Wafik Boulos Lotfallah

A fuzzy logic approach to the selection of cranes

This paper presents a fuzzy logic approach to select the best crane type in a construction project from the main crane types, namely, mobile, tower and derrick cranes. Each factor of the project is classified as being dynamic or static according to whether the factor does or does not depend on the particular project. Linguistic information about the suitability of each crane type with respect to each factor of the project is translated into either fuzzy sets (for static factors) or fuzzy if–then rules (for dynamic factors). The fuzzy rules are then aggregated into a fuzzy relation between the space of factor property and the space of crane efficiency. In a particular project the experts describe the property as well as the relative importance of each factor. The rules are then fired using the max–min extension principle, and the resulting efficiencies are aggregated with their importance weights. The process identifies the best crane as the one with the highest expected overall efficiency.

Quantitative Methods for Design-Build Team Selection

Use of design-build (DB) contracting by transportation agencies has been steadily increasing as a project delivery system for large complex highway projects. However, moving to DB from traditional design-bid-build procurement can be a challenge. One significant barrier is gaining acceptance of a best value selection process in which technical aspects of a proposal are considered separately and then combined with price to determine the winning proposal. These technical aspects mostly consist of qualitative criteria, thus making room for human errors or biases. Any perceived presence of bias or influence in the selection process can lead to public mistrust and protests by bidders. It is important that a rigorous quantitative mathematical analysis of the evaluation process be conducted to determine whether bias exists and to eliminate it. The paper discusses two potential sources of bias – the evaluators and the weighting model – in the DB selection process and presents mathematical models to detect and remove biases should they exist. A score normalization model deals with biases from the evaluators; then a graphical weight space volume model and a Monte Carlo statistical sampling model are developed to remove biases from the weighting model. The models are then tested and demonstrated using results from the DB bridge replacement project for the collapsed Mississippi River bridge of Interstate 35W in Minneapolis, Minnesota.

The logic of tied implications, part 1: Properties, applications and representation

A conjunction T ties an implication operator A if the identity A(a,A(b,z))=A(T(a,b),z) holds [A.A. Abdel-Hamid, N.N. Morsi, Associatively tied implications, Fuzzy Sets and Systems 136 (2003) 291-311]. We study the class of tied adjointness algebras (which are five-connective algebras on two partially ordered sets), in which the implications are tied by triangular norms. This class contains, besides residuated implications, several other implications employed in fuzzy logic. Nevertheless, we show that the algebraic inequalities of residuated algebras remain true for our tied implications, but in forms that distribute roles over the five connectives of the algebra. We apply the properties of tied implications to a generalized modus ponens inference scheme with two successive rules. We prove its equivalence to a scheme with one compound rule, when both schemata are interpreted by the compositional rule of inference, and all connectives are taken from one tied adjointness algebra. Then we quote another application of this rich theory, a notion of many-valued rough sets, which exhibit the basic mathematical behaviour of the rough sets of Pawlak. A comparator H is said to be prelinear if it satisfies H(y,z)@?H(z,y)=1 for all y,z (Hajek). We introduce prelinear tied adjointness algebras, in which two comparators are prelinear. We provide a representation of those algebras, as subdirect products of tied adjointness chains, on the lines of Hajeks representation of BL-algebras. But our representations are more economical, because we employ minimal prime filters (on residuated lattices) only; rather than all prime filters.

The logic of tied implications, part 2: Syntax

An implication operator A is said to be tied if there is a binary operation T that ties A; that is, the identity A(a, A(b, z)) = A(T (a, b), z) holds for all a, b, z. We aim at the construction of a complete predicate logic for prelinear tied adjointness algebras. We realize this in three steps. In the first step, we establish a propositional calculus AdjTPC, complete for the class of all tied adjointness algebras on partially ordered sets; without prelinearity and ignoring the lattice operations. For that we supply a Hilbert system based on seven axioms and one deduction rule (modus ponens). In the second and third steps, we extend AdjTPC to propositional and predicate calculi; complete for prelinear tied adjointness algebras. We apply a duality principle, due to Morsi, in all three calculi; through which we manage to cut down the number of proofs.

