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In real-life scenarios, both the vertex weight and edge weight in a network are hard to define exactly. We can incorporate the fuzziness into a network to handle this type of uncertain situation. Here, we use triangular fuzzy number to describe the vertex weight and edge weight of a fuzzy network G. In this paper, we consider weighted k-domination problem in fuzzy network. The weighted k-domination (WKD) problem is to find a k dominating set D which minimizes the cost f (D) : = ∑u∈Dw (u) + ∑v∈V\D min {∑u∈Sw (uv) |S ⊆ N (v) ∩ D, |S| = k}. First, we put forward an integer linear programming model with a polynomial number of constrains for the WKD problem. If G is a cycle, we design a dynamic algorithm to determine its exact weighted 2-domination number. If G is a tree, we give a label algorithm to determine its exact weighted 2-domination number. Combining a primal-dual method and a greedy method, we put forward an approximation algorithm for general fuzzy network on the WKD problem. Finally, we describe an application of the WKD problem to police camp problem. [ABSTRACT FROM AUTHOR]

This study designs a new variant of the capacitated vehicle routing problem (CVRP) under a fuzzy environment. In CVRP, several vehicles start their journey from a central depot to provide services to different cities and finally return to the depot. This paper introduces an additional time beyond the service time at each city to fulfill the pre-ordered demands. The need for this excess service time is to provide the services to new customers who are not enlisted at the start of the process. It is a market enhancement step. The proposed model's main objective is to find the maximum time-dependent profit by using the optimum number of vehicles in an appropriate route and spending optimum excess service time in each city. The model considers travel time and travel cost as fuzzy numbers. An expected value model (EVM) is formulated using the credibility approach on fuzzy variables. A hybrid meta-heuristic method combining a genetic algorithm (GA) and bacteria foraging optimization algorithm (BFOA) is designed to solve the proposed model. The proposed model is explained with the help of some numerical examples. Sensitivity analyses based on different independent parameters of the algorithms are also conducted. [ABSTRACT FROM AUTHOR]

An interactive α-satisfactory method via relaxed order of desirable α-satisfactory degrees is proposed for multi-objective optimization with fuzzy parameters and linguistic preference in this paper. Fuzzy parameters existing in objectives and constraints of multi-objective optimization are defined as fuzzy numbers and α-level set is used to build the feasible domain of parameters. On the basis, the original problem with fuzzy parameters is transformed into multi-objective optimization with fuzzy goals. Linguistic preference of decision-maker is modelled by the relaxed order of desirable α-satisfactory degrees of all the objectives. In order to achieve a compromise between optimization and preference, the multi-objective optimization problem is divided into two single-objective sub-problems: the preliminary optimization and the linguistic preference optimization. A preferred solution can be found by parameter adjustment of inner-outer loop. The minimum stable relaxation algorithm of parameter is developed for calculating the relaxation bound of maximum desirable satisfaction difference. The M-α-Pareto optimality of solution is guaranteed by the test model. The effectiveness, flexibility and sensitivity of the proposed method are well demonstrated by numerical example and application example to heat conduction system. [ABSTRACT FROM AUTHOR]

The main proposal of this paper is to derive two different reduction process for a trapezoidal type-2 fuzzy number. The first reduction method is based on critical values and the second method is based on α-cut of fuzzy number. As an application a multi-objective solid transportation problem, minimizing the cost and time has been developed using trapezoidal type-2 fuzzy number as system parameters and hereby solved. Finally after solving the proposed multi-objective problem by intuitionistic fuzzy programming technique a comparison between the two proposed reduction methods are discussed briefly. The proposed models and techniques are finally illustrated by providing numerical examples at the end. Also this paper present a comparative study between the proposed method to the KM algorithm and NT method for type reduction. [ABSTRACT FROM AUTHOR]

