Max-min Rule Research Articles

How can one improve SAW and max-min multi-criteria rankings based on uncertain decision rules?

The paper aims to improve a simple additive weighting method (SAW) and the max-min rule designed for M-DMC (multi-13 criteria decision making under certainty) based on already developed extensions for the Laplace and Wald rules (applied to one-criterion decision making under uncertainty, i.e., 1-DMU). Some evident analogies between scenario-based 1-DMU and M-DMC have been recently revealed in the literature, which gives the possibility to implement necessary amendments in M-DMC procedures, particularly in the multiple solutions case. The suggested modifications consist of applying additional decision tools (for SAW) and using the lexicographic approach (for the max-min rule). Thanks to them, options, treated as equivalent according to original M-DMC procedures, may obtain different ranks in the ranking. Such an improvement facilitates the decision making process. Both modified methods are illustrated by employing an example concerning the ranking creation for UE countries.

Noncoherent space-time coding for correlated massive MIMO channel with Riemannian distance

This paper considers a massive multiple-input multiple-output (MIMO) uplink system in correlated Rayleigh fading channels. A transmitter with two antennas needs to send data timely to a base station with a large number of antennas. We assume the channel coefficients keep constant during two consecutive time slots and change independently in the following two successive time slots. We construct a Riemannian-distance (RD) based noncoherent detector for such a system. Also, we propose a novel noncoherent parametric space-time coding method. We first attain the closed-form solutions of the optimal sub-constellation structures for fixed modulation orders with the max-min rule. Then, we determine the optimal modulation order for each sub-constellation. The analytical results show that our proposed scheme can attain a larger RD distance than the existing massive uniquely factorable constellation coding (MUFC) scheme. Further, we illustrate that our proposed coding scheme enables a low-complexity RD decoding algorithm. Simulation results show that our proposed scheme performs better than the current phase shift keying modulation scheme and MUFC scheme.

Wavelet Transform Based CT and PET Lung Image Fusion

The lung cancer reduces the breathing ability and it causes due to uncontrollable cells in the lungs. The fusion of Computed Tomography (CT) and Positron Emission Tomography (PET) has clear information about lungs comparing with individual CT and PET images. The fused image helps to find cancer in a starting stage. In this study, a novel method for fusion of CT and PET lung images using Wavelet Transform (WT) and MaxMin (MM) rule is presented. Initially, the CT and PET lung images are decomposed by WT. The subband coefficients of WT are extracted by using entropy features. Then MM rule is applied, after that the image is reconstructed to form the fused lung image. The performance is evaluated by Reference Image Database to Evaluate therapy Response (RIDER) lung database. Results and discussion shows the performance of Lung Image Fusion (LIF).

Delay Guarantee and Effective Capacity of Downlink NOMA Fading Channels

Nonorthogonal multiple access (NOMA) is promising for increasing connectivity and capacity. But there has been little consideration on the quality of service of NOMA; let alone that in generic fading channels. This paper establishes closed-form upper bounds for the delay violation probability of downlink Nakagami- $m$ and Rician NOMA channels, by exploiting stochastic network calculus (SNC). The key challenge addressed is to derive the Mellin transforms of the service processes in the NOMA fading channels. The transforms are proved to be stable, and incorporated into the SNC to provide the closed-form upper bounds of the delay violation probability. The paper also applies the Mellin transforms to develop the closed-form expressions for the effective capacity of the NOMA fading channels, which measures the channel capacity under statistical delay guarantees. By further applying the min–max and max–min rules, two new power allocation algorithms are proposed to optimize the closed-form expressions, which can provide the NOMA users fairness in terms of delay violation probability and effective capacity. Simulation results substantiate the derived upper bounds of the delay violation probabilities, and the effective capacity. The proposed power allocation algorithms are also numerically validated.

An Efficient Max-Min Rule Selection for Lung Image Fusion using Wavelet Energy Based Fuzzy Logic

In this paper, the fusion of lung images using Positron Emission Tomography (PET) and Computed Tomography to identify the cancer part in (CT) images based on Discrete Wavelet Transform (DWT) is presented. The fused lung image is more informative than their individual counterpart and consists of the necessary information to diagnose diseases at the earliest. At first, the PET and CT images are decomposed by DWT, and it produces low and high-frequency subbands. Then Wavelet Energy based Fuzzy Logic (WEFL) is employed to select the MAX-MIN rule for the fusion of low and high-frequency subband coefficients of PET and CT image features to identify cancer parts in lungs. Finally, the fused lung image in low frequency and high-frequency components are combined to reconstruct the image. Results show that the performance of lung image fusion for the identification of the cancer part in CT and PET images.

