There are presented the basic operations on real intervals: pseudo-addition and pseudo multiplication which induce the semiring structure. Application of special pseudo-operations on the unit interval: t-norms and t-conorms, in the theory of fuzzy sets and fuzzy logics are given. Pseudo-convolution as a generalization of the classical convolution is given, with many important special cases. Fur...

We discuss a formal many-valued logic called EQlogic which is based on a recently introduced special class of algebras called EQ-algebras. The latter have three basic binary operations (meet, multiplication, fuzzy equality) and a top element and, in a certain sense, generalize residuated lattices. The goal of EQ-logics is to present a possible direction in the development of mathematical logics...

As can be seen from the definition of extended operations on fuzzy numbers, subtraction and division of fuzzy numbers are not the inverse operations to addition and multiplication . Hence, to solve the fuzzy equations or a fuzzy system of linear equations analytically, we must use methods without using inverse operators. In this paper, a novel method to find the solutions in which 0 is not the ...

The aim of this discussion is to introduce a new fuzzy regression model, based on the distance between the outputs of the model in terms of its measurements along with the optimal confidence level ‘h’ using the shape preserving operations. Simple fuzzy regression models with fuzzy inputfuzzy outputs are also considered in which the coefficients of the models are themselves triangular fuzzy numb...

In this paper, the concepts of intuitionistic fuzzy α-translation (IFAT), α-multiplication (IFAM), and magnified βα-translation (IFMBAT) are introduced in setup PS-algebra. Some properties PS-ideal PS-subalgebra investigated by applying IFAT, IFAM, IFMBAT. Intersection union PS-ideals explained through results examples.

We have defined and studied the weighted Nakano sequence spaces of fuzzy functions. constructed ideal generated by extended s -fuzzy functions present some topological geometric structures this class multiplication mappings acting on space Moreover, existence Caristi’s fixed point is examined. To show how work done, exam...

− The fuzzy weighted average (FWA) is used in many engineering problems where aggregation of fuzzy information is dealt with. In this framework, many algorithms have been proposed to compute efficiently the FWA according to Zadeh's extension principle. However, due to fuzzy interval calculus, the exact solution presents a characteristic that may be viewed as an important drawback. Indeed, repla...

A novel formalism is presented, which enables the processing of heterogeneous data including numeric-, interval-valued-, or fuzzydata. The data in question are represented herein as interval-supported fuzzy sets with suitable membership functions. The term Fuzzy Interval Number (FIN) denotes one of the aforementioned types of data. A FIN can have either a positive or a negative membership funct...