Iranian Journal of Fuzzy Systems
https://ijfs.usb.ac.ir/
Iranian Journal of Fuzzy Systemsendaily1Tue, 01 Feb 2022 00:00:00 +0330Tue, 01 Feb 2022 00:00:00 +0330cover vol.19-no.1 February 2022
https://ijfs.usb.ac.ir/article_6561.html
Distributivity laws for quasi-linear means
https://ijfs.usb.ac.ir/article_6547.html
Aggregation operations play a fundamental &nbsp;role in a large number of disciplines, from mathematics and natural sciences to economics and social sciences. This paper is focused on &nbsp;the problem of distributivity for some special classes &nbsp;of aggregation operations, and quasi-linear means. Characterization of distributivity pairs for uninorms, semi-uninorms and associative a-CAOA vs quasi-linear means is given.Design and analysis of process capability indices cpm and cpmk by neutrosophic sets
https://ijfs.usb.ac.ir/article_6548.html
Process capability indices (PCIs) have been widely used to analyze capability of the process that measures how the customer expectations have been conformed. Two of the well-known PCIs, named indices&nbsp; C_{pm}&nbsp; and&nbsp; C_{pmk}&nbsp; have been developed to consider customers' ideal value that called target value ( T ). Although, these indices have similar features of the well-known indices C_{p}&nbsp; and&nbsp; C_{pk} , one of the most important differences is to consider \textit{T}. In real case problems, we need to add some uncertainties related with human's evaluations into process capability analysis (PCA). One of the uncertainty modelling methods called neutrosophic sets (NSs), have an important role in modeling uncertainty based on incomplete and inconsistent information. For this aim, the PCIs have been designed by using NSs to manage the uncertainties of systems and to increase sensitiveness, flexibility and to obtain more detailed results of PCA in this paper. For this aim, the indices&nbsp; C_{pm} and C_{pmk} have been performed and re-designed by using single valued neutrosophic numbers for the first time in the literature. Additionally, specification limits (SLs) have been re-considered by using NSs. The neutrosophic state of the SLs provide us to have more knowledge about the process and easily applied for engineering problems that includes uncertainty. Finally, the neutrosophic process capability indices (NPCIs) \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} have been obtained and the main formulas of them have been produced. Additionally, the proposed \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} have been applied on real case studies from manufacturing industry. The obtained results show that the indices \widetilde{\dddot{C}}_{pm} and \widetilde{\dddot{C}}_{pmk} include more informative and flexible results to evaluate capability of process.Type 2 adaptive fuzzy control approach applied to variable speed DFIG based wind turbines with MPPT algorithm
https://ijfs.usb.ac.ir/article_6549.html
In this research, a Type 2 adaptive fuzzy controller approach is formulated and designed to be applied to variable speed doubly fed induction generator-based wind turbines directly connected to the grid. It brings this study to evaluate the whole operation of the system to capture the highest rate of power in the wind turbines. The controlling approach is considered to keep the stator reactive power to the ideal value. In contrast to the other researches, here the controlling technique is developed through the nonlinear systems. &nbsp;By the aim of making progress in system operation, in contrast with the Type 1 adaptive fuzzy system, type two adaptive fuzzy theory is proposed to approximate a large number of uncertainties and the dynamic nonlinearities, exists in tracking errors which may limit the system performance. Feedback linearization control approach helps us to algebraically alter the system into a linearized plant. Thanks to the Lyapunov theorem, the introduced type two adaptive fuzzy approach is proved to meet the uniformly ultimately boundness (UUB) property. On the other hand, it results better tracking function. The simulation outputs represent that the proposed technique is robust enough in presence of parameter variations and unstructured uncertainties.Solvability of fuzzy fractional stochastic Pantograph differential system
https://ijfs.usb.ac.ir/article_6550.html
In this paper, a new type of &nbsp;equation namely &nbsp;fuzzy fractional stochastic Pantograph delay differential system &nbsp;(FSPDDS) is proposed. In our previous work, &nbsp;a first &nbsp;extension of fuzzy stochastic differential system into &nbsp; fuzzy fractional stochastic differential system by using Granular differentiability has been established. Here we study the existence and uniqueness &nbsp;results for the fuzzy FSPDDS which &nbsp;are obtained by using &nbsp;generalized Granular &nbsp;differentiability &nbsp;and contraction principle with weaker conditions. This kind of equation is used in many real world problems. Finally, we provide two numerical examples for the effectiveness of the theoretical results.A fuzzy non-parametric time series model based on fuzzy data
https://ijfs.usb.ac.ir/article_6551.html