Preferences with changing ambiguity aversion

We provide two extensions of Gilboa and Schmeidler (J Math Econ 18:141–153, 1989)’s maxmin expected utility decision rule to accommodate a decision maker’s changing ambiguity attitudes. The two rules are, respectively, a weighted maxmin rule and a variant constraint rule. The former evaluates an act by a weighted average of its worst and best possible expected utilities over a set of priors, with the weights depending on the act. The latter evaluates an act by its worst expected utility over a neighborhood of a set of approximating priors, with the size of the neighborhood depending on the act. Canonical representations of the two rules are provided for classes of preference relations that exhibit, respectively, ambiguity aversion a la Schmeidler (Econometrica 57:571–587, 1989) and ambiguity aversion a la Ghirardato and Marinacci (J Econ Theory 102:251–289, 2002). In the second part of this paper, we study wealth effect under ambiguity. We propose axioms on absolute and relative ambiguity aversion and derive three representations for the ambiguity averse preference relations exhibiting decreasing (increasing) absolute ambiguity aversion. In particular, decreasing absolute ambiguity aversion implies that as the baseline utility of an act increases, a weighted maxmin decision maker puts less weight on the worst case, and a variant constraint decision maker considers a smaller neighborhood of approximating priors.

Fuzzy Matrix Theory and Infertility Management – Measures Follicle Fertilization Possibility

In this paper, we are exploring fuzzy logic in medical diagnosis of infertility where our aim is to predict the possibility of total fertility using fuzzy matrix theory by measuring the follicle fertilization possibility based on follicle size. Also developed a computer program to calculate fuzzy matrix based on MaxMin rule using JavaScript.

Dynamic Load Balancing Strategy for Cloud Computing with Ant Colony Optimization

How to distribute and coordinate tasks in cloud computing is a challenging issue, in order to get optimal resource utilization and avoid overload. In this paper, we present a novel approach on load balancing via ant colony optimization (ACO), for balancing the workload in a cloud computing platform dynamically. Two strategies, forward-backward ant mechanism and max-min rules, are introduced to quickly find out the candidate nodes for load balancing. We formulate pheromone initialization and pheromone update according to physical resources under the cloud computing environment, including pheromone evaporation, incentive, and punishment rules, etc. Combined with task execution prediction, we define the moving probability of ants in two ways, that is, whether the forward ant meets the backward ant, or not, in the neighbor node, with the aim of accelerating searching processes. Simulations illustrate that the proposed strategy can not only provide dynamic load balancing for cloud computing with less searching time, but can also get high network performance under medium and heavily loaded contexts.

퍼지 융합 등식 제약식을 갖는 퍼지 선형계획법 문제

퍼지 선형계획법은 불확실성하에서의 문제들을 해결하는데 유용한 의사결정 모형이다. 본 연구에서는 목적함수 값이 퍼지수이고 우변 상수도 퍼지수인 융합 등식 제약식을 갖는 퍼지 선형계획법 문제를 다룬다. 연구의 목적은 퍼지 해를 정의하고 그것을 구하는 절차를 모색하는 것이다. 목적함수 값에 대한 소속 함수로 부분 선형함수를, 제약식의 소속 함수로는 사다리꼴 함수를 도입한다. 사다리꼴 함수는 구간별 선형 함수 들로 나누어 나타낼 수 있다. 따라서 모든 소속 함수들을 선형식 들로 대체함으로써 퍼지 선형계획 모형을 Zimmermann의 대칭 선형 모형으로 바꿀 수 있다. 여기에 최대-최소 기준을 적용하여 일반 선형계획법 문제를 도출해 내고, 이 문제의 최적해로부터 원 문제의 퍼지 해를 얻게 된다. 본 논문에서는 사다리꼴 소속 함수에 대해 살펴보았는데 앞으로는 오목 부분 선형함수와 같은 좀 더 일반화된 소속 함수에 대한 연구가 필요하다. The fuzzy linear programming(FLP) is the useful approach to many real world problems under uncertainty. This paper deals with a FLP whose objective value is fuzzy. And the right hand sides of convergent equality constraints are fuzzy numbers. We assume that the membership function of the objective value is piecewise linear and those of the right hand side are trapezoidal. Each of these trapezoidal functions can be algebraically replaced with three linear functions. Then the FLP problem is transformed into the Zimmermann's symmetric model. The fuzzy solution based on the max-min rule can be obtained by solving the crisp linear programming problem derived from the symmetric model. A numerical example has illustrated our approach. The application of our approach to the inconsistent linear system can enable generate us to get define the useful and flexible inexact solutions within acceptable tolerance. Further research is required to generalize the membership function.

Solving a Fuzzy Linear Programming Problem with Triangular Membership Function

This paper deals with the linear problem under the equality constraints whose right hand side parameters are asymmetric triangular fuzzy numbers. The right hand side values are defuzzified by using the triangular membership functions. Each of these triangular functions is algebraically replaced with two piecewise linear functions. And the desired objective value is also a fuzzy number. The membership function of the objective is assumed to be piecewise linear. Then, according to Zimmermann’s approach, by using these membership functions and the max-min rule, the fuzzy linear problem is transformed into the crisp linear programming problem. Consequently a fuzzy solution is obtained by solving this linear programming problem.