Network flows over time (also called Dynamic Network Flows) are considered as generalized form of standard (static) networks by adding an element of time. The factor of transit time on the arcs which specify the amount of time it takes for one unit of the flows to pass through a particular arc, make these networks different to traditional form of networks. While in most of network flow problems, transit times and capacities are given constant, stochastic or Fuzzy numbers, in this paper we suppose that transit times, capacities and consequently flows on arcs fall within specific ranges expressed as compact intervals. This vagueness in transit times, capacities and flows could arise in a number of ways: 1) when determining the exact capacity or transit time quantities is hard and there may happen errors in determining them which intervals reflect the measurement errors; 2) when it is impossible or even it is not needed to produce neither a distribution nor fuzzy functions but transit times, capacities and flows lie within specific ranges, or vary in time within these ranges. While determining the exact time for traveling in specific path in network transportation system is extremely difficult or almost impossible, determination of interval which can describe the range of required time for travelling in the network would be easy and fully operational. Our contribution in this paper is producing maximum flow and quickest s - t flow algorithms, first to network flows over time with interval-valued capacities and then to T-length bounded network flows over time with interval-valued transit times and capacities. [ABSTRACT FROM AUTHOR]

Dhanasekar et al. (International Journal of Fuzzy Systems 19 (2017) 1479-1491) proposed a fuzzy Hungarian MODI algorithm to solve fully fuzzy transportation problems. Dhanasekar et al. have used the standard multiplication of trapezoidal fuzzy numbers in their proposed method. In this paper, it is pointed out that the method, proposed by Dhanasekar et al., is not valid for standard multiplication of trapezoidal fuzzy numbers and is valid only if a special type of multiplication of fuzzy numbers is used. [ABSTRACT FROM AUTHOR]

This paper addresses a selective maintenance optimization problem for a fuzzy multi-state system composed of fuzzy multi-state elements. Due to insufficient data and unpredictable external working conditions, both the performance capacity and states transition intensities of multi-state elements cannot be known precisely, but are represented by fuzzy numbers. Additionally, both the durations of a break and a succeeding mission are also treated as fuzzy values. To maximize the fuzzy probability of a system successfully completing a succeeding mission, a selective maintenance model is proposed to identify an optimal subset of maintenance activities to be performed on some elements in the system. A solution algorithm containing three rules to eliminate inferior solutions and narrowdown elements' states combinations is proposed to resolve the new selective maintenance model in a computationally efficient manner. An illustrative example of an archibald is presented to demonstrate the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

In some cases of using multi-criteria decision making methods for solving real-world problems ratings of alternatives cannot be determined precisely, and that is why they are expressed in the form of intervals. Therefore, the aim of this paper is to extend the MOORA method for solving decision making problems with interval data. By extending the ratio system part of MOORA method, an algorithm to determine the most preferable alternative among all possible alternatives, when performance ratings are given as intervals, is presented. Finally, an example is shown to highlight the proposed procedure, at the end of this paper. [ABSTRACT FROM AUTHOR]

There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the maximal flow problems. In this paper, the existing algorithm is modified to find fuzzy maximal flow between source and sink by representing all the parameters as generalized triangular fuzzy numbers. To illustrate the modified algorithm a numerical example is solved and the obtained results are compared with the existing results. If there is no uncertainty about the flow between source and sink then the proposed algorithm gives the same result as in crisp maximal flow problems. [ABSTRACT FROM AUTHOR]

Fuzzy Number Ranking (FNR), plays a very important role in decision making and some other fuzzy application systems. Several strategies have been proposed for ranking Fuzzy Numbers (FNs). Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper, a new algorithm has been introduced for ranking FNs which considers both left and right (LR) sides. Through using several distinct points, this algorithm, provides the result with higher degree of certainty with respect methods which using one point. This algorithm, as shown by several examples, can be easily used for comparing triangular and trapezoidal FNs. [ABSTRACT FROM AUTHOR]

