We introduce bi-capacities as a natural generalization of capacities (or fuzzy measures) through the identity of Choquet integral of binary alternatives with fuzzy measures. We examine the underlying structure and derive the Möbius transform of bi-capacities. Next, the Choquet and Sugeno integrals w.r.t bicapacities are introduced. It is shown that symmetric and asymmetric integrals are recover...

Abstract: With respect to the interval neutrosophic multi-attribute decision-making (MADM) problems, the MADM method based on some interval neutrosophic aggregation operators is developed. Firstly, the induced generalized interval neutrosophic hybrid arithmetic averaging (IGINHAA) operator and the induced generalized interval neutrosophic hybrid geometric mean (IGINHGM) operator are proposed, w...

olds ( α̃, β̃ ) and interval valued fuzzy generalized bi-ideals with thresholds ( α̃, β̃ ) , which are generalization of interval valued fuzzy ideals, interval valued fuzzy interior ideals, interval valued fuzzy quasi ideals and interval valued fuzzy generalized bi-ideals, in a semigroup are introduced, and related properties are investigated. Characterizations of regular semigroups by the properti...

Abstract.With respect to interval-valued hesitant fuzzy multi-attribute decision making, this study first presents a new ranking method for interval-valued hesitant fuzzy elements. In order to obtain the comprehensive values of alternatives, two induced generalized interval-valued hesitant fuzzy hybrid operators based on the Shapley function are defined, which globally consider the importance o...

Hesitant fuzzy evaluation strategy related to the interval-valued membership and nonmembership degrees should be an appropriate choice due lack of experience, ability knowledge some decision experts. In addition, it is important reasonably model interrelationship these this work, firstly, generalized q-rung orthopair hesitant sets (GIVqROHFSs) are defined, operational rules with respect GIVqROF...

The fuzzy rough sets and generalized fuzzy rough sets have been extended by three pairs of fuzzy logical operators to deal with real-valued data for a variety of models. Three pairs of fuzzy logical operators are triangular norm or t-norm and its dual (t-conorm), residual implicator or R-implicator and its dual, fuzzy implicator and t-norm, which are frequently discussed in generalization model...