Zhou’s aggregation theorems with multiple welfare weights

This paper extends the aggregation theorems of Zhou (1997) to incorporate a social preference for randomization. We establish variations of Harsanyi’s utilitarianism theorems for general societies in which there exists a set of welfare weights, and a maxmin rule is applied.

The Storage Capacity of FBAM

The storage capacity of the fuzzy bidirectional associative memories (FBAMs) is studied in this paper. The necessary and sufficient conditions in theory are established for the associations to be reliably stored and recalled in an FBAM. Based on them, the probability for associations to be reliably stored and recalled in an FBAM is studied. For the binary FBAMs, particularly, those constructed by the max-min learning rule, the representation of attractors is presented, and the formula for calculating the number of attractors is obtained.

Pooling multivariate data under W, LR and LM tests

Two independent random samples are drawn from two multivariate normal populations with mean vectors μ1 and μ2 and a common variance-covariance matrix Σ. Ahmed and Saleh (1990) considered preliminary test maximum likelihood estimator (PMLTE) for estimating μ1 based on the Hotelling's T N 2, when it is suspected that μ1=μ2. In this paper, the PTMLE based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests are considered. Using the quadratic risk function, the conditions of superiority of the proposed estimator for departure parameter are derived. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated that the PTMLE based on W test produces the highest minimum guaranteed efficiencies compared to UMLE among the three test procedures.

Choice under complete uncertainty: axiomatic characterizations of some decision rules

Summary. We provide characterizations of four new rules for individual decision-making under complete uncertainty. They are what we call the min-max rule, the max-min rule, the lexicographic min-max rule and the lexicographic max-min rule. These rules provide orderings of the sets of possible outcomes associated with uncertain prospects. They provide significant alternatives to commonly-used rules that focus on worst outcomes or best outcomes only, and lexicographic versions of those rules.

Fuzzy sets and vague environments

In this paper we propose a natural approach to handle imprecise numbers as they arise for example from measurements. Fuzzy sets turn out to be a canonical representation for such imprecise numbers that are induced by taking different tolerance or error bounds into account. Fuzzy sets are induced by scaling factors that describe the magnitude of the imprecision. On the other, the scaling factors can be derived from given fuzzy sets so that we have a correspondence between scaling factors and fuzzy sets. When these concepts are applied, to control problems, the max-min rule is rediscovered as an interpolation technique. Viewing fuzzy control as an interpolation technique in vague environments enables us to validate various concepts for the design and tuning of fuzzy controllers and also suggests new methods based on clear semantics.

Combining poisson means

The problem of estimating the Poisson mean is considered based on the two samples in the presence of uncertain prior information (not in the form of distribution) that two independent random samples taken from two possibly identical Poisson populations. The parameter of interest is λ1 from population I. Three estimators, i.e. the unrestricted estimator, restricted estimator and preliminary test estimator are proposed. Their asymptotic mean squared errors are derived and compared; parameter regions have been found for which restricted and preliminary test estimators are always asymptotically more efficient than the classical estimator. The relative dominance picture of the estimators is presented. Maximum and minimum asymptotic efficiencies of the estimators relative to the classical estimator are tabulated. A max-min rule for the size of the preliminary test is also discussed. A Monte Carlo study is presented to compare the performance of the estimator with that of Kale and Bancroft (1967).

Pooling multivariate data

In case it is doubtful whether two sets of data have the same mean vector, four estimation strategies have been developed for the target mean vector. In this situation, the estimates based on a preliminary test as well as on Stein-rule are advantageous. Two measures of relative efficiency are considered; one based on thequadratic loss function, and the other on the determinant of the mean square error matrix. A max-min rule for the size of the preliminary test of significance is presented. It is demonstrated that the shrinkage estimator dominates the classical estimator, whereas none of the shrinkage estimator and the preliminary test estimator dominate each other. The range in the parameter space where preliminary test estimator dominates shrinkage is investigated analytically and computationally. It is found that the shrinkage estimator outperform the preliminary test estimator except in a region around the null hypothesis. Moreover, for large values of a, the level of statistical significance, shrinkag...

Image Enhancement Using Smoothing with Fuzzy Sets

A model for grey-tone image enhancement using the concept of fuzzy sets is suggested. It involves primary enhancement, smoothing, and then final enhancement. The algorithm for both the primary and final enhancements includes the extraction of fuzzy properties corresponding to pixels and then successive applications of the fuzzy operator contrast intensifier on the property plane. The three different smoothing techniques considered in the experiment are defocussing, averaging, and maxmin rule over the neighbors of a pixel. The reduction of the index of fuzziness and entropy for different enhanced outputs (corresponding to different values of fuzzifiers) is demonstrated for an English script input. Enhanced output as obtained by histogram modification technique is also presented for comparison.