Generalized triangular norm and conorm aggregation operators on ordinal spaces

We describe the basic features of the t-norm operator and then introduce a family of t-norm operators that are defined on an ordinal space. We then do the same for the t-conorms. We note the strong limitation that the requirement of associativity places on the t-norm and t-conorm operators. We particularly note how it limits our ability to model different types of reinforcement. We then define a generalization of the t-conorm aggregation operator, which relaxes the requirement of associativity, we denote these operators as GENOR operators. We show that these operators have the same functionality as the t-conorm. We provide some examples of GENOR operators which allow us to control the reinforcement process. We define a related extension for the t-norm, the GENAND operator and provide some examples.     

Cumulative distribution functions from Dempster-Shafer belief structures

We discuss the Dempster-Shafer belief structure. We introduce the idea of a cumulative distribution induced by a Dempster-Shafer belief structure. We call these belief-cumulative distribution (B-CDs) functions. We study the properties of these distribution functions and show that they are interval functions. We investigate the possibility of using these distribution functions as a tool for knowledge representation.     

Pythagorean Membership Grades,Complex Numbers,and Decision Making

We describe the idea of Pythagorean membership grades and the related idea of Pythagorean fuzzy subsets. We focus on the negation and its relationship to the Pythagorean theorem. We look at the basic set operations for the case of Pythagorean fuzzy subsets. A relationship is shown between Pythagorean membership grades and complex numbers. We specifically show that Pythagorean membership grades are a subclass of complex numbers called Π‐i numbers. We investigate operations that are closed under Π‐i numbers. We consider the problem of multicriteria decision making with satisfactions expressed as Pythagorean membership grades, Π‐i numbers. We look at the use of the geometric mean and ordered weighted geometric operator for aggregating criteria satisfaction.     

OWA aggregation over a continuous interval argument with applications to decision making

We briefly describe the ordered weighted average (OWA) operator. We discuss its role in decision making under uncertainty. We provide an extension of the OWA operator to the case in which our argument is a continuous valued interval rather than a finite set of values. We look at some examples of this type of aggregation. We show how it can be used in some tasks that arise in decision making. We consider the extension of the continuous interval argument OWA operator to the more general case in which the argument values have importance weights. We use this to introduce the idea of an attitudinal-based expected value associated with a continuous random variable.     

An object-oriented database system Jasmine: implementation,application, and extension

We have devised an object oriented DBMS called Jasmine for advanced applications. The paper describes the implementation, application and extension of Jasmine in detail. We focus on the impact of the design of its object oriented model and language on database implementation technology. We describe what part of traditional relational database technology we extend to handle object oriented features such as object identifiers, complex objects, class hierarchies, and methods. We introduce nested relations to efficiently store and access clustered complex objects. We use hash based methods to efficiently access nonclustered complex objects. We provide user defined functions directly evaluated on page buffers to efficiently process method invocation. We devise object oriented optimization of queries including class hierarchies, complex objects, and method invocation. We incorporate dedicated object buffering to allow efficient access to objects through object identifiers. We also describe nontrivial applications of Jasmine and discuss the validity of object oriented databases. We focus on a constraint management facility, which can be implemented by taking advantage of the extensibility of Jasmine. The facility includes constraint rules, called design goals, for automatic database population required by engineering applications. Finally, we describe a view facility for schema integration also needed by engineering applications in distributed environments. We focus on how we extend Jasmine to implement the facility     

On the dempster-shafer framework and new combination rules

We discuss the basic concepts of the Dempster-Shafer approach, basic probability assignments, belief functions, and probability functions. We discuss how to represent various types of knowledge in this framework. We discuss measures of entropy and specificity for belief structures. We discuss the combination and extension of belief structures. We introduce some concerns associated with the Dempster rule of combination inherent in the normalization due to conflict. We introduce two alternative techniques for combining belief structures. The first uses Dempster's rule, while the second is based upon a modification of this rule. We discuss the issue of credibility of a witness.     

ON THE THEORY OF BAGS

We introduce the bag structure as a set-like object in which repeated elements are significant. We discuss operations on bags such as intersection, union and addition. We introduce the operation of selecting elements from a bag based upon their membership in a set. We show the usefulness of the bag structure in relational data bases. We provide a definition for fuzzy bags. In these fuzzy bags the count of the number of elements itself becomes a crisp bags. We investigate a calculus for fuzzy bags.     

On models of developing systems and their applications

We consider integral models based on the mathematical model proposed by V.M. Glushkov. We describe a two-sector version of the Glushkov model and consider the identification problem for model parameters. We propose a numerical identification method and present results of test computations. We consider the problem of power grid field described with a one-sector version of the Glushkov model. We give computational results based on real data.     

Appliances for whom? Considering place

We discuss homes as potential settings for the products of appliance design. We catalog the large international and regional differences. We look at differences in terms of infrastructure: heating, plumbing, electricity, and telephony. We examine differences in the home itself in terms of number of household members, and size of dwelling. We explore the implications of this variation for future ethnographies as well as product creation as we ask the question “appliances for whom?”     

A line-space analysis of light-field representations

We study how to build optimal light-field or plenoptic models. We quantify geometric errors in light-field representations and show how geometric error bounds directly affect rendering artifacts. Artifacts depend on how the light-field is parameterized, stored, reconstructed and rendered. We present the rendering artifacts and relate them to the presence of geometric errors in the four most common light-field implementations.We show how to optimize a light-field model. We take an arbitrary bounded object and construct the best possible representation using each of the four parameterizations. The best representation has the least geometric error bounds. We use two geometric errors, a positional and a directional error. We also quantify pixelation artifacts. Our analysis is useful to decide how to build a light-field model. It helps select a parameterization, build an optimal representation, and choose the samplings of the parameter spaces so that geometric errors and rendering artifacts are minimized.     

