Fuzzy Information and Engineering

Cao, Bingyuan

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509516

While deeply acknowledging the death of Prof. Zadeh, the father of fuzzy mathematics and intelligent control all over the world, our magazine has also cherished the memory of his life and his great contribution, and has started a special issue of the journal, which honourably commemorates the honourary editor of our journal. This article begins with Prof. Zadeh's cooperation and support with the Journal and me, recalling his love for us, hoping to look back at his voice and smile, recollecting his enthusiasm for his speech, and collecting papers from his friends in their research achievements in z-numbers, Factors space, general type-2 fuzzy sets, Dombi fuzzy graphs, OWA linear operators for decision making, multi-objective FLP, uncertainty data envelopment analysis, and starplus-compactness in L-topological spaces, commemorating him and opening up a new future in the field of fuzzy.

Dubois, Didier; Prade, Henri

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509517

This paper proposes a new approach to the notion of Z-number, i.e., a pair of fuzzy sets modelling a probability-qualified fuzzy statement. Originally, a Z-number is viewed as the fuzzy set of probability functions stemming from the flexible restriction of the probability of a fuzzy event by a fuzzy probability. This representation leads to complex calculations and does not reduce to the original fuzzy event when the attached probability is 1. Simpler representations are proposed, that avoid these pitfalls. We note that when both fuzzy sets forming the Z-number are crisp, the generated set of probabilities is representable by a special kind of belief function that corresponds to a probability box (p-box). Two proposals are made to generalise this approach when the two sets are fuzzy. One approach considers a Z-number as a weighted family of crisp Z-numbers, obtained by independent cuts of the two fuzzy sets. In the alternative approach, a Z-number can be turned into a pair of possibility distributions forming a generalized p-box. In that case, the probability of each cut of the fuzzy event is upper and lower bounded by two probability values. Then computation with Z-numbers come down to uncertainty propagation with random intervals.

Wang, Peizhuang; Bao, Yanke

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509518

Professor L. A. Zadeh is a special inspiring leader in cybernetics and machine intelligence. As a tribute to his pioneer work in fuzzy sets theory, this paper follows his treatment in fuzzy membership functions and operations and introduces the factors space theory which further explains the relationships between them. The factors space theory calculates the membership degree of a human concept by first surveying the sampling interval statistics around a concept, and then introducing the vision of ‘falling shadow’ to convert the covering probability of a random interval in the power set of the concept domain to membership degree. This paper introduces the factorial probability and transfers typical probability density to typical falling membership curves. Based on this idea, a subjective scoring system used on fuzzy evaluation and decision-making is suggested. Facing the question on the selection of fuzzy operations, the paper indicates that the source is in the joint distribution of random sets and a selection proposition is given. Factors space opens a new frontier for the developments of fuzzy sets theory.

Castro, Juan R.; Sanchez, Mauricio A.; Gonzalez, Claudia I.; Melin, Patricia; Castillo, Oscar

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509519

In this paper a new method for the parameterization of general type-2 fuzzy membership functions. The proposed method describes the methodology, equations and pseudo-code for building a set of general type-2 membership functions, which are a combination of two Gaussian-type primary membership functions (Gaussian with uncertain mean, and Gaussian with uncertain standard deviation), with multiple combinations of secondary membership functions (Gaussian, double Gaussian, general bell and trapezoidal). In addition, several application cases are used to illustrate the advantages of the proposed parameterization of general type-2 fuzzy sets; where the membership functions are designed using the parameterization approach and the general type-2 inference system is approximated using the α-planes theory. Simulation results illustrate that the parameterization offers an efficient way to represent these fuzzy sets. The main idea of the approach is to facilitate the use of general type-2 fuzzy systems in real world applications. The main contribution is a proposed new form of parameterizing general type-2 fuzzy sets that simplifies the efficient design of this type of sets.

Ashraf, S.; Naz, S.; Kerre, E. E.

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509520

A fuzzy graph is useful in representing structures of relationships between items where the existence of a concrete item (vertex) and relationship between two items (edge) are matters of degree. In this paper, the novel concept of Dombi fuzzy graph is introduced. We shall use graph terminology and introduce fuzzy analogs of several basic graph-theoretical concepts using Dombi operator. Moreover, we consider these results on Dombi fuzzy graphs preserving strong property.

Cables Pérez, E. H.; Lamata, M. T.; Pelta, D.; Verdegay, J. L.

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509521

When we deal with problems of decision making where we need to give an order of alternatives and the rewards (number of points earned in a race) are not associated with the criteria, but with positions, it makes sense to deal with ordered weighted averaging (OWA) operators. Within the class of OWA operators we can consider those that are based on a linear function. This paper is related to a study of the properties that verify the linear functions set. Taking these properties into account we shall see how the final classification for drivers in Formula One changes when the number of points earned in a race is given by means of a linear function as opposed to the current assignments.

Nasseri, S. H.; Zavieh, H.

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509522

In this paper, we present a new method to solve a fuzzy linear programming problem with fuzzy coefficients in the constraints and the objective function based on solving an associated multi-objective model. In particular, we present a weighted method for linear semi-infinite programming (LSIP) model to solve the original problem. Finally, a numerical example is included to illustrate the suggested solving process.

Mohammadzaheri, M.; AlQallaf, A.; Ghodsi, M.; Ziaiefar, H.

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509523

This paper proposes a fuzzy model to estimate the head of gaseous petroleum fluids (GPFs) driven by electrical submersible pumps (ESPs). The proposed fuzzy model is an alternative to widely used empirical models. Numerical and analytical models have been also proposed to estimate heads of GPFs in ESPs, which have failed to reliably serve the function. The developed fuzzy model evidently outperforms comparable empirical models in terms of accuracy and presents a mean absolute estimation error of 52.4% less than the most accurate existing empirical model.

Fatemipour, F.; Akbarzadeh-T, M. R.

2018 Fuzzy Information and Engineering

doi: 10.1080/16168658.2018.1509524

A key challenge in decision fusion systems is to determine the best performing combination of local decision makers. This selection process can be performed statically at the training phase or dynamically at the execution phase, taking into consideration various features of the data being processed. Dynamic algorithms for the selection of competent sources are generally more accurate, but they are also computationally more intensive and require more memory. In this research, we propose a fuzzy rule-based approach for dynamic source selection (FDSS) that compresses the knowledge from local sources using a divide-and-conquer strategy along with the basic concepts of coverage and truth value criteria, leading to less memory requirement and faster processing. A top-down approach to FDSS is then used to reach a parameter-free algorithm, i.e. one that avoids the restrictive parameters/threshold settings of FDSS. The rule bases in both approaches are created recursively and use the conditional probabilities of each class's correctness as the rule's weight. The proposed approaches are compared against several competing dynamic classifier selection methods based on local accuracy. Results indicate that the proposed fuzzy rule structures are generally faster and require less memory, while they also lead to more accurate decisions from the uncertain decisions from multiple sources.