Multi-attribute decision-making (MADM) is commonly used to investigate fuzzy information effectively. However, selecting the best alternative not always symmetric because alternatives do have complete information, so asymmetric often involved. Expressing under uncertainty using closed subintervals of [0, 1] beneficial and effective instead crisp numbers from 1]. The goal this paper enhance noti...

The morphological gradient is a widely used edge detector for grey-level images in many applications. In this paper, we generalize the definition of the morphological gradient of the fuzzy mathematical morphology based on t-norms. Concretely, instead of defining the morphological gradient from the usual definitions of fuzzy dilation and erosion, where the minimum and the maximum are used, we de...

Uninorms as binary operations on the unit interval have been widely applied in the fuzzy set theory. This paper presents some 7 properties of uninorm-like operations for which the underlying operations are given by ordinal sums. If the underlying operations of a uninorm are given by ordinal sums, then the Cartesian product of the union of two arbitrary intervals (one in [0, e] and the other in ...

The triangular linguistic cubic fuzzy sets (TLCFSs) can express the data easily and is also very useful in modeling of uncertain decision making (DM) problems. First all, on basis Dombi t-norm t-conorm (DTT), we propose novel operational rules numbers (TLCFNs). We some new aggregation operators TLCFNs based newly developed operations, i.e., weighted averaging (TLCFDWA), geometric (TLCFDWG), ord...

In intelligent systems where fuzzy rule base and reasoning mechanism are applied, like fuzzy control systems, decision support and expert systems, one of the key issues is the problem of aggregation of information represented by membership functions. Since the pioneering work of Prof. Lotfi Zadeh [21] a great number of fuzzy connectives, aggregation operators have been introduced. The results o...

The OWA operators gained interest among researchers as they provide a continuum of aggregation operators able to cover the whole range of compensation between the minimum and the maximum. In some circumstances, it is useful to consider a wider range of values, extending below the minimum and over the maximum. ST-OWA are able to surpass the boundaries of variation of ordinary compensatory operat...

In this paper, a new method for merging multiple inconsistent knowledge bases in the framework of possibilistic logic is presented. We divide the fusion process into two steps: one is called the splitting step and the other is called the combination step. Given several inconsistent possibilistic knowledge bases (i.e. the union of these possibilistic bases is inconsistent), we split each of them...

We define some operations over Atanassov’s intuitionistic fuzzy sets (AIFSs), such as Einstein intersection, Einstein product, Einstein scalar multiplication and Einstein exponentiation, etc., and then define new concentration and dilation of AIFSs. These definitions will be useful while dealing with various linguistic hedges like “very”, “more or less”, “highly”, “very very” etc., involved in ...

Based on a new hesitant fuzzy partial ordering proposed by Garmendia et al.~cite{GaCa:Pohfs}, in this paper a fuzzy disjunction ${D}$ on the set ${H}$ of finite and nonempty subsets of the unit interval and a t-conorm ${S}$ on the set $bar{{B}}$ of equivalence class on the set of finite bags of unit interval based on this partial ordering are introduced respectively. Then, hesitant fuzzy negati...