On Pythagorean and Complex Fuzzy Set Operations

Complex fuzzy sets are the novel extension of Zadeh’s fuzzy sets. In this paper, we comprise the introduction to the concept of ξ -complex fuzzy sets and proofs of their various set theoretical properties. We define the notion of α , δ -cut sets of ξ -complex fuzzy sets and justify the representation of an ξ -complex fuzzy set as a union of nested intervals of these cut sets. We also apply this newly defined concept to a physical situation in which one may judge the performance of the participants in a given task. In addition, we innovate the phenomena of ξ -complex fuzzy subgroups and investigate some of their fundamental algebraic attributes. Moreover, we utilize this notion to define level subgroups of these groups and prove the necessary and sufficient condition under which an ξ -complex fuzzy set is ξ -complex fuzzy subgroup. Furthermore, we extend the idea of ξ -complex fuzzy normal subgroup to define the quotient group of a group G by this particular ξ -complex fuzzy normal subgroup and establish an isomorphism between this quotient group and a quotient group of G by a specific normal subgroup G A ξ .

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Extension of competition graphs under complex fuzzy environment

Complex & Intelligent Systems ◽

10.1007/s40747-020-00217-5 ◽

2020 ◽

Author(s):

Muhammad Akram ◽

Aqsa Sattar ◽

Faruk Karaaslan ◽

Sovan Samanta

Keyword(s):

Unit Circle ◽

Fuzzy Set ◽

Economic Competition ◽

Complex Fuzzy Set ◽

Fuzzy Environment ◽

Research Article ◽

Fuzzy Graphs ◽

Proposed Model ◽

Present Complex ◽

Phase Term

Abstract A complex fuzzy set (CFS) is a remarkable generalization of the fuzzy set in which membership function is restricted to take the values from the unit circle in the complex plane. A CFS is an efficient model to deal with uncertainties of human judgement in more comprehensive and logical way due to the presence of phase term. In this research article, we introduce the concept of competition graphs under complex fuzzy environment. Further, we present complex fuzzy k-competition graphs and p-competition complex fuzzy graphs. Moreover, we consider m-step complex fuzzy competition graphs, complex fuzzy neighborhood graphs (CFNGs), complex fuzzy economic competition graphs (CFECGs) and m-step complex fuzzy economic competition graphs with interesting properties. In addition, we describe an application in ecosystem of our proposed model. We also provide comparison of proposed competition graphs with existing graphs.

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PYTHAGOREAN FUZZY MULTI SET AND ITS APPLICATIONS IN FISH FEED FOR INDIAN MAJOR CARP

Advances in Mathematics: Scientific Journal ◽

10.37418/amsj.9.11.90 ◽

2020 ◽

Vol 9 (11) ◽

pp. 9803-9811

Author(s):

R. Sophia Porchelvi ◽

V. Jayapriya

Keyword(s):

Decision Making ◽

Fuzzy Set ◽

Fish Feed ◽

Uncertain Environments ◽

Pythagorean Fuzzy Set ◽

Indian Major Carp ◽

Set Operations ◽

Basic Set ◽

Decision Making Problem ◽

Exponential Distance

Pythagorean fuzzy set is an extension of Intutionistic fuzzy set, which is more capable of expressing and handling the uncertainty under uncertain environments, so that it was broadly applied in various fields. In this paper, we explored the concept of Pythagorean fuzzy multi set (PFMS). We describe some basic set operations of Pythagorean fuzzy multi set and also, we proposed sine exponential distance function. Finally, through an illustrative example it is shown how the proposed distance works in decision-making problem.

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An Inference Algorithm for Electronic System Diagnostics at the Block Diagram Level

Journal of Advanced Computational Intelligence and Intelligent Informatics ◽

10.20965/jaciii.2006.p0168 ◽

2006 ◽

Vol 10 (2) ◽

pp. 168-172

Author(s):

Celso Bation Co ◽

Keyword(s):

Fuzzy Set ◽

Block Diagram ◽

Algorithm Design ◽

Complete Information ◽

Electronic System ◽

Inference Algorithm ◽

Input Information ◽

Set Operations

Mathematical processes are designed to enable computers to emulate human inference in troubleshooting. Crisp set operations facilitate the interactive handling of incomplete but precise input information. Fuzzy set operations handle imprecise but complete information. The algorithm design we discuss here is limited to crisp set operations. We use diagnostics at the electronic system block diagram level to illustrate inference algorithm methodology. The algorithm deduces root causes and excludes intermediary causes in its conclusions. It also provides information for anticipating subsequent moves. We also consider results providing no conclusion, as is normally experienced by human troubleshooters under certain conditions.

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