In a previous paper [10] we explored the notion of coherent fuzzy consequence operator. It is well-known that the operator induced by a fuzzy preorder through Zadeh’s compositional rule is always a coherent fuzzy consequence operator. It is also known that the relation induced by a fuzzy consequence operator is a fuzzy preorder if such operator is coherent [7]. Fuzzy closing operators of mathem...

As an extension of the intuitionistic fuzzy set, intuitionistic trapezoidal fuzzy set is an invaluable mathematical theory to express uncertain phenomenon in our real word. In this article, the aggregation methods of the intuitionistic trapezoidal fuzzy information are chief researched. Firstly, the generalized aggregation operator is introduced for aggregating intuitionistic trapezoidal fuzzy ...

In this paper‎, ‎we study some properties of analytic extension of a $n$th roots of $M$-hyponormal operator‎. ‎We show that every analytic extension of a $n$th roots of $M$-hyponormal operator is subscalar of order $2k+2n$‎. ‎As a consequence‎, ‎we get that if the spectrum of such operator $T$ has a nonempty interior in $mathbb{C}$‎, ‎then $T$ has a nontrivial invariant subspace‎. ‎Finally‎, ‎w...

In this work we introduce the concept of a fusion operator for type-2 fuzzy sets as a mapping that takes m functions from [0, 1] to [0, 1] and brings back a new function of the same type. We study in depth the properties of pointwise fusion operators and representable fusion operators. Finally, we study the union and intersection of type2 fuzzy sets and we analyze when these functions are point...

Einstein product and Einstein sum are good alternatives to the algebraic product and algebraic sum, respectively. Nevertheless, it seems that in the literature there is little investigation on aggregation techniques using the Einstein operations on IFS for aggregating a collection of intuitionistic fuzzy value (IFV). The induced ordered weighted averaging operator is more suitable for aggregati...

This paper describes a comparative evaluation of two fuzzy-derived techniques for modelling fuel spray penetration in the cylinders of a diesel internal combustion engine. The first model is implemented using conventional fuzzy-based paradigm, where human expertise and operator knowledge were used to select the parameters for the system. The second model used an adaptive neuro-fuzzy inference s...

In this paper, we present the induced generalized intuitionistic fuzzy ordered weighted averaging (IGIFOWA) operator. It is a new aggregation operator that generalized the IFOWA operator, including all the characteristics of both the generalized IFOWA and the induced IFOWA operators. It provides a very general formulation that includes as special cases a wide range of aggregation operators for ...

With respect to multiple attribute decision making (MADM) problems in which the attribute value takes the form of intuitionistic trapezoidal fuzzy number, a new decision making analysis method is developed. Firstly, some operational laws and expected values of intuitionistic trapezoidal fuzzy numbers, and distance between two intuitionistic trapezoidal fuzzy numbers, are introduced, and the com...