Parametric time series models &nbsp; typically consists of model identification, parameter estimation, model diagnostic checking, and forecasting. However compared with parametric methods, nonparametric time series models often provide &nbsp;a very flexible approach to bring out the features of the observed time series. This paper suggested a novel fuzzy nonparametric method in time series models with fuzzy observations. For this purpose, a fuzzy forward fit kernel-based smoothing method was introduced to estimate fuzzy smooth functions corresponding to each observation. A simple optimization algorithm was also suggested to evaluate optimal bandwidths and autoregressive order. Several common goodness-of-fit criteria were also extended to compare the performance of the proposed fuzzy time series method compared to other fuzzy time series model based on fuzzy data. Furthermore, the effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results indicate that the proposed model performs better than the previous ones in terms of both scatter plot criteria and goodness-of-fit evaluations.A note on divisible discrete triangular norms
https://ijfs.usb.ac.ir/article_6552.html
Triangular norms and conorms on [0,1] as well as on finite chains are characterized by 4 independent properties, namely by the associativity, commutativity, monotonicity and neutral element being one of extremal points of the considered domain (top element for t-norms, bottom element for t-conorms). In the case of [0,1]domain, earlier results of Mostert and Shields on I-semigroups can be used to relax the latest three properties significantly, once the continuity of the underlying t-norm or t-conorm is considered. The aim of this short note is to show a similar result for finite chains, we significantly relax 3 basic properties of t-norms and t-conorms (up to the associativity) when the divisibility of a t-norm or of a t-conorm is considered.Ordinal sum constructions for aggregation functions on the real unit interval
https://ijfs.usb.ac.ir/article_6553.html
We discuss ordinal sums as one of powerful tools in the aggregation theory serving, depending on the context, both as a construction method and as a representation, respectively. Up to recalling of several classical results dealing with ordinal sums, in particular dealing, e.g., &nbsp;with continuous t-norms, copulas, or recent results, e.g., concerning uninorms with continuous underlying functions, we present also several new results, such as the uniqueness of the link between t-norms or t-conorms, and related Archimedean components, problems dealing with the cardinality of the considered index sets in ordinal sums, or infinite ordinal sums of aggregation functions covering by one type of ordinal sums both t-norms and t-conorms ordinal sums.Arithmetic operations and ranking of hesitant fuzzy numbers by extension principle
https://ijfs.usb.ac.ir/article_6554.html
A hesitant fuzzy number (HFN) is important as a generalization of the fuzzy number for hesitant fuzzy analysis and takes some applications that were discussed in recent literature. In this paper, we develop the hesitant fuzzy arithmetic, which is based on the extension principle for hesitant fuzzy sets. Employing this principle, standard arithmetic operations on fuzzy numbers are extended to HFNs and we show that the outcome of these operations on two HFNs are an HFN.Also we use the extension principle in HFSs for the ranking of HFNs, which may be an interesting topic.In this paper, we show that the HFNs can be ordered in a natural way. To introduce a meaningful ordering of HFNs, we use a new lattice operation on HFNs based upon extension principle and &nbsp;defining the Hamming distance on them.Finally, the applications of them are explained on optimization and decision-making problems.Monte Carlo statistical test for fuzzy quality
https://ijfs.usb.ac.ir/article_6555.html
Testing the capability of a productive process on the basis of the flexible fuzzy quality &nbsp;using Yongting's index is proposed in this paper by the Monte Carlo simulation.The theoretical approach and detailed steps of an algorithm are given to simulate the critical-value-based and also p-value-based approaches to statistical testing fuzzy quality. Also, the probability of type \textit{II} error of the quality test simulated by Monte Carlo &nbsp;approach. Moreover, a real-world case study is provided to show the performance of the proposed algorithm for triangular and trapezoidal fuzzy qualities.Constructing t-norms and t-conorms by using interior and closure operators on bounded lattices
https://ijfs.usb.ac.ir/article_6556.html
In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods by Ertu\u{g}rul, Kara\c{c}al, Mesiar \cite{Ertugrul} and \c{C}ayl{\i} \cite{Gul} as results. Also, we give some illustrative examples. Finally, we show that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices. This paper has further constructed the t-norms and t-conorms on bounded lattices from a mathematical viewpoint.Stability problem for Pexiderized Cauchy-Jensen type functional equations of fuzzy number-valued mappings
https://ijfs.usb.ac.ir/article_6557.html
