Continuing to pursue a research direction that we already explored in connection with Gödel-Dummett logic and Ruspini partitions, we show here that Lukasiewicz logic is able to express the notion of pseudo-triangular basis of fuzzy sets, a mild weakening of the standard notion of triangular basis. En route to our main result we obtain an elementary, logic-independent characterisation of triangu...

In this article, we would like to study the determinant theory of fuzzy matrices. The purpose of this article is to present a new way of expanding the determinant of fuzzy matrices and thereafter some properties of determinant are considered. Most of the properties are found to be analogus to the properties of determinant of matrices in crisp cases. Index Terms — reference function, membership ...

Here at first we are going to give a brief history of the development of fuzzy entropy. Finally, new measures for entropy of fuzzy sets in continuous cases are introduced. In this article, our main purpose is to show that the entropy of fuzzy number is very much dependent on the selection of intervals. Another important thing which can be observed from the cases discussed is that the entropy of...

In this paper, deriving the fuzzy weights of criteria from the fuzzy pair-wise comparison matrix with triangular fuzzy elements is investigated. In the proposed method we first use the ranking function to convert the triangular fuzzy data into crisp one. Then by using the goal programming method we derive the fuzzy weights of criteria. We propose two new methods, and it is shown that these meth...

This paper deals with the simplest fuzzy PID controllers which employ two fuzzy sets for each of the three input variables and four fuzzy sets for the output variable. Mathematical model for a fuzzy PID controller is derived by using asymmetric Γ-function type and L-function type membership functions for each input, asymmetric trapezoidal membership functions for output, algebraic product trian...

Process capability indices (PCIs) can be used as an effective tool for measuring product quality and process performance. In classic quality control there are some limitations which prevent a deep and flexible analysis because of the crisp definition of PCA‟s parameters. Fuzzy set theory can be used to add more flexibility to process capability analyses. In this study, the fuzzy X ba and MRx ba...

Risk assessment is a popular and important tool in decision making process. Risk assessment is generally performed using models and model is a function of some parameters which are usually affected by uncertainty. Here, we consider that model parameters are affected by epistemic uncertainty. To represent epistemic uncertainty in general triangular fuzzy number or trapezoidal fuzzy numbers are u...

In this paper, we consider fuzzy inventory with backorder. First, we fuzzify the storing cost a, backorder cost b, cost of placing an order c, total demand r, order quantity q, and shortage quantity s as the triangular fuzzy numbers in the total cost. From these, we can obtain the fuzzy total cost. Using the signed distance method to defuzzify, we get the estimate of the total cost in the fuzzy...

The effect and quality of education is the fundamental of higher education, and instructional reform is the core one of all reforms in higher education. In order to motivate the instructional reform and enhance the quality of education, the department of education in China has evaluated and rewarded the study performance in instructional practice of educators in higher learning instructions sin...

The main contribution of this paper is to introduce an autonomous definition of the connective “fuzzy exclusive or” (fuzzy Xor, for short), which is independent from others connectives. Also, two canonical definitions of the connective Xor are obtained from the composition of fuzzy connectives, and based on the commutative and associative properties related to the notions of triangular norms, t...