On Rough Intuitionistic Fuzzy Ideals（Filters） in Lattices

In this paper, we introduce a new algebraic structure, called a rough intuitionistic fuzzy ideal(filter) which is a generalized intuitionistic fuzzy ideal(filter) of a lattice and study some related properties of such ideals(filters).

Implicative and Fuzzy Implicative Ideals of Lattice Implication Algebras

In this paper, we defined the concept of implicative and fuzzy implicative ideals of lattice implication algebras, and discussed the properties of them. And then, we pointed out the relations between implicative ideal and LI _ideal, implicative iedal and implicative filter, implicative ideal and fuzzy implicative ideal, fuzzy implicative ideal and fuzzy implicative filter, and fuzzy implicative ideal and fuzzy LI _ideal.

Fuzzy dot ideals and fuzzy dot H-ideals of BCH-algebras

The notions of fuzzy dot ideals and fuzzy dot H-ideals in BCH-algebras are introduced, several appropriate examples are provided, and their some properties are investigated. The relations among fuzzy ideal, fuzzy H-ideal, fuzzy dot ideal and fuzzy dot H-ideals in BCH- algebras are discussed, several equivalent depictions of fuzzy dot ideal are obtained. How to deal with the homomorphic image and inverse image of fuzzy dot ideals （fuzzy dot H-ideals） are studied. The relations between a fuzzy dot ideal （fuzzy dot H-ideal） in BCH-algebras and a fuzzy dot ideal （fuzzy dot H-ideal） in the product algebra of BCH-algebras are given.

The Pointwise Characterizations of Fuzzy Ideals and Fuzzy Prime Ideals

In this paper, the auther programs and discusses the fuzzy subrings, fuzzy ideals generated by fuzzy points.

Bipolar Valued Fuzzy α-Ideal of BF-Algebra

In the mathematical applications, ideal concepts are involved. They have been studied and analyzed in various ways. Already ideal and α-ideal concepts were discussed in BF-algebras. In this paper the idea of bipolar valued fuzzy α-ideal of BF algebra is proposed. The relationship between bipolar valued fuzzy ideal and bipolar valued fuzzy α-ideal is studied. Some interesting results are also discussed.

Some properties of fuzzy positive implicative ideals in a BCK-algebras

In this paper, we use the notion of fuzzy point to study ideal and positive implicative ideal in BCK algebras, then we clarify the links between the fuzzy point approach, the classical fuzzy approach and the ordinary case.

Fuzzy TOPSIS method to primary crusher selection for Golegohar Iron Mine(Iran)

Selection of the crusher required a great deal of design regarding to the mine planning. Selection of suitable primary crusher from all of available primary crushers is a multi-criterion decision making(MCDM) problem. The present work explores the use of technique for order performance by similarity to ideal solution(TOPSIS) with fuzzy set theory to select best primary crusher for Golegohar Iron Mine in Iran. Gyratory, double toggle jaw, single toggle jaw, high speed roll crusher, low speed sizer, impact crusher, hammer mill and feeder breaker crushers have been considered as alternatives. Also, the capacity, feed size, product size, rock compressive strength, abrasion index and application of primary crusher for mobile plants were considered as criteria for solution of this MCDM problem. To determine the order of the alternatives, closeness coefficient is defined by calculating the distances to the fuzzy positive ideal solution(FPIS) and fuzzy negative ideal solution(FNIS). Results of our work based on fuzzy TOPSIS method show that the gyratory is the best primary crusher for the studied mine.

Fuzzy rough sets in Sostak sense

In this paper,we defined the fuzzy operator Φ_(λ) in a fuzzy ideal approximation space(X,R,I)associated with a fuzzy rough set λ in Sostak sense.Associated with Φ_(λ),there are fuzzy ideal interior and closure operators int_(Φ)^(λ) and cl_(Φ)^(λ),respectively.r-fuzzy separation axioms,r-fuzzy connectedness and r-fuzzy compactness in fuzzy ideal approximation spaces are defined and compared with the relative notions in r-fuzzy approximation spaces.There are many differences when studying these notions related with a fuzzy ideal different from studying these notions in usual fuzzy approximation spaces.Lastly,using a fuzzy grill,we will get the same results given during the context.

