Narrow Results

The transformation method has been proposed as a practical tool for the simulation and the analysis of systems with uncertain, fuzzy-valued model parameters using fuzzy arithmetic. Up to now, this method has been available in two forms: in a general form, which can be used for the simulation and the analysis of arbitrarily non-monotonic problems, and in a reduced form, which reduces the computational costs of the method to a large extent, but requires, instead, an additional condition to be fulfilled. In this paper, the extended transformation method will be introduced as an advanced version of the previously presented formulations of the transformation method. This extended version includes the former versions as marginal cases and allows a pre-adjustment of the method subject to the number of model parameters that are expected to cause non-monotonic behavior of the model output. Furthermore, to set up the method properly, a novel approach, again based on the transformation method, is presented to practically detect those parameters that are responsible for a non-monotonic behavior of the model output. Finally, to show its effectiveness, the method is applied to a static and a dynamic model with uncertain parameters.

In this paper we propose the new extended class of t-norm operators called the boundary weak. The aim of the extension of this operator is that the sum of the fuzzy numbers in the arithmetic based on such t-norm gives the more narrow fuzzy number if compared to arithmetic based on standard t-norm. This extension is based on the replacement of the condition T(x,1)=x by the weaker one: T(x,1)≤x, for x∈[0,1].

In this paper we investigate whether the fuzzy arithmetic based on Zadeh's extension principle could be improved by redefining the fuzzy addition and multiplication so that the class of fuzzy numbers combined with these operations would constitute a field. We will prove that such a fuzzy arithmetic does not exist. This has important consequences for solving systems of linear fuzzy equations. Despite the lack of inverses, we propose a method to solve approximately such systems.

Fuzzy mathematics is a generalization in which fuzzy numbers replace real numbers and fuzzy arithmetic replaces real arithmetic. It is an excellent scope for modeling vague and uncertain aspects of the actual environments. In this important area, Dubois and Prade¹ defined a fuzzy matrix as a rectangular array of fuzzy numbers. They have also defined the LR type fuzzy numbers with some useful approximate arithmetic operators. The aim of this paper is to extend some useful aspects of linear algebra e.g. determinant, norm and eigenvalue for fuzzy matrices with LR fuzzy number entries by the use of fuzzy arithmetic. Finally, applications in fuzzy analytical hierarchy process (AHP) are investigated.

Recently Ganesan and Veeramani introduced a new approach for solving a kind of linear programming problems involving symmetric trapezoidal fuzzy numbers without converting them to the crisp linear programming problems. But their approach is not efficient for situations in which some or all variables are restricted to lie within fuzzy lower and fuzzy upper bounds. In this paper, by a natural extension of their approach we obtain some new results leading to a new method to overcome this shortcoming.

Identification of important design requirements for product development is critical because it leads to successful products with shorter development time. Quality Function Deployment (QFD) is a tool to help the product development team to systematically determine the design requirements for developing a product with higher customer satisfaction. Therefore, determining the Importance rating of Engineering Characteristics should be robust and reliable. Generally, in QFD charts the relationships between Customer Attributes and Engineering Characteristics can be defined using linguistic variables that have three values: Weak, Medium and Strong. Reversing priority of results (rank reversing) is possible when various scales such as 1-3-5 or 1-3-9 are employed. In this paper, the effect of using fuzzy numbers in rank reverse reduction is studied. For this study a statistical experiment for measuring rank reverse with fuzzy numbers was designed. This experiment was replicated for 7 sets, which included symmetrical and non-symmetrical triangular and trapezoidal fuzzy sets with various degrees of fuzziness. This experiment was extended for cases involving relative importance for Customer Attributes with various fuzzy sets used for weights of importance. The results showed a major reduction in rank reversal using symmetrical membership functions. Furthermore, results did not depend on system fuzziness, and there were not any major differences between the use of triangular and trapezoidal membership functions.

Intuitionistic fuzzy set (IFS) is the straight simplification of fuzzy set theory (FST). Nevertheless, estimation of the arithmetic operation on generalized intuitionistic fuzzy number (GIFNs) is a critical apprehension. This paper presents an attempt to set up a novel method for effectively resolving the drawbacks of conform arithmetic operations on generalized triangular intuitionistic fuzzy numbers (GTIFNs). For this purpose, decomposition theorems for generalized trapezoidal intuitionistic fuzzy numbers (GTrFNs) are studied. Numerical examples are illustrated herewith. Finally, to validate the requirement of a novel elucidation, an application in medical analysis has been carried out under this setting.

This paper proposes two new computational methods for solving linear programming problem under trapezoidal and triangular fuzzy uncertainties with equality constraints. The coefficients of the constraints and the objective functions are assumed to be crisp. However, the decision variables and the right-hand side vector of the constraints are considered as uncertain in nature. The concepts of fuzzy addition and subtraction have been used to develop the proposed methods. In the first method, the coefficients are considered as non-negative, whereas mixed coefficients (i.e. both negative and non-negative) are considered in the second method. The obtained results are compared with Behera et al. [D. Behera, K. Peters and S. A. Edalatpanah, Alternative methods for linear programming problem under triangular fuzzy uncertainty, Journal of Statistics and Management Systems, 25 (2022) 521–539; D. Behera, K. Peters, S. A. Edalatpanah and D. Qiu, New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty, Journal of Information and Optimization Sciences, 42 (2021) 603–629], and Saati et al. [S. Saati, M. Tavana, A. Hatami-Marbini and E. Hajiakhondi, A fuzzy linear programming model with fuzzy parameters and decision variables, International Journal ofInformation and Decision Sciences, 7 (2015) 312–333.] for the validation.

New non standard operations of subtraction (⊝) and division (Ø), acting on fuzzy numbers, are introduced to solve fuzzy equations with the effect of reducing fuzziness in successive computations. Their properties are presented and it is shown how these operations are combined or related with the usual operations of addition (+) and multiplication (×) in a hybrid fuzzy arithmetic.