Operations Research, Systems Engineering and Industrial Engineering Commons^™

Shortest Path Problem Under Trapezoidal Neutrosophic Information, Florentin Smarandache, Said Broumi, Mohamed Talea, Assia Bakali

Branch Mathematics and Statistics Faculty and Staff Publications

In this research paper, a new approach is proposed for computing the shortest path length from source node to destination node in a neutrosophic environment. The edges of the network are assigned by trapezoidal fuzzy neutrosophic numbers. A numerical example is provided to show the performance of the proposed approach.

A Critical Path Problem Using Triangular Neutrosophic Number, Florentin Smarandache, Mai Mohamed, Yongquan Zhou, Mohamed Abdel-Baset

Branch Mathematics and Statistics Faculty and Staff Publications

The Critical Path Method (CPM) is one of several related techniques for planning and managing of complicated projects in real world applications. In many situations, the data obtained for decision makers are only approximate, which gives rise of neutrosophic critical path problem. In this paper, the proposed method has been made to find the critical path in network diagram, whose activity time uncertain. The vague parameters in the network are represented by triangular neutrosophic numbers, instead of crisp numbers. At the end of paper, two illustrative examples are provided to validate the proposed approach.

A Comparison Of Combined Overlap Block Fuzzy Cognitive Maps (Cobfcm) And Combined Overlap Block Neutrosophic Cognitive Map (Cobncm) In Finding The Hidden Patterns And Indeterminacies In Psychological Causal Models: Case Study Of Adhd, Hojjatollah Farahani, Florentin Smarandache, Lihshing Leigh Wang

Branch Mathematics and Statistics Faculty and Staff Publications

In spite of researchers’ concerns to find causalities, reviewing the literature of psychological studies one may argue that the classical statistical methods applied in order to find causalities are unable to find uncertainty and indeterminacies of the relationships between concepts.

In this paper, we introduce two methods to find effective solutions by identifying “hidden” patterns in the patients’ cognitive maps. Combined Overlap Block Fuzzy Cognitive Map (COBFCM) and Combined Overlap Block Neutrosophic Map (COBNCM) are effective when the number of concepts can be grouped and are large in numbers. In the first section, we introduce COBFCM, COBNCM, their applications, and …

Neutrosophic Precalculus And Neutrosophic Calculus, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis.

Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of indeterminate change.

The Neutrosophic Precalculus and Neutrosophic Calculus can be developed in many ways, depending on the types of indeterminacy one has and on the methods used to deal with such indeterminacy.

In this book, the author presents a few examples of indeterminacies and several methods to deal with these specific indeterminacies, but many other indeterminacies there exist in our everyday life, and they have to be studied …

Indeterminate Masses, Elements And Models In Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper at the beginning, we make a short history of the logics, from the classical Boolean logic to the most general logic of today neutrosophic logic. We define the general logic space and give the definition of the neutrosophic logic. Then we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses.

The best approach for dealing with such models is the neutrosophic logic, which is part of neutrosophy. Neutrosophic logic is connected with neutrosophic set and neutrosophic probability and statistics.

Neutrosophic Masses & Indeterminate Models Applications To Information Fusion, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper we introduce the indeterminate models in information fusion, which are due either to the existence of some indeterminate elements in the fusion space or to some indeterminate masses. The best approach for dealing with such models is the neutrosophic logic.

Fusion Of Imprecise Qualitative Information, Florentin Smarandache, Xinde Li, Xianzhong Dai, Jean Dezert

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, we present a new 2-tuple linguistic representation model, i.e. Distribution Function Model (DFM), for combining imprecise qualitative information using fusion rules drawn from Dezert-Smarandache Theory (DSmT) framework. Such new approach allows to preserve the precision and efficiency of the combination of linguistic information in the case of either equidistant or unbalanced label model. Some basic operators on imprecise 2-tuple labels are presented together with their extensions for imprecise 2-tuple labels. We also give simple examples to show how precise and imprecise qualitative information can be combined for reasoning under uncertainty. It is concluded that DSmT can deal …