Iranian journal of fuzzy systems
Volume:19 Issue: 2, Mar-Apr 2022

This article poses and solves the problem of evaluating the feasibility of innovative project's 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 relationship between 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.

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 emph{proof-theoretically} by introducing and eliminating density rule. This paper introduces emph{model-theoretic} completeness for such logics. To this end, it is 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 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 fixpointed systems.

We characterize all functions that can be obtained as a $z$-ordinal sum of semigroups related to continuous t-norms, t-conorms, representable uninorms and idempotent semigroups. We show that this class of functions is bigger than the class of $n$-uninorms with continuous underlying functions. Vice versa, we show that the characterization of $n$-uninorms with continuous underlying functions via $z$-ordinal sum can be extendedto any  commutative, associative and non-decreasing binary function on the unit interval, which has continuous Archimedean components and is continuous on the diagonal.

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 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.

The conventional fuzzy least-squares time series models show undesirable performance when the fuzzy data set involves the outliers. By introducing a strategy to detect the outliers, this paper introduced a method for reducing the influence of outliers on the future predictions. For this purpose, according to the weighted square distance error, an estimation procedure was suggested for determining the exact coefficients in the presence of outliers. The parameters of the fuzzy time series model were then estimated using an iterative algorithm. In order to identify the potential outliers of the fuzzy data, a  quality control chart was employed based on the center of gravity criterion of fuzzy data. The defuzzification method was also employed to examine the performance of the proposed method via some  scatter plots. Several common goodness-of-fit criteria used in traditional time series models were also extended to compare the performance of the proposed fuzzy time series method to an existing method. The effectiveness of the proposed method was illustrated through two numerical examples including a simulation study. The results clearly indicated that the proposed model performs well in terms of the both scatter plot criteria and goodness-of-fit evaluations in cases where the potential outliers exist among the fuzzy data.

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-criteria decision-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 data set and using the existing methods.

In the framework of fuzzy transferable-utility games, Wu cite{wu1} derived the coincidences among of the proper core and the dominance core by providing some suitable conditions. By extending the results proposed by Wu cite{wu1}, we provide alternative relations to show that the proper core coincides with the dominance core under some necessary and sufficient conditions.

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, in this 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 can be used in decision-making. Finally, the approaches given and some of the important approaches in the literature are compared and analyzed.

This paper introduces the idea of deferred-statistical A-convergence of order β of the sequence of  fuzzy numbers by using  a regular matrix Aand deferred Ces`{a}ro mean $D_{p,q}$. Also,  we establish some relations between the proposed idea and the strong  deferred A-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 justify the results obtained from this investigation.

We show, for a commutative and integral quantale, that the recently introduced  category of $top$-uniform convergence spaces is a topological category which possesses natural function spaces, making it Cartesian closed. Furthermore, as two important examples for $top$-uniform convergence spaces, we study probabilistic uniform spaces and quantale-valued metric spaces. The underlying $top$-convergence spaces are also described and it is shown that in the case of a probabilistic uniform space this $top$-convergence is the convergence of a fuzzy topology with conical neighbourhood filters. Finally it is shown that the category of $top$-uniform convergence spaces can be embedded into the category of stratified lattice-valued uniform convergence spaces as a reflective subcategory.

This paper aims to establish the Karush-Kuhn-Tucker type optimality criteria for linear fractional optimization problems with fuzzy parameters. To evolve the desired criteria first, the fractional optimization problem is transformed into the non-fractional optimization problem with fuzzy parameters. Then Hukuhara differentiability for the differentiation of functions with fuzzy parameters and Hausdorff metric to expound the distance between the fuzzy numbers is invoked. Optimality criteria are then elicited for the non-fractional optimization problems by introducing Lagrange multipliers and Riemann integration theory. In order to validate the developed theory, two numerical optimization problems are also verified.

Due to the fact that Zadeh's quantifiers constitute the usual method to modify fuzzy propositions, the so-called family of T-power based implications was proposed. In this paper,  the four basic distributive laws  related to T-power based fuzzy implications  and fuzzy logic operations (t-norms and t-conorms) are deeply studied. This study shows that two of the four distributive laws of the T-power based implications have a unique solution, while the other two have multiple solutions.

Fuzzy modeling is a well-known solution for simplified modeling and predicting nonlinear systems behavior. Dynamic TSK Fuzzy Systems are an important branch in fuzzy modeling and are used for complex nonlinear dynamic systems modeling vastly. High order fuzzy systems have been developed recently in the fuzzy modeling field, aiming to reduce number of the fuzzy model rules compared to zero and first order systems, not in cost of a larger modeling error. Employing high order TSK in dynamic TSK fuzzy systems, motivates finding a better model for nonlinear dynamic systems. Closed loop control system design is an important usage of dynamic TSK models, including the stability analysis as the first step.\While stability investigation is a main part of any Controller design process, in this paper, a criterion has been investigated based on Lyapunov second method, for High Order Dynamic TSK Fuzzy System stability. Although the controller design process is not totally discussed in this paper, however some examples are provided to verify the proposed stability criterion.