Iranian journal of fuzzy systems
Volume:18 Issue: 3, May-Jun 2021

We consider a category C enriched over the segment [0,1] whose hom-objects are real numbers from [0,1]. For a suitably defined function $hat{v}$  assigning to each formula $varphi$ some object of $C$, the hom-object $C(hat{v} (varphi),hat{v}(psi))$ represents the degree of derivability of $psi$ from $varphi$. We reformulate completeness result for intuitionistic propositional logic, as well as H' ajek's completeness results concerning the product, G" odel and L ukasiewicz fuzzy logic in the context of enriched category theory.

We generalize set-based extended functions, recently introduced by Mesiar et al., into 2-set-based extended functions. In both cases, an efficient reduction of repeated  data to be fused is considered which prepares a sound background for big data processing. We discuss and study several types of 2-set-based extended functions, in particular,  2-set-based extended aggregation functions, including t-norms, t-conorms, uninorms, nullnorms and OWA operators.

Always the decision of the government to the private sector is faced with the challenges and high level of importance, because these decisions should be taken at the meeting of standards and functional requirements to overcome investors' interests. These decisions include education, and due to the governance nature of education and the governments' strategies in this area, the private sectors who act in it, have been affected by the consequences of different decisions. \In this paper, our motivation is to propose a system to decide on how to develop applied academic educations at the Applied ScienceEducation Centers (ASEC's) which are supervised by the University of Applied Science and Technology (UAST) in Iran. The method used is theFuzzy Inference System (FIS) to reach this goal. The model performed in this study consists of a two-part FIS for two purposes straight ahead.The first concerns the quantitative development of higher applied education, including the number of Course Request (CR) for each ASEC with 4 inputs and 242 rules. The latter, is related to the qualitative development of higher applied education, including the assessment of the capability and competence of each ASEC for specific CR with the course and student admission background, specialty, committee's and council’s opinion, and frequency of course in city or province with 9 inputs, 350 rules, and an output. Each section has its inputs and rules that are determined and used by experts in this domain. \Our results show that using this method, provides some cost and time savings. This model analyzes in less than 2 minutes, while in practice it could be gain within 1650 person /hours work in different committees that all of them have their costs. Also, results are very close to reality with the advantage that there is no way to apply personal preferences, which largely meets the needs of research.

Data Envelopment Analysis (DEA) is a multi-criteria technique based on linear programming to deal with many real-life problems, mostly in nonprofit organizations. The slacks-based measure (SBM) model is one of the DEA model used to assess the relative efficiencies of decision-making units (DMUs). The SBM DEA model directly used input slacks and output slacks to determine the relative efficiency of DMUs. In order to deal with qualitative or uncertain data, a fuzzy SBM DEA model is used to assess the performance of DMUs in this study. The credibility measure approach, transform the fuzzy SBM DEA model into a crisp linear programming model at different credibility levels is used. The results came from the fuzzy DEA model are more rational to the real-world situation than the conventional DEA model. In the end, the data of Indian oil refineries is collected, and the efficiency behavior of the companies obtained by applying the proposed model for its numerical illustration.

The main purpose of this paper is to obtain an analytical solution for the time-fractional fuzzy equation. To do this, the time-fractional equation is  transformed into an algebraic equation using the fuzzy Laplace and Fourier transforms. The fractional derivatives are described in the Caputo gH-differentiability. In addition, to demonstrate the efficiency of the method some various examples are solved.

In this paper, we develop the C-continuity via Scott Q-cotopological spaces, where Q is a commutative and integral quantale.The main results are: (1) The set of all C-compact elements of a completeQ-ordered set is irreducible complete; (2) The Scott Q-cotopology of a Q-ordered set under the fuzzy inclusion order is C-continuous, evenC-prealgebraic; (3) We establish an adjunction between the category of irreducible complete Q-ordered sets and the category of C-prealgebraic complete Q-ordered sets.

In this study, new methods to construct triangular norms and triangular conorms on appropriate bounded lattices are introduced. Some illustrative examples are given for clarity. Also, the relation between introduced methods and some other approaches is investigated. Finally, it is shown that the introduced construction methods can be generalized by induction to a modified ordinal sum for triangular norms and triangular conorms on appropriate bounded lattices. And some illustrative examples are given.