We investigate the stability problems of the $n$-dimensional Cauchy-Jensen type and the n-dimensional Pexiderized Cauchy-Jensen type fuzzy number-valued functional equations in Banach spaces by using the metric defined on a fuzzy number space.Under some suitable conditions, some properties of the solutions for these equations such as existence and uniqueness are discussed. Our results can be regarded as important extensions of stability results corresponding to single-valued functional equations and set-valued functional equations, respectively.An approach based on $\alpha$-cuts and max-min technique to linear fractional programming with fuzzy coefficients
https://ijfs.usb.ac.ir/article_6558.html
This paper presents an efficient and straightforward method with less computational complexities to address the linear fractional programming with fuzzy coefficients (FLFPP). To construct the approach, the concept of $\alpha$-cut is used to tackle the fuzzy numbers in addition to rank them. &nbsp;Accordingly, the fuzzy problem is changed into a bi-objective linear fractional programming problem (BOLFPP) by the use of interval arithmetic. Afterwards, an equivalent BOLFPP is defined in terms of the membership functions of the objectives, which is transformed into a bi-objective linear programming problem (BOLPP) applying suitable non-linear variable transformations. Max-min theory is utilized to alter the BOLPP into a linear programming problem (LPP). It is proven that the optimal solution of the LPP is an $\epsilon$-optimal solution for the fuzzy problem. Four numerical examples are given to illustrate the method and comparisons are made to show the efficiency.An identification model for a fuzzy time based stationary discrete process
https://ijfs.usb.ac.ir/article_6559.html
A new approach of fuzzy processes, the source of which are expert knowledge reflections on the states on Stationary Discrete Extremal Fuzzy Dynamic &nbsp;System (SDEFDS) in extremal fuzzy time intervals, are considered. &nbsp;A fuzzy-integral representation of a stationary discrete &nbsp; extremal fuzzy process is given.A method and an algorithm &nbsp;for identifying the transition operator of SDEFDS are developed. &nbsp;The SDEFDS transition operator is restored by means of &nbsp;expert knowledge reflections on the states of SDEFDS. The regularization condition for obtaining of the quasi-optimal estimator of the transition operator is represented by the theorem. The corresponding calculating algorithm is provided. The results obtained are illustrated by an example in the case of a finite set of SDEFDS states.Construction of 2-uninorms on bounded lattices
https://ijfs.usb.ac.ir/article_6560.html
Uninorms and nullnorms are special 2-uninorms. In this work, we &nbsp;construct 2-uninorms on bounded lattices. Let L be a bounded lattice with a nontrivial element d. Given two uninorms U_1 and U_2, defined on sublattices [0,d] and [d,1], respectively, this paper presents two methods for constructing binary operators on L which extend both U_1 and U_2. &nbsp;We show that our first construction is a 2-uninorm on L if and only if U_2 is &nbsp;conjunctive &nbsp;and our second construction is a 2-uninorm on L if and only if U_1 is &nbsp;disjunctive. Moreover, we prove that the two &nbsp;2-uninorms are, respectively, &nbsp;the &nbsp;weakest &nbsp;and the strongest 2-uninorm among all 2-uninorms, the restrictions of which on [0,d]^2 and [d,1]^2 are respectively U_1 and U_2.translate vol.19-no.1 February 2022
https://ijfs.usb.ac.ir/article_6562.html
(2007-6024) Ranking of generalized fuzzy numbers based on accuracy of comparison
https://ijfs.usb.ac.ir/article_6164.html
Ranking generalized fuzzy numbers plays an important role in many applied models and, in particular, decision-making procedures. In ranking process of two generalized fuzzy numbers, it is natural to compare the sets of values in support of two the generalised fuzzy numbers. Accordingly, the comparison of a real number and a generalised fuzzy number as well as two generalised fuzzy numbers have to be considered. On the other hand, it is seen that a definitive process of comparison of a real number and a generalised fuzzy number, as well as two generalised fuzzy numbers, is not possible. So in this study, a method for comparing a real number and a generalised fuzzy number with a degree of accuracy (between a zero and one) is defined and then the method is generalized to compare two generalised fuzzy numbers. In general, an index to rank a real number and generalised fuzzy number is constructed. Eventually, this index is extended to rank two generalised fuzzy numbers based on the concept of accuracy of comparison. The advantage of our method is that it can compare two generalised fuzzy numbers with an accuracy of comparison. Also, a definition is introduced to make a definitive comparison. Finally, the proposed method is illustrated by some numerical examples.(2011-6276) Spherical fuzzy soft sets: Theory and aggregation operator with its applications
https://ijfs.usb.ac.ir/article_6376.html
