Iranian journal of fuzzy systems
Volume:16 Issue: 6, Nov-Dec 2019

Molodtsov initiated soft set theory that provided a general mathematicalframework for handling with uncertainties in which we encounter the data by affix parameterized factor during the information analysis as differentiated to fuzzy as well as bipolar fuzzy set theory.The main object of this paper is to lay a foundation for providing a new application of bipolar fuzzy soft tool in considering many problems that contain uncertainties. In present study, aggregation of bipolar fuzzy soft numbers haveso far not yet been applied for ranking of alternatives in decision-making problems.To this propose, bipolar fuzzy soft weighted arithmetic averaging (BFSWAA) operator, bipolar fuzzy soft weighted geometric averaging (BFSWGA) operatorhave been used to compare two bipolar fuzzy soft numbers (BFSNs) for aggregating different bipolar fuzzy soft input arguments in bipolar fuzzy soft environment.Then, their related properties have been investigated.Finally, a practical example for selection of alternatives is given to demonstratethe utility and application of the proposed work.

This paper presents an adaptive neuro-fuzzy controller ANFIS (Adaptive Neuro-Fuzzy Inference System) for a bilateral teleoperation system based on FPGA (Field Programmable Gate Array). The proposed controller combines the learning capabilities of neural networks with the inference capabilities of fuzzy logic, to adapt with dynamic variations in master and slave robots and to guarantee good practical robustness against the disturbances, by adjusting neuro-fuzzy network output parameters in a short time, thanks to the computing power of FPGA and its high sampling frequency. The design methodology adopted to design the control algorithm aims to minimize the hardware resources used by the FPGA in order to optimize the execution and the design times, and this by using the Fixed-Point Tool and HDL Coder features of MATLAB-Simulink. The proposed controllers were experimentally validated on a teleoperation system comprising a pair of one degree of freedom. The experimental results clearly show that the proposed ANFIS control algorithm significantly outperformed the conventional control methods (PID).

In this paper, we propose a new method to analyze the difference and similarity of biological sequences, based on the fuzzy sets theory. Considering the sequence order and some chemical and structural properties, we present a computational method to cluster the biological sequences. By some examples, we show that the new method is relatively easy and we are able to compare the sequences of arbitrary lengths.

The purpose of this paper is to construct a weak hyper semi-quantale as a generalization of the concept of semi-quantale and used it as an appropriate hyperlattice-theoretic basis to formulate new lattice-valued topological theories. Based on such weak hyper semi-quantale, we aim to construct the notion of a weak hypervalued-topology as a generalized form of the so-called lattice-valued topology (or many-valued topology). Some properties of weak hyper semi-quantales and weak hypervalued-topologies will be studied. An adjunction between the category of weak hyper semi-quantales and the category of weak hypervalued quasi-topological spaces will be established.

Let $L$ be an integral and commutative quantale. In this paper, by fuzzifying the notion of generalized neighborhood systems, the notion of $L$-fuzzy generalized neighborhoodsystem is introduced and then a pair of lower and upperapproximation operators based on it are defined and discussed. It is proved that these approximation operators include generalized neighborhood system-based approximation operators, $L$-fuzzyrelation-based approximation operators and $L$-fuzzycovering-based approximation operators as their specialcircumstances. Therefore, the research on $L$-fuzzy generalizedneighborhood system-based approximation operators has more generalsignificance. In addition, when the $L$-fuzzy generalizedneighborhood system is serial, reflexive, unary and transitive,then the corresponding approximation operators are discussed and characterized, respectively.

In this paper, the concept of fuzzy automata normed linear structure spaces is introduced and suitable examples are provided. ;The ;concepts of fuzzy automata $alpha$-open sphere, fuzzy automata $mathscr{N}$-locally compact spaces, fuzzy automata $mathscr{N}$-Hausdorff spaces are also discussed. Some properties related with to fuzzy automata normed linear structure spaces and fuzzy automata $mathscr{N}$-Hausdorff spaces are discussed.

In this paper, we first characterize the convex $L$-subgroup of an $L$-ordered group by means of fourkinds of cut sets of an $L$-subset. Then we consider the homomorphic preimages and the product of convex $L$-subgroups.After that, we introduce an $L$-convex structure constructed by convex $L$-subgroups.Furthermore, the notion of the degree to which an $L$-subset of an $L$-ordered group is a convex $L$-subgroup is proposed and characterized. An $L$-fuzzy convex structure which results from convex $L$-subgroup degree is imported naturally, and its $L$-fuzzy convexity preserving mappings investigated.

