For a small quantaloid Q, a Q-closure space is a small category enriched in Q equipped with a closure operator on its presheaf category. We investigate Q-closure spaces systematically with specific attention paid to their morphisms and, as preordered fuzzy sets are a special kind of quantaloid-enriched categories, in particular fuzzy closure spaces on fuzzy sets are introduced as an example. By...

This paper examines type-2 fuzzy arithmetic using interval analysis. It relies heavily on alpha-cuts and alpha-planes. Furthermore, we discuss the use of quasi type-2 fuzzy sets proposed by Mendel and Liu and define quasi type-2 fuzzy numbers. Arithmetic operations of such numbers are defined and a worked example is presented. Keywords— Fuzzy Arithmetic, Type-2 Fuzzy Arithmetic, Type-2 Fuzzy Nu...

In this paper an adaptive neuro fuzzy inference system based on interval Gaussian type-2 fuzzy sets in the antecedent part and Gaussian type-1 fuzzy sets as coefficients of linear combination of input variables in the consequent part is presented. The capability of the proposed method (we named ANFIS2) to function approximation and dynamical system identification is shown. The ANFIS2 structure ...

Abstract. Recently, a number of extensions to classical fuzzy logic systems (type-1 fuzzy logic systems) have been attracting interest. One of the most widely used extensions is the interval type-2 fuzzy logic systems. An interval type-2 TSK fuzzy logic system can be obtained by considering the membership functions of its existed type-1 counterpart as primary membership functions and assigning ...

Finding a product with high quality and reasonable price online is a difficult task due to the fuzzy nature of data and queries. In order to handle the fuzzy problem, a new type-2 fuzzy reasoning based decision support system, the Web Shopping Expert for online users is proposed. In the Web Shopping Expert, an interval type-2 fuzzy logic system is used and a fuzzy output can be obtained using t...

in this paper, new definitions of $l$-fuzzy closure operator, $l$-fuzzy interior operator, $l$-fuzzy remote neighborhood system, $l$-fuzzy neighborhood system and $l$-fuzzy quasi-coincident neighborhood system are proposed. it is proved that the category of $l$-fuzzy closure spaces, the category of $l$-fuzzy interior spaces, the category of $l$-fuzzy remote neighborhood spaces, the category of ...

The challenges we face in today’s world are increasingly complex, and effectively managing uncertainty when modeling control problems can yield significant benefits. However, the complexity of these models often leads to higher computational costs. Therefore, main contribution this article is use theory shadowed type-2 fuzzy sets address search space exploration harmony algorithm by employing t...

In this paper, following the ideas of (continuous) t-norm and interval numbers, a concept of (continuous) interval-valued t-norm is proposed. Based on the interval-valued fuzzy set and the continuous interval-valued t-norm, we propose a notion of interval-valued fuzzy metric space, which is a generalization of fuzzy metric space in the sense of George and Veeramani [Fuzzy Sets and Systems 64 (1...

This paper presents a literature review of applications using type-2 fuzzy systems in the area of image processing. Over the last years, there has been a significant increase in research on higher-order forms of fuzzy logic; in particular, the use of interval type-2 fuzzy sets and general type-2 fuzzy sets. The idea of making use of higher orders, or types, of fuzzy logic is to capture and repr...

In recent years, the type-2 fuzzy sets theory has been used to model and minimize the effects of uncertainties in rule-base fuzzy logic system (FLS). In order to make the type-2 FLS reasonable and reliable, a new simple and novel statistical method to decide interval-valued fuzzy membership functions and probability type reduce reasoning method for the interval-valued FLS are developed. We have...