MAXIMUM ENTROPY ALGORITHMS FOR UNCERTAINTY MEASURES

Author(s):  
Y. MAEDA ◽  
H. T. NGUYEN ◽  
H. ICHIHASHI

In decision-making problems when probabilistic information is incomplete (e.g. Nguyen and Walker [1]) as well as in measuring the non-specificity and conflict in the theory of evidence (e.g. Maeda and Ichihashi [2, 3]), one is led to consider the problem of maximizing probabilistic entropy under a functional constraint induced by the available evidence. This paper is devoted specifically to developing computational algorithms for this optimization problem.

Author(s):  
S. Raza Wasi ◽  
J. Darren Bender

An interesting, potentially useful, and fully replicable application of a spatially enabled decision model is presented for pipeline route optimization. This paper models the pipeline route optimization problem as a function of engineering and environmental design criteria. The engineering requirements mostly deal with capital, operational and maintenance costs, whereas environmental considerations ensure preservation of nature, natural resources and social integration. Typically, pipelines are routed in straight lines, to the extent possible, to minimize the capital construction costs. In contrast, longer pipelines and relatively higher costs may occur when environmental and social considerations are part of the design criteria. Similarly, much longer pipelines are less attractive in terms of capital costs and the environmental hazard associated with longer construction area. The pipeline route optimization problem is potentially a complex decision that is most often undertaken in an unstructured, qualitative fashion based on human experience and judgement. However, quantitative methods such as spatial analytical techniques, particularly the least-cost path algorithms, have greatly facilitated automation of the pipeline routing process. In the past several interesting studies have been conducted using quantitative spatial analytical tools for finding the best pipeline route or using non-spatial decision making tools to evaluate several alternates derived through conventional route reconnaissance methods. Most of these studies (that the authors are familiar with) have concentrated on integrating multiple sources of spatial data and performing quantitative least-cost path analysis or have attempted to make use of non-spatial decision making tools to select the best route. In this paper, the authors present a new framework that incorporates quantitative spatial analytical tools with an Analytical Hierarchical Process (AHP) model to provide a loosely integrated but efficient spatial Decision Support System (DSS). Specifically, the goal is to introduce a fully replicable spatial DSS that processes both quantitative and qualitative information, balances between lowest-cost and lowest-impact routes. The model presented in this paper is implemented in a four step process: first, integration of multiple source data that provide basis for engineering and environmental design criteria; second, creation of several alternate routes; third, building a comprehensive decision matrix using spatial analysis techniques; and fourth, testing the alternative and opinions of the stakeholder groups on imperatives of AHP model to simplify the route optimization decision. The final output of the model is then used to carry out sensitivity analysis, quantify the risk, generate “several what and if scenarios” and test stability of the route optimization decision.


2014 ◽  
Vol 20 (2) ◽  
pp. 193-209 ◽  
Author(s):  
Guiwu Wei ◽  
Xiaofei Zhao

With respect to decision making problems by using probabilities, immediate probabilities and information that can be represented with linguistic labels, some new decision analysis are proposed. Firstly, we shall develop three new aggregation operators: generalized probabilistic 2-tuple weighted average (GP-2TWA) operator, generalized probabilistic 2-tuple ordered weighted average (GP-2TOWA) operator and generalized immediate probabilistic 2-tuple ordered weighted average (GIP-2TOWA) operator. These operators use the weighted average (WA) operator, the ordered weighted average (OWA) operator, linguistic information, probabilistic information and immediate probabilistic information. They are quite useful because they can assess the uncertain information within the problem by using both linguistic labels and the probabilistic information that considers the attitudinal character of the decision maker. In these approaches, alternative appraisal values are calculated by the aggregation of 2-tuple linguistic information. Thus, the ranking of alternative or selection of the most desirable alternative(s) is obtained by the comparison of 2-tuple linguistic information. Finally, we give an illustrative example about selection of strategies to verify the developed approach and to demonstrate its feasibility and practicality.


2014 ◽  
Vol 13 (06) ◽  
pp. 1119-1133 ◽  
Author(s):  
Aleksandras Krylovas ◽  
Edmundas Kazimieras Zavadskas ◽  
Natalja Kosareva ◽  
Stanislav Dadelo

This study presents a new KEmeny Median Indicator Ranks Accordance (KEMIRA) method for determining criteria priority and selection criteria weights in the case of two separate groups of criteria for solving multiple criteria decision making (MCDM) problem. Kemeny median method is proposed to generalize experts' opinion. Medians are calculated applying three different measure functions. Criteria weights are calculated and alternatives ranking accomplished by solving optimization problem — minimization of ranks discrepancy function calculated for two groups of criteria. A numerical example for solving specific task of elite selection from security personnel is given to illustrate the proposed method.


Complexity ◽  
2018 ◽  
Vol 2018 ◽  
pp. 1-22 ◽  
Author(s):  
Alberto Pajares ◽  
Xavier Blasco ◽  
Juan M. Herrero ◽  
Gilberto Reynoso-Meza

Traditionally, in a multiobjective optimization problem, the aim is to find the set of optimal solutions, the Pareto front, which provides the decision-maker with a better understanding of the problem. This results in a more knowledgeable decision. However, multimodal solutions and nearly optimal solutions are ignored, although their consideration may be useful for the decision-maker. In particular, there are some of these solutions which we consider specially interesting, namely, the ones that have distinct characteristics from those which dominate them (i.e., the solutions that are not dominated in their neighborhood). We call these solutions potentially useful solutions. In this work, a new genetic algorithm called nevMOGA is presented, which provides not only the optimal solutions but also the multimodal and nearly optimal solutions nondominated in their neighborhood. This means that nevMOGA is able to supply additional and potentially useful solutions for the decision-making stage. This is its main advantage. In order to assess its performance, nevMOGA is tested on two benchmarks and compared with two other optimization algorithms (random and exhaustive searches). Finally, as an example of application, nevMOGA is used in an engineering problem to optimally adjust the parameters of two PI controllers that operate a plant.


2004 ◽  
Vol 40 (6) ◽  
pp. 647-681 ◽  
Author(s):  
Thibault Gajdos ◽  
Jean-Marc Tallon ◽  
Jean-Christophe Vergnaud

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