High-technology projects are known as tools that help achieving productive forces through scientific and technological knowledge. These knowledge-based projects are associated with high levels of risks and returns. The process of high-technology project and project portfolio selection has technical complexities and uncertainties. This paper presents a novel two-parted method of high-technology project portfolio selection. In the first part, a new decision-making model under Pythagorean fuzzy set (PFS) uncertainty is introduced that is last aggregation and avoids defuzzification until the last step of the process. In the last step, a new PFS ranking method is used to make crisp and comparable values. Outcomes from this part form the objective function of a new integer programming (IP) of the project portfolio selection. To display the model’s application, data from a real case study of high-technology project evaluation and selection is presented, and the steps of the approach are illustrated in addition to presenting the efficacy of the model.

In this paper, we study residuated lattices in order to give new characterizations for dense, regular and Boolean elements in residuated lattices and investigate special residuated lattices in order to obtain new characterizations for the directly indecomposable subvariety of Stonean residuated lattices. Free algebra in varieties of Stonean residuated lattices is constructed. We introduce in residuated lattice a new type of filter called special filter and investigate its properties. Finally, regular filter property in residuated lattices is introduced and is studied in details.

In this paper, the orders induced by the residual implications obtained from uninorms are investigated. A necessary and sufficient condition is presented so that the ordinal sum of fuzzy implications satisfies the law of importation with a t-norm $T$. Some relationships between the orders induced by an ordinal sum implication and its summands are determined. The algebraic structures obtained from the orders induced by the residual implications and the ordinal sum implications are discussed.

In cite{Kats84}, Katsaras introduced a method for constructing a Hu-tton $[0,1]$-quasi-uniformity from a crisp uniformity. In this paper we present other different methods for making this based mainly in the concept of a fuzzy uniform structure. Furthermore, we prove that some of these methods preserve the completeness property of the quasi-uniformity.  Moreover, we also show that Katsaras' construction allows to develop a theory of completion of a Hu-tton [0,1]-quasi-uniform space obtained from a uniform space.

The hesitant fuzzy soft set (HFSS), as a combination of hesitant fuzzy and soft sets, is regarded as a useful tool for dealing with the uncertainty and ambiguity of real-world problems. In HFSSs, each element is defined in terms of several parameters with arbitrary membership degrees. In addition, distance and similarity measures are considered as the important tools in different areas such as pattern recognition, clustering, medical diagnosis, and the like. For this purpose, the present study aimed to evaluate the distance and similarity measures for HFSSs by using well-known Hamming, Euclidean, and Minkowski distance measures. Further, some examples were used to demonstrate that these measures fail to perform well in some applications. Accordingly, new distance and similarity measures were proposed by considering a hesitance index for HFSSs and the effect of considering hesitance index was shown by using an example of pattern recognition. Finally, the application of the proposed measures and hesitance index was investigated in the clustering and decision-making problem, respectively. In conclusion, the use of the proposed measures in clustering and hesitance index in decision-making can provide better and more reasonable results.

This paper presents a robust Fault Tolerant Tracking Control (FTTC) design for nonlinear uncertain systems describedby Takagi Sugeno (T-S) fuzzy models with unmeasurable premise variables subject to sensor faults. A ProportionalIntegral Observer (PIO) is proposed to estimate the faulty states and the time-varying sensor faults. The FTTC issynthesized based on the estimation derived from the PIO with a guaranteedH1performance to minimize the effect ofthe external disturbance. The trajectory tracking performances and the stability of the closed loop system are analyzedbased on the Lyapunov theory and theL2optimization. The stability condition are formulated in terms of LinearMatrix Inequality (LMI). The proposed robust FTTC is illustrated using simulation results

Fuzzification of support vector machine has been utilized to deal with outlier and noise problem. This importance is achieved, by the means of fuzzy membership function, which is generally built based on the distance of the points to the class centroid. The focus of this research is twofold. Firstly, by taking the advantage of robust statistics in the fuzzy SVM, more emphasis on reducing the impact of outliers on the generalizability of SVM has been placed. Moreover, the variety of membership function for the elliptical data has been designated, based on the classic and robust Mahalanobis distance. Minimum covariance determinant and orthogonalised Gnanadesikan Kettenring estimators are employed in the structure of the robust--fuzzy SVM.By implementing the new membership function, the disadvantages of the traditional fuzzy membership function has been rectified. Simulated and real benchmarking data set confirm the effectiveness of the proposed methods. Compared with the traditional SVM and fuzzy SVM, these methods give a better performance on reducing the effects of outliers and significantly improves the classification accuracy and generalization.