INTRODUCTION TO A LEARNING GENERAL THEORY

We explain the significance of a learning general theory. We work in a resolution informational level that is defined on a population. The populational magnitude changes through the creation or destruction of individual systems; we express this creation or destruction by means of the reproducibility, which produces a selective discrimination on the population. We define the reinforcement as far as a goal variable is concerned and separate the reinforcement by selective discrimination and the reinforcement by a change of the conditional probability. We also define memory accumulation and reinforcement on individual systems and study The effectiveness and the regularity of reinforcement in relation to the goal. We define the information on a variable and its learning; we study the relation between learning and reinforcement and the transference of learning. We define the controlled system and its information and study its learning. We define organized learning, with memory accumulation, and closed control. We introduce axiomatics and study their consequences, their testing through modeling, and the possible repercussions of the theory.     

The law of large numbers for fuzzy processes and the estimation problem

We study how the law of large numbers can be extended to the case of fuzzy numbers. We work with L-fuzzy sets, where L is a CL_∞ commutative monoid with an operation 1. We define the 1-independence of fuzzy numbers. We find, when 1 is the operation Λ of the lattice, that the arithmetical mean of Λ-independent fuzzy numbers does not converge. We think that this case could be a limit one; we show, for particular cases of the 1-operation, that generally convergence holds. We build estimators for fuzzy models; we particularly consider the “minimum fuzziness estimator.” We study the convergence of these estimators and compare them by way of the fuzzy subsets they induce. We lastly study the case where we have dependent fuzzy numbers and particularly the case of linearly filtered “1-autoindependent” fuzzy processes.     

H∞ control for discrete-time Takagi-Sugeno fuzzy systems

We consider the design problem of H X controllers for discrete-time fuzzy systems. We introduce two Riccati inequalities from the standard H X theory, one for the state feedback controller, the other for the filter gain. We rewrite the second inequality and obtain an equivalent inequality for the inverse. We then rewrite this using LMI to obtain the final form of the inequality and show that the proposed output feedback controller is n -suboptimal. We give two examples and construct n -suboptimal controllers for them.     

Measures of assurance and opportunity in modeling uncertain information

Our focus is on the representation of uncertain information using set measures. We first discuss the basic properties of monotonic set measures. We then discuss the appropriateness of their use in modeling uncertain information. We look at some notable types of measures of uncertain information and investigate in considerable detail cardinality‐based measures. We look at the Sugeno measure and provide a formulation of the underlying cardinality‐based measures. We then look at quasi‐additive uncertainty measures. We discuss the entropy and attitudinal character of an uncertainty measure. Finally, we introduce the ideas of the assurance and opportunity of the occurrence of an outcome. © 2012 Wiley Periodicals, Inc.     

Solving Uncalibrated Photometric Stereo Using Fewer Images by Jointly Optimizing Low-rank Matrix Completion and Integrability

We introduce a new, integrated approach to uncalibrated photometric stereo. We perform 3D reconstruction of Lambertian objects using multiple images produced by unknown, directional light sources. We show how to formulate a single optimization that includes rank and integrability constraints, allowing also for missing data. We then solve this optimization using the Alternating Direction Method of Multipliers (ADMM). We conduct extensive experimental evaluation on real and synthetic data sets. Our integrated approach is particularly valuable when performing photometric stereo using as few as 4–6 images, since the integrability constraint is capable of improving estimation of the linear subspace of possible solutions. We show good improvements over prior work in these cases.     

Probabilities in the OWA operator

We analyze the use of the probability in the ordered weighted average (OWA). We introduce the probabilistic OWA (POWA) operator. It is an aggregation operator that provides a parameterized family of aggregation operators between the minimum and the maximum that considers the degree of importance that the probability and the OWA operator have in the aggregation. We study some of its main properties and particular cases. We also study the construction of interval and fuzzy numbers with POWA operators. We study the applicability of the POWA operator and we see that it is very broad because all the previous studies that use the probability can be revised with this new approach. We develop an application in a group decision making problem regarding investment selection.     

Analysis of integer programming algorithms with L-partition and unimodular transformations

We study algorithms for solving integer linear programming problems, in particular, set packing and knapsack problems. We pay special attention to algorithms of lexicographic enumeration of L-classes and their combinations with other approaches. We study the problems of using unimodular transformations in order to improve the structure of the problems and speed up the algorithms. We construct estimates on the number of iterations for the algorithms that take into account the specific structure of the problems in question. We also show experimental results.     

Modeling multi-criteria objective functions using fuzzy measures

We introduce the idea of a measure. We describe several important finite integrals useful for obtaining an average value of a collection of argument values weighted by a measure. We particularly look at the case of binary measures and show that all integrals in this case evaluate to the same value. We describe the use of measures in multi-criteria decision making as a way of expressing a decision maker’s objective function in terms of collection of relevant criteria. We look at the role of an integral as a way to evaluate an alternative’s overall satisfaction to their objective function in terms of its satisfaction to the individual criteria. We look at a number of special types of measure based decision objective functions.     

Constrained traffic equilibrium in routing

We study noncooperative routing in which each user is faced with a multicriterion optimization problem, formulated as the minimization of one criterion subject to constraints on others. We address the questions of existence and uniqueness of equilibrium. We show that equilibria indeed exist but uniqueness may be destroyed due to the multicriteria nature of the problem. We obtain uniqueness in some weaker sense under appropriate conditions: we show that the link utilizations are uniquely determined at equilibrium. We further study the normalized constrained equilibrium and apply it to pricing.