As a fuzzy set extension, the hesitant set is effectively used to model situations where it is allowable to determine several possible membership degrees of an element to a set due to the ambiguity between different values. Some new hesitant fuzzy operational rules are introduced based on the Hamacher t-conorm and t-norm, whereby we present a multi attribute decision making method under hesitan...

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...

Let α1 be a formula from N5 logic, and let α2 be the formula that is obtained from α1 by replacing conjunction, disjunction and implication by respectively a t-norm ⊗, a t-conorm ⊕ and an implicator →. Noting that V − 2 (w, a) ∈ {0, 1} and V + 2 (w, a) ∈ {0, 1} for all a ∈ At and w ∈ {h, t}, it follows easily from the definitions (17)–(23) that V1(w,α1) = 1 iff V2(w,α2) = [1, 1], V1(w,α1) = 1 i...

The objective of this paper is to present and to evaluate the performance of particular fusion rules based on fuzzy T-Conorm/T-Norm operators for two tracking applications: (1) Tracking object’s type changes, supporting the process of objects’ identification (e.g. fighter against cargo, friendly aircraft against hostile ones), which, consequently is essential for improving the quality of genera...

Using the strength of a single-valued neutrosophic set (SVNS) with flexibility hesitant fuzzy (HFS) yields robust model named (SVNHFS). Due to ability utilize three independent indexes (truthness, indeterminacy, and falsity), an SVNHFS is efficient for optimization computational intelligence (CI) as well intelligent decision support system (IDSS). Taking advantage operational parameters in Domb...

Abstract The Pythagorean fuzzy sets are more robust than and intuitionistic in dealing with the problems involving uncertainty. To compare two sets, distance measures play a crucial role. In this paper, we have proposed some novel for using t-conorms. We also discussed their various desirable properties. With help of suggested measures, introduced new knowledge sets. Through numerical compariso...

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...

Fuzzy relations are mappings from pairs of elements into the interval [0, 1]. As a replacement for the complement operation one can use the mapping that sends x to 1 − x. Together with the concepts of t-norm and t-conorm a weak form of Boolean algebra can be defined. However, to our knowledge so far no notion of domain or codomain has been investigated for fuzzy relations. These might, however,...

The notion of S-fuzzy left h-ideals in a hemiring is introduced and it’s basic properties are investigated.We also study the homomorphic image and preimage of S-fuzzy left h-ideal of hemirings.Using a collection of left h-ideals of a hemiring, S-fuzzy left h-ideal of hemirings are established.The notion of a finitevalued S-fuzzy left h-ideal is introduced,and its characterization is given.S-fuz...

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...