Iranian journal of fuzzy systems
Volume:16 Issue: 4, Jul-Aug2019

In face recognition, one of the most important problems to tackle is a large amount of data and the redundancy of information contained in facial images. There are numerous approaches attempting to reduce this redundancy. One of them is information aggregation based on the results of classifiers built on selected facial areas being the most salient regions from the point of view of classification both by humans and computers. In this study, we report on a series of experiments and offer a comprehensive comparison between various methods of aggregation of outputs of these classifiers based on essential facial features such as eyebrows, eyes, nose, and mouth areas. For each of them, we carry the recognition process utilizing the well-known Fisherfaces transformation. During the comparisons of the vectors representing the features of images (faces) after the transformations, we consider 16 similarity$/$dissimilarity measures for which we select the best aggregation operator. The set of operators to compare was selected on a basis of the comprehensive literature review regarding aggregation functions.

This paper considers a bi-objective model for a scheduling problem of unrelated parallel batch processing machines to minimize the makespan and maximum tardiness, simultaneously. Each job has a specific size and the data corresponding to its ready time, due date and processing time-dependent machine are uncertain and determined by trapezoidal fuzzy numbers. Each machine has a specific capacity, in which the number of jobs assigned to each batch on the machine does not violate the machine capacity. The batch processing time, the batch ready time and the batch due date are presented by the longest processing time, the longest ready time and the shortest due date of the jobs that belong to the batch, respectively. To determine the longest and shortest time, the method suggested by Jiménez et al.cite{c18} is used for ranking the fuzzy numbers. A bi-objective fuzzy mixed-integer linear programming model is proposed and solved by two exact methods (i.e., two-phase fuzzy and $epsilon$-constraint) for small-sized problems to obtain a set of Pareto solutions. Because the problem belongs to the class NP-hard, two meta-heuristics, namely fuzzy non-dominated sorting genetic algorithm (FNSGA-II) and fuzzy multi-objective discrete teaching–learning-based optimization (FMODTLBO), are proposed. Then, the comparison of results is illustrated to show their performances. Furthermore, a new representation of the solutions is a matrix with two rows and $N$ columns (i.e., jobs) used to assign the jobs to the batches that processed on the machines.

There has been a growing interest in the study of the notion of $alpha$-migrativity and generalizations in recent years, and it has been investigated for families of certain operators such as t-norms, t-conorms, uninorms, nullnorms.This paper is mainly devoted to investigating the migrativity equations between semi-t-operators or semi-uninorms, and Mayor's aggregation operators. The results that we obtain are complete and different from the known ones concerning migrativity for t-norms, t-conorms, uninorms and nullnorms.

Uncertainty plays a significant role in modeling and optimization of real world systems. Among uncertain approaches, fuzziness describes impreciseness while for ambiguity another definition is required. Vagueness is a probabilistic model of uncertainty being helpful to include ambiguity into modeling different processes especially in industrial systems. In this paper, a vague set based on distance is used to model a flow-shop scheduling problem being an important problem in assembly production systems. The vagueness being used as octagon numbers are employed to represent vague processes for the manufacturing system. As a modeling effort, first a flow-shop scheduling problem is handled with vagueness. Then, for solving and analyzing the proposed vague flow-shop scheduling model, a modified Branch and Bound algorithm is proposed. As an implementation, an example is used to explain the performance and to analyze the sensitivity of the proposed vague approach. The validity of the proposed model and modified algorithm is demonstrated through a robust ranking technique. The outputs help the decision makers to counteract the vagueness and handle operational decisions in flow-shop scheduling problems within dynamic environments.

To address the hesitancy, inconsistency and uncertainty of decision makers’ cognitions, linguistic interval hesitant fuzzy sets (LIHFSs) are efficient tools. This paper focuses on studying the application of LIHFSs. To do this, two correlation coefficients of LIHFSs are defined, which needn't consider the length of elements in LIHFSs or the arrangement of their possible interval values. To address the situation where the weights of elements in a set are different and correlative, two linguistic interval hesitant fuzzy Shapley weighted correlation coefficients are defined. Considering the situation where the weight information of features/attributes is partly known, programming models to determine the optimal fuzzy measures on them are constructed, respectively. After that, an approach to pattern recognition and multi-attribute decision making with linguistic interval hesitant fuzzy information is developed, respectively. Meanwhile, illustrative examples about medical diagnosis and selecting constructors for tunnel bidding are selected to verify the application of new approaches, and comparison with a previous method is offered.

The problem of the sample variance computation for epistemic inter-val-valued data is, in general, NP-hard. Therefore, known efficient algorithms for computing variance require strong restrictions on admissible intervals like the no-subset property or heavy limitations on the number of possible intersections between intervals. A new asymptotic algorithm for computing the upper bound of the sample variance in a feasible time is proposed. Conditions required for its application with finite samples are discussed and some properties of the algorithm are also given. It appears that our new algorithm could be effectively applied in definitely more situations than methods used so far.

