p<∞, the holomorphic function spaces Q_p and Q_p,0 on the unit ball of are defined as

and

In this paper, we give some derivative-free, mixture and oscillation characterizations for Q_p and Q_p,0 spaces in the unit ball of .     

On convergence theory in fuzzy topological spaces and its applications

In this paper we introduce and study new concepts of convergence and adherent points for fuzzy filters and fuzzy nets in the light of the Q-relation and the Q-neighborhood of fuzzy points due to Pu and Liu [28]. As applications of these concepts we give several new characterizations of the closure of fuzzy sets, fuzzy Hausdorff spaces, fuzzy continuous mappings and strong Q-compactness. We show that there is a relation between the convergence of fuzzy filters and the convergence of fuzzy nets similar to the one which exists between the convergence of filters and the convergence of nets in topological spaces.     

A Method of Deducing L-Polyhedra for n-Lattices

We suggest a method for selecting an L-simplex in an L-polyhedron of an n-lattice in Euclidean space. By taking into account the specific form of the condition that a simplex in the lattice is an L-simplex and by considering a simplex selected from an L-polyhedron, we present a new method for describing all types of L-polyhedra in lattices of given dimension n. We apply the method to deduce all types of L-polyhedra in n-dimensional lattices for n=2,3,4, which are already known from previous results.     

Equivalence and existence of weak Pareto optima for multiobjective optimization problems with cone constraints

In this work, a differentiable multiobjective optimization problem with generalized cone constraints is considered, and the equivalence of weak Pareto solutions for the problem and for its η-approximated problem is established under suitable conditions. Two existence theorems for weak Pareto solutions for this kind of multiobjective optimization problem are proved by using a Karush–Kuhn–Tucker type optimality condition and the F-KKM theorem.     

Zero-Term Ranks of Real Matrices and Their Preservers

Zero-term rank of a matrix is the minimum number of lines (rows or columns) needed to cover all the zero entries of the given matrix. We characterize the linear operators that preserve zero-term rank of the m× nreal matrices. We also obtain combinatorial equivalent condition for the zero-term rank of a real matrix.     

Q-Operator and the Drinfeld Equation

We show that the TQ equation is satisfied by the trace over the quantum space of the product of R-matrices intertwining two representations of the quantum double of the Borel subalgebra of the affine algebra (the standard two-dimensional and the N-dimensional cyclic representations).     

Cubically convergent method for locating a nearby vertex in linear programming

Given a point sufficiently close to a nondegenerate basic feasible solutionx* of a linear program, we show how to generate a sequence {p ^k} that converges to the 0–1 vector sign(x*) at aQ-cubic rate. This extremely fast convergence enables us to determine, with a high degree of certainty, which variables will be zero and which will be nonzero at optimality and then constructx* from this information.This research was supported in part by NSF Cooperative Agreement No. CCR-8809615, by AFOSR Grant No. 89-0363, and by DOE Grant No. DEFG05-86ER 25017. The authors would like to thank Bob Bixby for helpful discussions.     

Q-curvature flow on 4-manifolds

We formulate an appropriate gradient flow in order to study the evolution of the Q-curvature to a prescribed function on a 4-manifold. For a class of prescribed functions, we show convergence and describe the asymptotic behaviour at infinity.     

Triangle-free distance-regular graphs

Let Γ denote a distance-regular graph with diameter d≥3. By a parallelogram of length 3, we mean a 4-tuple xyzw consisting of vertices of Γ such that ∂(x,y)=∂(z,w)=1, ∂(x,z)=3, and ∂(x,w)=∂(y,w)=∂(y,z)=2, where ∂ denotes the path-length distance function. Assume that Γ has intersection numbers a ₁=0 and a ₂≠0. We prove that the following (i) and (ii) are equivalent. (i) Γ is Q-polynomial and contains no parallelograms of length 3; (ii) Γ has classical parameters (d,b,α,β) with b<−1. Furthermore, suppose that (i) and (ii) hold. We show that each of b(b+1)²(b+2)/c ₂, (b−2)(b−1)b(b+1)/(2+2b−c ₂) is an integer and that c ₂≤b(b+1). This upper bound for c ₂ is optimal, since the Hermitian forms graph Her₂(d) is a triangle-free distance-regular graph that satisfies c ₂=b(b+1). Work partially supported by the National Science Council of Taiwan, R.O.C.     

The Subconstituent Algebra of an Association Scheme (Part III)

This is the continuation of an article from the previous issue. In this part, we focus on the thin P- and Q-polynomial association schemes. We provide some combinatorial characterizations of these objects and exhibit the known examples with diameter at least 6. For each example, we give the irreducible modules for the subconstituent algebra. We close with some conjectures and open problems.     

The Subconstituent Algebra of an Association Scheme, (Part I)

We introduce a method for studying commutative association schemes with many vanishing intersection numbers and/or Krein parameters, and apply the method to the P- and Q-polynomial schemes. Let Y denote any commutative association scheme, and fix any vertex x of Y. We introduce a non-commutative, associative, semi-simple -algebra T = T(x) whose structure reflects the combinatorial structure of Y. We call T the subconstituent algebra of Y with respect to x. Roughly speaking, T is a combinatorial analog of the centralizer algebra of the stabilizer of x in the automorphism group of Y.In general, the structure of T is not determined by the intersection numbers of Y, but these parameters do give some information. Indeed, we find a relation among the generators of T for each vanishing intersection number or Krein parameter.We identify a class of irreducible T-moduIes whose structure is especially simple, and say the members of this class are thin. Expanding on this, we say Y is thin if every irreducible T(y)-module is thin for every vertex y of Y. We compute the possible thin, irreducible T-modules when Y is P- and Q-polynomial. The ones with sufficiently large dimension are indexed by four bounded integer parameters. If Y is assumed to be thin, then sufficiently large dimension means dimension at least four.We give a combinatorial characterization of the thin P- and Q-polynomial schemes, and supply a number of examples of these objects. For each example, we show which irreducible T-modules actually occur.We close with some conjectures and open problems.     

QK空间的插值序列

本文研究了Q_K空间的插值问题.利用复分析和调和分析的方法,获得了单位圆盘上的一个序列{z_n}是Q_K∩H^∞空间的插值序列的一个充分必要条件,推广了Q_p空间的部分结果.