Iranian journal of fuzzy systems
Volume:15 Issue: 5, Sep-Oct 2018

In the study, we propose the Associated Probability Intuitionistic Fuzzy Weighted Averaging (As-P-IFWA) and the Associated Probability Intuitionistic Fuzzy Weighted Geometric (As-P-IFWG) aggregation operators with associated probabilities of a fuzzy measure presenting an uncertainty. Decision makers' evaluations are given as intuitionistic fuzzy values and are used as the arguments of the aggregation operators. In the paper, we prove correctness of extensions and show the conjugate connections between the constructed operators. Several versions of the new operators are successfully used in the business start-up decision making problem.

A novel approach is proposed for the problem of testing statistical hypotheses about the fuzzy mean of a fuzzy random variable.The concept of the (uniformly) most powerful test is extended to the (uniformly) most powerful fuzzy-valued test in which the test function is a fuzzy set representing the degrees of rejection and acceptance of the hypothesis of interest.For this purpose, the concepts of fuzzy test statistic and fuzzy critical value have been defined using the $\alpha$ cuts (levels) of the fuzzy observations and fuzzy parameter.In order to make a decision as a fuzzy test, a well-known method is employed to compare the observed fuzzy test statistic and the fuzzy critical value.In this work, we focus on the case in which the fuzzy data are observations of a normal fuzzy random variable.The proposed approach is general so that it can be applied to other kinds of fuzzy random variables as well.Numerical examples, including a lifetime testing problem, are provided to illustrate the proposed optimal tests

The problem of disturbance rejection in the control of nonlinear systems with additive disturbance generated by some unforced nonlinear systems, was formulated and solved by {\itshape Mukhopadhyay} and {\itshape Narendra}, they applied the idea of increasing the order of the system, using neural networks the model of multilayer perceptron on several systems of varying complexity, so the objective of this work is using the same idea with two other recent methods fast and reliable ; fuzzy set systems and hybrid neuro-fuzzy systems respectively to compute the control law which minimizes the effect of the disturbance at the output of nonlinear systems. The application of the methods previously cited in form of results is presented to determine the identification model and to provide theoretical justification to existence a solution of disturbance rejection. Our better results with fuzzy systems and neuro-fuzzy systems are presented and discussed in detail in this paper with several systems of increasing complexity.

The objective of this work is to present a triangular interval type-2 (TIT2) intuitionistic fuzzy sets and their corresponding aggregation operators, namely, TIT2 intuitionistic fuzzy weighted averaging, TIT2 intuitionistic fuzzy ordered weighted averaging and TIT2 intuitionistic fuzzy hybrid averaging based on Frank norm operation laws. Furthermore, based on these operators, an approach to multi-criteria decision-making, in which assessments are in the form of TIT2 intuitionistic fuzzy numbers has been developed. A practical example to illustrate the decision-making process has been presented and compared their results with the existing operator results.

Firstly, two kinds of natural distances between intuitionistic fuzzy sets are generated by the classical natural distance between fuzzy sets under a unified framework of residual intuitionistic implication operators. Secondly, the continuity and approximation property of a method for solving intuitionistic fuzzy reasoning are defined. It is proved that the triple implication method for intuitionistic fuzzy modus ponens has both continuity and approximation property with respect to these two kinds of natural distances based on {\L}ukasiewicz implication, meanwhile the triple implication method for intuitionistic fuzzy modus tollens possesses unconditional continuity and conditional approximation property. Finally, some robustness results about the triple implication method of intuitionistic fuzzy reasoning are given.

In this paper, a method is introduced which reduces the harmonic distortion of the inverter output current, connecting the fuel cell to the AC load. Using FUZZY LOGIC-PI (FLPI), the controlling method is engaged in optimum tuning of the PI controller coefficients of this converter. This converter has only one DC-AC boost inverter and simultaneously has the task of increasing voltage level and generating the AC power. In order to control the inverter output voltage, an internal current control loop and an external voltage control loop are used. Designing the control of each loop is done separately based on FLPI controller. Simulation results for proposed fuel cell energy system in the presence of this controller imply good performance of FLPI and suitable mitigation of inverter output current ripple

In this paper, a novel problem of observer-based adaptive fuzzy fractional control for fractional order dynamic systems with commensurate orders is investigated; the control scheme is constructed by using the backstepping and adaptive technique. Dynamic surface control method is used to avoid the problem of “explosion of complexity” which is caused by backstepping design process. Fuzzy logic systems are used to approximate the unknown nonlinear functions. A fractional order Lyapunov function is defined at each stage and the negativity of an overall Lyapunov function is ensured by proper selection of the control law. It is proven that the proposed controller guarantees the boundedness property for all the signals and also the tracking error can converge to a small neighborhood of the origin. Simulation examples are given to demonstrate the effectiveness and robustness of the proposed controllers.

In this contribution, we first introduce the concept of metrical T-norm-based similarity measure for hesitant fuzzy sets (HFSs) {by using the concept of T-norm-based distance measure}. Then, the relationship of the proposed {metrical T-norm-based} similarity {measures} with the {other kind of information measure, called the metrical T-norm-based} entropy measure {is} discussed. The main feature of the proposed { metrical T-norm-based similarity measures} is a possibility of comparing {similarity between HFSs} without regarding what {value is returned by} the similarity measure.{To illustrate the application of the proposed metrical T-norm-based similarity measures, we consider two problems of} medical diagnosis {and pattern recognition} to compare the proposed {metrical T-norm-based similarity measures} with a number of {the} existing HFS similarity measures