Iranian journal of fuzzy systems
Volume:17 Issue: 2, Mar-Apr 2020

In this paper, pretopological and topological operators are introduced based on partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets.On the other hand it is a generalization of the fuzzy set pretopological operators introduced by Wenzhong and Kimfung.

In this paper, we study the fuzzy Ulam-Hyers-Rassias stability for two kinds of fuzzy fractional integral equations by employing the fixed point technique.

Currently, cellular networks are one of the essential communication methods for people. Providing proper coverage for the users and also offering high-quality services to them are two of the most important issues of concern in cellular networks. The fifth-generation cellular communication networks can provide higher data transmission rates, which lead to a higher quality of service but this higher rate has let to reduced antenna coverage in these networks. Besides this, natural and unnatural events in the environment can also affect the coverage of users in the cellular network. One way to resolve this issue is using drones as cellular antennas. The most important factor in providing good coverage and high-quality service for users is the optimal placement of antennas. In this article, the problem of finding the appropriate locations of drone base stations (DBSs) is modeled as a $P$-median optimization problem, where P is the number of required antennas to cover the users. We have used a fuzzy clustering algorithm to define a set of specified candidate points that are required to select the locations of DBSs in the $P$-median model. The optimal value of P was obtained using the bisection algorithm. Finally, the optimal positions of DBSs have been determined by solving the optimization problem. According to the results, in the case of a proper selection of fuzzy clustering parameters, better results will be obtained in comparison to the results of other approaches.

Market demand of the  perishable bakery  products are volatile. Hence, demand of such items are random variable. The most appealing demand distribution of such items is lognormal demand distribution. Using historical data, the parameters of lognormal distribution are obtained. But, there is a problem of overestimation or underestimation of the parameters. Fuzzy triangular numbers are used to overcome such problems. Single period (newsboy) inventory model is used to obtain an optimal order quantity. The retailers and manufacturers profit is obtained by using the supply chain coordination model. At the end of day, all the remaining items rotted. Hence, there is no gain from unsold items. Also, the some items are defective at the time of purchase. Thus, loss sharing strategy is proposed between manufacturers and retailers. All of these aspects are incorporated in the supply chain coordination model. The  data is collected from Koregaon Park, Pune market, India to illustrate the methodology.

This paper extends the idea of switching T-S fuzzy systems with linear consequent parts to nonlinear ones. Each nonlinear subsystem is exactly represented by a T-S fuzzy system with Lure’ type consequent parts, which allows to model and control wider classes of switching systems and also reduce the computation burden of control synthesis. With the use of a switching fuzzy Lyapunov function, the LMI conditions for asymptotic stability of the system with maximum decay-rate and disturbance attenuation properties under arbitrary switching law are derived. Moreover, several numerical examples are provided to demonstrate the effectiveness of the proposed approaches to reduce the computational burden of control synthesis and improving the closed-loop performance of the system.

This paper reviews and compares two R packages ``FPV" and ``Fuzzy.p.value".These packages are designed for testing hypotheses in a fuzzy environment using a fuzzy $p$-value based approach.In fact, the packages ``FPV" and ``Fuzzy.p.value" propose some useful functions for testing hypotheses when the data / hypotheses are fuzzy rather than crisp.The proposed methods and functions have been presented together with illustrative practical examples.

Facility location-network design (FLND) problem, which determines the location of facilities and also communication links between the demand and facility nodes, is arisen from the combination of the facility location and network design problems. This paper deals with fuzzy capacitated facility location-network design model which aims to select the facilities and candidate links in a way that yield to minimize the total costs, containing: costs of opening facilities, link construction and transportation costs. In this study, several types of links have been considered for connecting two nodes in which their capacity, transportation and construction costs are distinct. Besides, the possibility of multiple link selection between two nodes and also the necessity of the existence of a facility in some nodes are considered. There are also several types of facilities which the budget for each type is unique. Moreover, to open the facilities and to construct the links, limited budgets are considered. As a result of the uncertainty in customers’ demand, an interactive fuzzy solution approach is applied. Because this problem is classified as an NP-hard class, a hybrid meta-heuristic algorithm based on Firefly and Invasive Weed Optimization (FIWO) is developed. Finally, the behavior of the model is tested, and the proposed algorithm’s performance is compared with some other solving methods.