Triangular intuitionistic fuzzy numbers (TIFNs) are a special kind of intuitionistic fuzzy sets (IFSs) on the real number set. TIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. How to measure the value and uncertainty of a TIFN is of great importance. In this paper, we introduce the concepts of the weighted possibility mean, variance and covariance of TIFNs. Furthermore, we show that the weighted possibility mean and the weighted possibility variance of linear combination of TIFNs can be computed in a similar manner to those in probability theory. The desirable properties for the possibility covariance of TIFNs are also investigated. The concepts of the weighted possibility mean, variance and covariance of TIFNs can be considered as a generalization of those of the triangular fuzzy numbers. [ABSTRACT FROM AUTHOR]

Triangular intuitionistic fuzzy numbers (TIFNs) are useful to deal with ill-known quantities in decision making problems. The focus of this paper is on multi-attribute decision making (MADM) problems in which the attribute values are expressed with TIFNs and the information on attribute weights is incomplete, which are solved by developing a new decision method based on possibility mean and variance of TIFNs. The notions of possibility mean and variance for TIFNs are introduced as well as the possibility standard deviation. A new ranking approach for TIFNs is developed according to the ratio of the possibility mean to the possibility standard deviation. Hereby we construct a bi-objective programming model, which maximizes the ratios of the possibility mean to the possibility standard deviation for membership and non-membership functions on alternative's overall attribute values. Using the lexicographic approach, the bi-objective programming model is transformed into two non-linear programming models, which are further transformed into the linear programming models by using the variable transformation. Thus, we can obtain the maximum ratios of the possibility mean to the possibility standard deviation, s are used to rank the alternatives. A numerical example is examined to demonstrate applicability and implementation process of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents fuzzy clustering algorithm for fuzzy data based on α-cuts. A new suitable definition for distance between two arbitrary fuzzy numbers based on α-cuts is proposed. We then reformulate fuzzy c-means (FCM) with fuzzy data and fuzzy centers based on α-cuts. The effectiveness of the proposed clustering algorithm is tested for three fuzzy data sets and then it is compared with other methods; the fuzzy c-number (FCN) algorithm, Hathaway's FCM algorithm and the mixed-type variables FCM (MVFCM) algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we generalize the bounded dual simplex algorithm for solving minimum cost flow problem with fuzzy cost, which its aim is to find the least fuzzy cost of a commodity through a capacitated network in order to satisfy demands at certain nodes using available supplies at other nodes. This algorithm begins with dual feasibility and iterates between dual and primal problems until optimality is achieved. Here, we use the linear ranking functions to compare fuzzy numbers. By using the proposed method the optimal solution of minimum cost flow problems with fuzzy costs can be easily obtained. To illustrate the proposed method a numerical example is solved and the obtained results are discussed. [ABSTRACT FROM AUTHOR]

This paper proposes a procedure for solving total time minimization in fuzzy transportation problem where the transportation time, source and destination parameters have been expressed as exponential fuzzy numbers by the decision maker. An algorithm is developed to obtain the optimal solution as exponential fuzzy number, which enables the decision maker to obtain more informing results and wider knowledge on the problem under consideration. A numerical example is solved to check the validity of the proposed procedure. [ABSTRACT FROM AUTHOR]

The clusters tend to have vague or imprecise boundaries in some fields such as web mining, since clustering has been widely used. Fuzzy clustering is sensitive to noises and possibilistic clustering is sensitive to the initialization of cluster centers and generates coincident clusters. Based on combination of fuzzy clustering and possibilistic clustering, a novel possibilistic fuzzy leader (PFL) clustering algorithm is proposed in this paper to overcome these shortcomings. Considering the advantages of the leader algorithm in time efficiency and the initialization of cluster, the framework of the leader algorithm is used. In addition, a λ-cut set is defined to produce the overlapping clusters autonomously. The comparative experiments with synthetic and standard data sets show that the proposed algorithm is valid, efficient, and has better accuracy. The experiments with the web users access paths data set show that the proposed algorithm is capable of clustering access paths at an acceptable computational expense. [ABSTRACT FROM AUTHOR]