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Author: Kiran Khatter
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 21
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Book Description
This paper discusses the trapezoidal fuzzy number(TrFN); Interval-valued intuitionistic fuzzy number(IVIFN); neutrosophic set and its operational laws; and, trapezoidal neutrosophic set(TrNS) and its operational laws. Based on the combination of IVIFN and TrNS, an Interval Valued Trapezoidal Neutrosophic Set (IVTrNS) is proposed followed by its operational laws. The paper also presents the score and accuracy functions for the proposed Interval Valued Trapezoidal Neutrosophic Number (IVTrNN). Then, an interval valued trapezoidal neutrosophic weighted arithmetic averaging (IVTrNWAA) operator is introduced to combine the trapezoidal information which is neutrosophic and in the unit interval of real numbers. Finally, a method is developed to handle the problems in the multi attribute decision making(MADM) environment using IVTrNWAA operator followed by a numerical example of NFRs prioritization to illustrate the relevance of the developed method.
Author: Kiran Khatter
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 21
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Book Description
This paper discusses the trapezoidal fuzzy number(TrFN); Interval-valued intuitionistic fuzzy number(IVIFN); neutrosophic set and its operational laws; and, trapezoidal neutrosophic set(TrNS) and its operational laws. Based on the combination of IVIFN and TrNS, an Interval Valued Trapezoidal Neutrosophic Set (IVTrNS) is proposed followed by its operational laws. The paper also presents the score and accuracy functions for the proposed Interval Valued Trapezoidal Neutrosophic Number (IVTrNN). Then, an interval valued trapezoidal neutrosophic weighted arithmetic averaging (IVTrNWAA) operator is introduced to combine the trapezoidal information which is neutrosophic and in the unit interval of real numbers. Finally, a method is developed to handle the problems in the multi attribute decision making(MADM) environment using IVTrNWAA operator followed by a numerical example of NFRs prioritization to illustrate the relevance of the developed method.
Author: Stephy Stephen
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book Description
In the real world problems, we are always dealing with uncertainty in almost all fields of approach. Neutrosophic sets helps us to deal with problems where inconsistent data are available. Application of Neutrosophic sets to real world problems, which are the generalized form of fuzzy sets is a platform where we can overcome this concept of uncertainty and obtain optimal results which can be relied on. In this paper, interval valued neutrosophic numbers are used to take into account the uncertainty in a still deeper way and Interval valued neutrosophic linear programming problem is solved with the help of the proposed ranking function and optimal results are obtained.
Author: Fahmi Aliya
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 25
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Book Description
The paper aims to give some new kinds of operational laws named as neutrality addition and scalar multiplication for the pairs of linguistic interval-valued intuitionistic neutrosophic fuzzy number. The main idea behind these operations is to include the linguistic interval-valued intuitionistic neutrosophic fuzzy number of the decision-maker and score function. We define the linguistic interval-valued intuitionistic neutrosophic fuzzy number and operational laws. We introduce the three geometric operators including, linguistic interval-valued intuitionistic neutrosophic fuzzy weighted geometric operator, linguistic interval-valued intuitionistic neutrosophic fuzzy ordered weighted geometric operator and linguistic interval-valued intuitionistic neutrosophic fuzzy weighted hybrid geometric operator.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 269
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Book Description
Neutrosophic theory and its applications have been expanding in all directions at an astonishing rate especially after of the introduction the journal entitled “Neutrosophic Sets and Systems”. New theories, techniques, algorithms have been rapidly developed. One of the most striking trends in the neutrosophic theory is the hybridization of neutrosophic set with other potential sets such as rough set, bipolar set, soft set, hesitant fuzzy set, etc. The different hybrid structures such as rough neutrosophic set, single valued neutrosophic rough set, bipolar neutrosophic set, single valued neutrosophic hesitant fuzzy set, etc. are proposed in the literature in a short period of time. Neutrosophic set has been an important tool in the application of various areas such as data mining, decision making, e-learning, engineering, medicine, social science, and some more.