Shrinking games and local formulas

Abstract Gaifmans normal form theorem showed that every first-order sentence of quantifier rank n is equivalent to a Boolean combination of “scattered local sentences”, where the local neighborhoods have radius at most 7 n −1 . This bound was improved by Lifsches and Shelah to 3×4 n −1 . We use Ehrenfeucht–Fraisse type games with a “shrinking horizon” to get a spectrum of normal form theorems of the Gaifman type, depending on the rate of shrinking. This spectrum includes the result of Lifsches and Shelah, with a more easily understood proof and with the bound on the radius improved to 4 n −1 . We also obtain bounds for a normal form theorem of Schwentick and Barthelmann.

Reducing Bias and Uncertainty in Multievaluator Multicriterion Decision Making

AbstractMany decisions are based on more than one criterion, judged by more than a single evaluator. Multievaluator multicriterion (MEMC) decision making can be controversial if bias or uncertainty find their way into the final decision. In fact, both public and private organizations have recently faced challenges when making decisions. In a previous study, the authors of this paper developed a multievaluator decision making model that reduces the effect of possible uncertainty resulting from an evaluator’s insufficient expertise in a particular criterion. This paper builds on the previous model by also correcting for any possible evaluator favoritism or bias. It presents a more comprehensive mathematical model that supports MEMC decisions and protects decision makers and their agencies from potential criticism. Testing of the model shows that it performs better than the simple averaging method on 100% of the simulations.

Characterizing unambiguous precedence systems in expressions without superfluous parentheses

When infix notation is used, parentheses are sometimes omitted according to specified rules, where it is assumed that the operators are stratified in precedence levels, and operators on each level are either left or right associative. Instead of making such an assumption, we carefully analyse the notion of superfluous parentheses by first giving a definition of a general precedence system, which declares the superfluous parenthesis pairs for any given expression. We provide a characterization of unambiguity in this general setting, and study the complexity of parsing expressions without superfluous parentheses. Also, we study the two notions of maximal unambiguous and complete precedence systems, and give a characterization for each one of these notions. Finally, we show that complete precedence systems can be equivalently described by a chain of left associative and right associative classes of operators, with some extra restrictions on the relative positions and the associativity of unary operators.

A local normal form theorem for infinitary logic with unary quantifiers

We prove a local normal form theorem of the Gaifman type for the infinitary logic L∞ω(Qu)ω whose formulas involve arbitrary unary quantifiers but finite quantifier rank. We use a local Ehrenfeucht-Fraisse type game similar to the one in [9]. A consequence is that every sentence of L∞ω(Qu)ω of quantifier rank n is equivalent to an infinite Boolean combination of sentences of the form (∃≥iy)ψ(y), where ψ(y) has counting quantifiers restricted to the (2n–1 – 1)-neighborhood of y. (© 2005 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Modeling Project Manager Competency: An Integrated Mathematical Approach

AbstractAlthough the construction industry is a major component of the U.S. economy, it has been suffering from declining productivity for decades. The human element, project managers (PMs) in particular, are key in solving these persisting problems. Measurement of a PM’s overall performance is important to identify training needs and enables executives to better match competent PMs with the appropriate projects. This paper provides the construction industry with a generic mathematical formulation to reliably weigh different PM competencies. The developed data-driven mathematical model reflects the relative importance that industry practitioners place on different PM competencies while distinguishing exceptional PMs from average ones. This developed model is applied to a data set of 124 PM assessments filled by 62 PM supervisors so that each PM supervisor selected and rated an exceptional PM and an average PM. The results presented in the paper suggest that PMs should focus on developing their cognitive s...

Uncertainty Reduction in Multi-Evaluator Decision Making

When selecting construction design-build teams, subjective multi-evaluator decision making can be controversial and can lead to project delay, loss of public trust, and increased legal fees. This paper introduces a mathematical algorithm that supports multi-evaluator selection decisions by detecting and reducing the effect of possible uncertainty in the scores given by the evaluators. The algorithm was coded and tested using several scenarios. The study results show that the model is robust and capable of extracting the maximum knowledge from the scores given by evaluators with varying degrees of expertise. Simulation results show that the proposed model performed better than the simple averaging method 89% of the time. The outcome of this research provides the decision maker with a justified basis to proceed with the selection decision.