In this paper, we introduce a general$(oplus,otimes)$-convex function based on semirings $([a,b],oplus, otimes)$ with pseudo-addition $oplus$ andpseudo-multiplication $otimes.$ The generalization of the finiteJensen's inequality, as well as pseudo-integral with respect to$(oplus,otimes)$-convex functions, is obtained. This also generalizes Jensen's inequalities for Lebesgue integral and the results of Pap and v{S}trboja cite{12}. Meanwhile, we also prove Jensen's inequalities for pseudo-integrals on semirings $([a,b], sup, otimes)$with respect to nondecreasing functions and present correspondingresults for generalized fuzzy integrals.

Functional equations involving aggregation functions play an important role in fuzzy sets and fuzzy logic theory. That the migrativity equation as a kind of restricted general associative equation have been proven to be useful in a wide range of fields like decision making, aggregation of information, image processing and so on. In the literature, the already existing results concerning the migrativity equation between overlap (grouping) functions and uninorms are based on the assumption that uninorms belong to one of the most studied classes. In this study we will explore it involving uninorms in a more general setting. To be specific, we investigate the migrativity properties between overlap (grouping) functions and uninorms in the case when uninorms have continuous underlying operators. We will show along the paper that many new solutions to the equation are characterized from this new point of view.

To solve fuzzy differential equations driven by Liu process, three Milstein schemes are proposed in this work, which are explicit Milstein scheme, semi-implicit Milstein scheme and improved Milstein scheme. Improved Milstein scheme is constructed by correcting the error with semi-implicit method, the error is the difference between the exact solution of fuzzy differential equations and the solution derived from Milstein scheme. These numerical methods are proved to have strong convergence with order two. Accompanying the results above, the concept of mean-stability of numerical schemes for fuzzy differential equations is put forward and analyzed. For a linear test equation, it is showed the mean-stability region of improved Milstein scheme is bigger than explicit Milstein scheme. Finally, the accuracy and effectiveness of these schemes are confirmed through numerical examples.

In this paper, we consider the Hyers-Ulam-Rassias stability of theimpulsive fuzzy nonlinear difference equations in the multidimensional fuzzy quaternion space.Some sufficient conditions of the Hyers-Ulam-Rassias stability are established for the quaternion multidimensional fuzzy nonlinear difference equations with impulses and several examples are demonstrated to show the feasibility of our obtained results.

The fuzzy support vector machine is one of the most exceptional methods to deal with uncertainty in the classification problem. The membership function is a proper way to model uncertainty. The goal of the membership function is to distinguish the different points in terms of their importance. The ordinary design of the membership function relies on the distance of the observations to the class center. However, the class center is affected by the presence of outliers.  To prevent this effect, we utilized an unsupervised learning method called the Gaussian mixture model in the structure of the membership function. The proposed membership function is presented in two different categories distance-based and Bayes-based. Unlike the classical membership function, the contribution of outliers in the training phase decreased by diminishing their degree of importance.  Hybridizing the classic fuzzy support vector machine classifier with the Gaussian mixture model will enhance the classification accuracy and also will prevent overfitting problems. The superiority of the proposed methods assessed by the synthetic and benchmarking dataset. The statistical significance is assessed by using the non-parametric Friedman and post-hoc Nemenyi tests.

In this paper, an improved Type2-PCM clustering algorithm based on improved adaptive particle swarm optimization called Type2-PCM-IAPSO is proposed. Firstly, a new clustering algorithm called Type2-PCM is proposed. The Type2-PCM algorithm can solve the problems encountered by fuzzy c-means algorithm (FCM), Gustafson-Kessel algorithm (G-K), possibilistic c-means algorithm (PCM) and NPCM (sensitivity to noise or aberrant points and local minimal sensitivity). . . etc. Secondly, we combined our Type2-PCM algorithm with the improved adaptive particle swarm optimization algorithm (IAPSO) to ensure proper convergence to a local minimum of the objective function. The effectiveness of the two proposed algorithms Type2-PCM and Type2-PCM-IAPSO was tested on a system described by a different equation, Box-Jenkins gas furnace, dryer system and the convection system. The validation tests used showed good performance of these algorithms. However, their average square error test (MSE) shows a better behaviour of the Type2-PCM-IAPSO algorithm compared to the FCM, G-K, PCM, FCM-PSO, Type2-PCM-PSO, RKPFCM and RKPFCM-PSO algorithms.