The topic of Doppler and Bearing Tracking (DBT) problem is to achieve a target trajectory using the Doppler and Bearing measurements. The difficulty of DBT problem comes from the nonlinearity terms exposed in the measurement equations. Several techniques were studied to deal with this topic, such as the unscented Kalman filter. Nevertheless, the performance of the filter depends directly on the prior knowledge, involving the accurate model, sufficient information of the noise distribution and the suitable initialization. To address these problems, in this paper, a new adaptive factor together with a fuzzy logic system is proposed for online adjusting the process and the measurement noise covariance matrices simultaneously. In the core of the proposed algorithm, the fault detection procedure is also adopted to reduce the computational time. The theoretical developments are investigated by simulations, which indicate the effectiveness of the proposed filter in DBT problem.

Interval-valued intuitionistic fuzzy sets (IVIFSs), a generalization of fuzzy sets, is characterized by an interval-valued membership function, an interval-valued non-membership function.The objective of this paper is to deal with criteria aggregation problems using IVIFSs where there exists a prioritization relationship over the criteria.Based on the ${L}$ukasiewicz triangular norm, we first propose a prioritized arithmetic mean to IVIF multi-criteria decision making (MCDM) problem where there is a linear ordering among the criteria.The proposed aggregation operator overcomes the existing prioritized aggregation operator's shortcomings that it is not monotone with respect to the total order on interval-valued intuitionistic fuzzy values (IVIFVs).We also prove that it is bounded and monotone with respect to the total order on IVIFVs, and therefore is a true generalization of such operations.We finally propose an aggregation operators-based two-step procedure to IVIF MCDM in the situation that more than one criteria exist at some priority level.

Recently, the TODIM$^1$(an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attributes, which restricts the applicability of TODIM method. Therefore, in this paper, we propose the 2-additive fuzzy Choquet integral-based hesitant fuzzy TODIM method to deal with this situation. To begin with, we propose the novel measured function to compare the magnitude of hesitant fuzzy elements, which has been proved to be more rational and efficient than existing approaches. Then we use nonlinear programming to obtain 2-additive fuzzy measures and then put forward novel Choquet integral based-dominance degree to calculate the dominance degree of one alternative over another under all attributes. Consequently, we then calculate the global value of each alternative whereby we can rank all the alternatives. Finally, an illustrate example is used to demonstrate the efficiency and applicability of the proposed approach with sensitivity analysis.

Interval type-2 fuzzy sets, each of which is characterized by the footprint of uncertainty, are a very useful means to depict the linguistic information in the process of decision making. In this article, we investigate the group decision making problems in which all the linguistic information provided by the decision makers is expressed as interval type-2 fuzzy decision matrices where each of the elements is characterized by interval type-2 fuzzy set, and the information about attribute weights is completely unknown.We first introduce the average centroid matrix of the interval type-2 fuzzy decision matrix, and then utilize the interval type-2 fuzzy averaging operator to aggregate all individual interval type-2 fuzzy decision matrices into a collective interval type-2 fuzzy decision matrix. Based on the average centroid matrix of the collective interval type-2 fuzzy decision matrix and information theory, we develop an optimization model by which a straightforward formula for deriving attribute weights can be obtained. Furthermore, based on the interval type-2 fuzzy averaging operator, we utilize the average centroid measure to give an approach to ranking the given alternatives and then selecting the most desirable one(s). Finally, we give an illustrative example.

In this paper, we investigate the multiple attribute decisionmaking (MADM) problems with 2-tuple intuitionistic fuzzylinguistic information. Then, we utilize arithmetic and geometricoperations to develop some 2-tuple intuitionistic fuzzy linguisticaggregation operators. The prominent characteristic of theseproposed operators are studied. Then, we have utilized theseoperators to develop some approaches to solve the 2-tupleintuitionistic fuzzy linguistic MADM problems. Finally, apractical example for enterprise resource planning (ERP) systemselection is given to verify the developed approach and todemonstrate its practicality and effectiveness.

This paper attempts to generalize universal algebras on classical sets to $L$-sets when $L$ is a GL-quantale. Some basic notions of fuzzy universal algebra on an $L$-set are introduced, such as subalgebra, quotient algebra, homomorphism, congruence, and direct product etc. The properties of them are studied. $L$-valued power algebra is also introduced and it is shown there is an onto homomorphism from $P(A)/R^{+}$ to $P(A/R)$ for any congruence $R$ on $L$-set $A$.

In this paper, we present a new vision for studying ${F}$-open, ${F}$-continuous, and ${F}$-irresolute function in $(L,M)$-fuzzy topological spaces based on the implication operation and $(L,M)$-fuzzy ${F}$-open operator cite{2}. These kinds of functions are generalized with their elementary properties to $(L,M)$-fuzzy topological spaces setting based on graded concepts. Moreover, a systematic discussion of their relationship with the degree of $mathbf{F}$-compactness, ${F}$-connectedness, ${F}T_1$, and ${F}T_2$ is carried out.}