Narrow Results

In this paper, we propose a method to calculate the correlation coefficient of fuzzy numbers by means of "α-cut". This value obtained from our formula tells us not only the strength of relationship between the fuzzy numbers, but also whether the fuzzy numbers are positively or negatively related. This approach looks better than previous methods which only evaluate the strength of the relation. Furthermore, we extend the "α-cut" method to interval-valued fuzzy numbers. The value of the correlation coefficient between interval-valued fuzzy numbers lies in the interval [-1, 1], as computed from our formula.

In this paper, we have studied representability of both fuzzy biorders and fuzzy weak orders. It has also been shown that union of a finite family of fuzzy weak orders with respect to a t-norm T is a fuzzy quasi-transitive relation with respect to T. In the last theorem, we have obtained a characterization for a T_L-representable fuzzy weak order.

In this paper, we provide a definition of α-fuzzified lower and upper approximations for fuzzy sets based on the α-cut of fuzzy binary relations. We show that the definition is a proper generalization of the previous one for approximations of crisp sets and compare it with an existing definition in the context of fuzzy tolerance relation.

As the number of parameters involved in an economic model is often uncertain, we propose that it be estimated using fuzzy numbers. Since we move in an environment of uncertainty, it is logical to leave room for deviation in estimating membership functions. We should recall that when soft max-min operators are used, the resulting deviation is never greater than the variation introduced in estimating the initial data. Often, the result of our calculations is not a triangular fuzzy number. In this paper we study the value of approximating the resulting non-linear fuzzy number using a triangular fuzzy number having the same support and kernel. Finally, we present a simple method for weighing this approximation.

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.

We present a soft computing approach to character recognition from printed documents. For feature extraction, we define a number of fuzzy sets on the Hough transform of character pattern pixels and synthesize additional fuzzy sets by t-norms. The height of each t-norm constitutes a feature element and a set of 'n' such feature elements form an n-dimensional feature vector for the character. A 3n-dimensional vector is then generated from the n-dimensional feature vector by defining three linguistic fuzzy sets, namely, weak, moderate and strong. These 3n-dimensional vectors form a Multilayer Perceptron (MLP) input for training by back propagation. The MLP outputs represent fuzzy sets denoting the belongingness of an input pattern to a number of fuzzy pattern classes. The feature set is chosen by optimizing a Feature Quality Index (FQI) using genetic algorithm. A two-state Markov chain is used to model degraded document images for simulation tests. The system can recognize characters with an accuracy of 98%.