Inequalities on Sasakian Statistical Manifolds in Terms of Casorati Curvatures

A statistical structure is considered as a generalization of a pair of a Riemannian metric and its Levi-Civita connection. With a pair of conjugate connections ∇ and ∇ * in the Sasakian statistical structure, we provide the normalized scalar curvature which is bounded above from Casorati curvatures on C-totally real (Legendrian and slant) submanifolds of a Sasakian statistical manifold of constant φ -sectional curvature. In addition, we give examples to show that the total space is a sphere.

Extensions of Probability Intuitionistic Fuzzy Aggregation Operators in Fuzzy MCDM/MADM

New family of intuitionistic fuzzy operators for aggregation of information on interactive criteria/attributes in Multi-Criteria/attributes Decision Making (MCDM/MADM) problems are constructed. New aggregations are based on the Choquet integral and the associated probability class of a fuzzy measure. Propositions on the correctness of the extension are presented. Connections between the operators and the compositions of dual triangular norms [Formula: see text] and [Formula: see text] are described. The conjugate connections between the constructed operators are considered. It is known that when interactions between criteria/attributes are strong, aggregation operators based on Choquet integral reflect these interactions at a certain degree, but these operators consider only consonant structure of criteria/attributes. New operators reflect interactions among all the combinations of the criteria/attributes in the fuzzy MCDM/MADM process. Several variants of new operators are used in the decision making problem regarding the assessment of software development risks.

Metallic conjugate connections

Properties of metallic conjugate connections are stated by pointing out their relation to product conjugate connections. We define the analogous in metallic geometry of the structural and the virtual tensors from the almost product geometry and express the metallic conjugate connections in terms of these tensors. From an applied point of view we consider invariant distributions with respect to the metallic structure and for a natural pair of complementary distributions, the above structural and virtual tensors are expressed in terms of O'Neill–Gray tensor fields.

Intuitionistic Fuzzy Probabilistic Aggregation Operators Based on the Choquet Integral: Application in Multicriteria Decision-Making

Associated Intuitionistic Fuzzy Probabilistic Averaging (As-IFPA) and Associated Intuitionistic Fuzzy Probabilistic Geometric (As-IFPG) operators based on the Choquet integral and an associated probability class of a fuzzy measure are constructed. Propositions on the correctness of the extensions are proved: (1) The As-IFPA (As-IFPG) operator for the fuzzy measure — capacity of order two coincides with the Intuitionistic Fuzzy Choquet Averaging (Intuitionistic Fuzzy Choquet Geometric) operator; (2) The As-IFPA (As-IFPG) operator coincides with the Intuitionistic Fuzzy Probabilistic Averaging (Intuitionistic Fuzzy Probabilistic Geometric) operator when a probability measure is used in the role of a fuzzy measure. Connections between the constructed operators and the compositions of dual triangular norms [Formula: see text] and [Formula: see text] are constructed. The conjugate connections between the constructed operators are shown. Two illustrative examples on the applicability of the As-IFPA and As-IFPG operators are presented. Several variants of the new operators (1) for the decision-making problem regarding the fiscal policy of a country; (2) for the decision-making problem regarding the best global supplier selection according to the core competencies of suppliers for a manufacturing company are used. Interactions and dependencies among all the combinations of the criteria in the decision-making process are considered.

Conjugate connections with respect to a quadratic endomorphism and duality

The goal of this paper is to consider the notion of conjugate connection in a unifying setting for both almost complex and almost product geometries, having as model the works of Mileva Prvanovic. A main interest is in finding classes of conjugate connections in duality with the initial linear connection; for example in the exponential case of almost complex geometry we arrive at a rule of quantization.