The aim of this paper is to redefine the notion of spherical fuzzy soft sets as a more general concept to make them more functional for solving multi-criteria decision-making problems. We first define the set operations under the new spherical fuzzy soft set environment and obtain some fundamental properties of them. Then, we construct the spherical fuzzy soft aggregation operator which allows establishing a more efficient and useful method to solve the multi-criteriadecision-making problems. We establish an algorithm for the decision-making process which is more useful, simple, and easier than the existing methods. After constructing the method for solving the decision-making problem, we give a numerical example based on linguistic terms to show that the validity of the proposed technique. Finally, we analyze the reliability of the results of this method with the help of the comparative studies by applying this to a real-time dataset and using the existing methods.(2102-6461) Two novel approaches that reduce the effectiveness of the decision maker in decision making under uncertainty environments
https://ijfs.usb.ac.ir/article_6430.html
Unlike other mathematical models, soft set theory provides a parameterization tool contribution. However, in this theory, since membership degrees are expressed as 0 and 1, for (0; 1), we cannot determine whether any object belongs to a parameter or not. Researchers have tried to overcome this situation by ensuring that the decision maker expresses these values. However, we cannot know the accuracy of the data provided to us by the decision maker. Therefore, inthis study, we introduced the concepts of relational membership function, relational non-membership function, inverse relational membership function and inverse relational non-membership function and examined the related properties of these concepts. Then, we propose two new approaches so that uncertainty can be expressed in an ideal way and canbe used in decision-making. Finally, the approaches given and some of the important approaches in the literature are compared and analyzed.(2106-6698) On deferred statistical A−convergence of fuzzy sequence and applications
https://ijfs.usb.ac.ir/article_6474.html
This paper introduces the idea of deferred-statistical A&minus;convergence of order &beta; of the sequence of fuzzy numbers by using a regular matrix A and deferred Cesaro mean Dp,q. Also, we establish some relations between the proposed idea and the strong deferred A&minus;summability of sequences of fuzzy numbers. As an application, we apply this newly statistical convergence for proving fuzzy Korovkin-type approximation theorem. Some illustrative examples are provided to justifythe results obtained from this investigation.(2102-6468) ⊤-uniform convergence spaces
https://ijfs.usb.ac.ir/article_6528.html
We show, for a commutative and integral quantale, that the recently introduced category of ⊤-uniform convergence spaces is a topological category which possesses natural function spaces, making it Cartesian closed. Furthermore, as two important examples for ⊤-uniform convergence spaces, we study probabilistic uniform spaces and quantale-valued metric spaces. The underlying ⊤-convergence spaces are also described and it is shown that in the case of a probabilisticuniform space this ⊤-convergence is the convergence of a fuzzy topology with conical neighbourhood filters. Finally it is shown that the category of ⊤-uniform convergence spaces can be embedded into the category of stratified lattice-valued uniform convergence spaces as a reflective subcategory.(2008-6105) Semilinear logics with knotted axioms
https://ijfs.usb.ac.ir/article_6532.html
Standard completeness, completeness on the real unit interval [0, 1], is one of important research areas in mathematical fuzzy logic. Recently, standard completeness for semilinear logics with knotted axioms has been investigated prooftheoretically by introducing and eliminating density rule. This paper introduces model-theoretic completeness for such logics. To this end, it is&nbsp; first shown that knotted axioms can be divided into left and right ones and then proved that mianorm-based logic systems with left and right knotted axioms are standard complete. This completeness is provided by embedding linearly ordered algebras into densely ordered ones and these algebras again into [0, 1]. More exactly, mianorm-based systems with left and right knotted axioms and their algebraic structures are&nbsp; first discussed. After some examples of mianorms satisfying left and right knotted properties are introduced, standard completeness for those logics is established model-theoretically using the above construction. Finally, this investigation is extended to their corresponding involutive&nbsp; fixpointed systems.( 2102-6470) Fuzzy-logic model for feasibility study of project implementation: Projects investment risk
https://ijfs.usb.ac.ir/article_6533.html
This article poses and solves the problem of evaluating the feasibility of innovative projects financing in the face of uncertainty due to the need to combine both quantitative and qualitative characteristics. It is suggested to build a range of tools for assessing the investment risks on the basis of the mathematical fuzzy logic methods, which allow the use and accumulation of specialists knowledge. A logical-linguistic model allowing the establishment of relationshipbetween input and output parameters when assessing the attractiveness level of projects has been developed on the basis of production rules compiled by experts. The model is implemented with the help of MATLAB system and allows, in conditions of uncertainty, making scientifically and quantitatively sound decisions when financing investment projects.