The aim of this paper is to present a fuzzy counterpart method of constructing the Hausdorff quasi-uniformity of a crisp quasi-uniformity. This process, based on previous works due to Morsi cite{Morsi94} and Georgescu cite{Georgescu08}, allows to extend probabilistic and Hutton $[0,1]$-quasi-uniformities on a set $X$ to its power set.  In this way, we obtain an endofunctor for each one of the categories of those objects. We will demonstrate the commutativity of these endofunctors with Lowen and Katsaras' functors. Furthermore, we will prove the compatibility of our construction with the Hausdorff fuzzy quasi-pseudometric introduced in cite{RLRoSA10}.

Many interval number ranking methods cannot representthe different attitudes of decision makers with different riskappetites. Therefore, interval numbers are expressed in the RectangularCoordinate System (RCS). After mining the interval numbers in the RCS,the Symmetry Axis Compensation Factor, which is known as (lambda),was introduced, and the Equivalent Function of the Goal Interval Number(GIN) was deduced. Thus, the interval number ranking method consideringsymmetry axis compensation was defined along with its applicationprocedures. Additionally, the feasibility and effectiveness of thismethod were verified through examples. This method is intuitive andsimple and can represent multiple attitudes of decision makers withdifferent risk appetites.

This paper deals with a new family of (A, N)-implications that derived from fuzzy negation and continuous monotone function, and some properties, like the left neutrally, the exchange principle, the ordering property and the laws of contraposition, of the proposed family of (A, N)-implications are studied. Moreover, the T-conditionality and the Modus tollens for the new family of (A, N)-implications are also studied and some results are obtained.

It is doubtless that intuitionistic fuzzy set (IFS) theory plays an increasingly important role in solving the problems under uncertain situation. As one of the most critical members in the theory, distance measure is widely used in many aspects. Nevertheless, it is a pity that part of the existing distance measures has some drawbacks in practical significance and accuracy. To make up for their drawbacks and pursue more accuracy and effectiveness, in this paper, we propose a new inclusion relation of IFSs and a new definition called strict distance measure. Based on this new relation, an analysis is given to point out that the common shortcoming of Hamming distance measure and Euclidean distance measure is the mishandling of hesitancy degree. Therefore, the role of hesitancy degree in distance measure is studied deeply and then three strict distance measures are put forward to overcome the above shortcoming. In addition, a novel definition called the characteristic function of distance measure is defined to describe the character of strict distance measure. On this basis, a theorem is presented to illustrate the inevitability of the occurrence of unrecognized result in pattern recognition problems in some special cases. This theorem also shows that the problem cannot be entirely attributed to distance measures. In view of this condition, we provide an appropriate solution. Compared with other existing distance measures in some examples, the superiorities of our improved distance measures are demonstrated to be more effective and more significant.

We prove a continuity inheritance property for super- and sub-additive transformations of non-negative continuous multivariate functions defined on the domain of all non-negative points and vanishing at the origin. As a corollary of this result we obtain that super- and sub-additive transformations of continuous aggregation functions are again continuous aggregation functions.

Inspired by the interactive discrete choice logit models [Aggarwal, 2019], this paper presents the advanced families of discrete choice models, such as nested logit, mixed logit, and probit models to consider the interaction among the attributes. Besides the DM's attitudinal character is also taken into consideration in the computation of choice probabilities. The proposed choice models make use of Choquet integal and the recent attitudinal Choquet integral. The models are termed as Choquet nested logit (CNL), Choquet mixed multinomial logit (CMMNL), and Choquet multinomial probit (CMP). These are further extended to represent the DM's attitudinal character, and termed as attitudinal CNL, attitudinal CMMNL, and attitudinal CMP.

Data envelopment analysis (DEA) is a linear programming based methodology to determine the relative performance efficiencies of homogeneous decision making units (DMUs). In real world applications, some input and output datas do not possess crisp/fuzzy essence but they possess intuitionistic fuzzy (IF) essence. So, in this study, we develop an IF BCC (IFBCC) and an IF super efficiency BCC (IFSEBCC) model with triangular IF numbers (TIFNs) input/output data. Firstly, the efficiencies of DMUs are determined using IFBCC model. If DMUs are efficient then the super efficiencies of DMUs are determined using IFSEBCC model. If DMUs do not have feasible (finite) efficiencies/super efficiencies in intuitionistic fuzzy environment, then we can not rank the DMUs. Therefore, we develop IF models to determine the efficiencies of DMUs and ranking the DMUs in the presence of infeasibility in intuitionistic fuzzy environment. Two illustrative examples and one real life application are provided to illustrate the applications of the proposed IF models. Finally, comparison has been performed with the existing crisp models.