Author: S. A. Edalatpanah
Publisher: Springer Nature
ISBN: 9819769728
Category :
Languages : en
Pages : 492
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Book Description
Author: Broumi, Said
Publisher: IGI Global
ISBN: 1668478374
Category : Mathematics
Languages : en
Pages : 386
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Book Description
Fuzzy sets have experienced multiple expansions since their conception to enhance their capacity to convey complex information. Intuitionistic fuzzy sets, image fuzzy sets, q-rung orthopair fuzzy sets, and neutrosophic sets are a few of these extensions. Researchers and academics have acquired a lot of information about their theories and methods for making decisions. However, only a small number of research findings discuss how neutrosophic sets theory and their extensions (NSTEs) are used in education. The Handbook of Research on the Applications of Neutrosophic Sets Theory and Their Extensions in Education implements fresh scientific approaches to enhance the quality of decisions under neutrosophic environments, particularly within education. Covering key topics such as data modeling, educational technologies, decision making, and learning management systems, this major reference work is ideal for instructional designers, researchers, academicians, scholars, practitioners, instructors, and students.
Author: Lawrence Chung
Publisher: Springer Science & Business Media
ISBN: 1461552699
Category : Computers
Languages : en
Pages : 458
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Book Description
Non-Functional Requirements in Software Engineering presents a systematic and pragmatic approach to `building quality into' software systems. Systems must exhibit software quality attributes, such as accuracy, performance, security and modifiability. However, such non-functional requirements (NFRs) are difficult to address in many projects, even though there are many techniques to meet functional requirements in order to provide desired functionality. This is particularly true since the NFRs for each system typically interact with each other, have a broad impact on the system and may be subjective. To enable developers to systematically deal with a system's diverse NFRs, this book presents the NFR Framework. Structured graphical facilities are offered for stating NFRs and managing them by refining and inter-relating NFRs, justifying decisions, and determining their impact. Since NFRs might not be absolutely achieved, they may simply be satisfied sufficiently (`satisficed'). To reflect this, NFRs are represented as `softgoals', whose interdependencies, such as tradeoffs and synergy, are captured in graphs. The impact of decisions is qualitatively propagated through the graph to determine how well a chosen target system satisfices its NFRs. Throughout development, developers direct the process, using their expertise while being aided by catalogues of knowledge about NFRs, development techniques and tradeoffs, which can all be explored, reused and customized. Non-Functional Requirements in Software Engineering demonstrates the applicability of the NFR Framework to a variety of NFRs, domains, system characteristics and application areas. This will help readers apply the Framework to NFRs and domains of particular interest to them. Detailed treatments of particular NFRs - accuracy, security and performance requirements - along with treatments of NFRs for information systems are presented as specializations of the NFR Framework. Case studies of NFRs for a variety of information systems include credit card and administrative systems. The use of the Framework for particular application areas is illustrated for software architecture as well as enterprise modelling. Feedback from domain experts in industry and government provides an initial evaluation of the Framework and some case studies. Drawing on research results from several theses and refereed papers, this book's presentation, terminology and graphical notation have been integrated and illustrated with many figures. Non-Functional Requirements in Software Engineering is an excellent resource for software engineering practitioners, researchers and students.
Author: Florentin Smarandache
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 10
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Book Description
In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.
Author: Amin Vafadarnikjoo
Publisher: Infinite Study
ISBN:
Category : Mathematics
Languages : en
Pages : 18
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Book Description
The analytic hierarchy process (AHP) is recognised as one of the most commonly applied methods in the multiple attribute decision-making (MADM) literature. In the AHP, encompassing uncertainty feature necessitates using suitable uncertainty theories, since dealing efficiently with uncertainty in subjective judgements is of great importance in real-world decision-making problems. The neutrosophic set (NS) theory and grey systems are two reliable uncertainty theories which can bring considerable benefits to uncertain decision-making. Thea im of this study is to improve uncertain decision-making by incorporating advantages of the NS and grey systems theories with the AHP in investigating sustainability through agility readiness evaluation in large manufacturing plants.
Author: Florentin Smarandache