Fuzzy Zorn’s lemma with applications

We introduced the fuzzy axioms of choice,fuzzy Zorn’s lemma and fuzzy well-ordering principle,which are the fuzzy versions of the axioms of choice,Zorn’s lemma and well-ordering principle,and discussed the relations among them.As an application of fuzzy Zorn’s lemma,we got the following results:(1)Every proper fuzzy ideal of a ring was contained in a maximal fuzzy ideal.(2)Every nonzero ring contained a fuzzy maximal ideal.(3)Introduced the notion of fuzzy nilpotent elements in a ring R,and proved that the intersection of all fuzzy prime ideals in a commutative ring R is the union of all fuzzy nilpotent elements in R.(4)Proposed the fuzzy version of Tychonoff Theorem and by use of fuzzy Zorn’s lemma,we proved the fuzzy Tychonoff Theorem.

Fuzzy Rough Ring and Its Properties

This paper is devoted to the theories of fuzzy rough ring and its properties. The fuzzy approximation space generated by fuzzy ideals and the fuzzy rough approximation operators were proposed in the frame of fuzzy rough set model. The basic properties of fuzzy rough approximation operators were analyzed and the consistency between approximation operators and the binarv operation of ring was discussed.

Fuzzy Ideals and Fuzzy Distributive Lattices

Our main objective is to study properties of a fuzzy ideals(fuzzy dual ideals).A study of special types of fuzzy ideals(fuzzy dual ideals) is also furnished.Some properties of a fuzzy ideals(fuzzy dual ideals) are furnished.Properties of a fuzzy lattice homomorphism are discussed.Fuzzy ideal lattice of a fuzzy lattice is defined and discussed.Some results in fuzzy distributive lattice are proved.

Some Characterizations of Left Weakly Regular Ordered Semigroups

In this paper, the notion of left weakly regular ordered semigroups is introduced. Furthermore, left weakly regular ordered semigroups are characterized by the properties of their left ideals, right ideals and （generalized） bi-ideals, and also by the properties of their fuzzy left ideals, fuzzy right ideals and fuzzy （generalized） bi-ideals.

On Fuzzy Interior Ideals in Semigroups

The concept of quasi-coincidence of a fuzzy interval value in an interval valued fuzzy set is a generalization of the quasi-coincidence of a fuzzy point in a fuzzy set. With this new concept, the interval valued （∈, ∈ Vq）-fuzzy interior ideal in semigroups is introduced. In fact, this kind of new fuzzy interior ideals is a generalization of fuzzy interior ideals in semigroups. In this paper, this kind of fuzzy interior ideals and related properties will be investigated. Moreover, the concept of a fuzzy subgroup with threshold is extended to the concept of an interval valued fuzzy interior ideal with threshold in semigroups.

Some Characterizations of Strongly Semisimple Ordered Semigroups

In this paper, the concept of quasi-prime fuzzy left ideals of an ordered semigroup S is introduced. Some characterizations of strongly semisimple ordered semigroups are given by quasi-prime fuzzy left ideals of S. In particular, we prove that S is strongly semisimple if and only if each fuzzy left ideal of S is the intersection of all quasi-prime fuzzy left ideals of S containing it.

Analysis of Supply Chain Sustainability Drivers in the Oil and Gas Industry under Covid-19 Pandemic

The supply chain of many industries,including Oil and Gas,was significantly affected by the disruption caused by the Covid pandemic.This,in turn,had a knock-on effect on other industries around the globe.Sustaining the impact of the disruption posed a major challenge for the industry.This study contributes to the existing literature by identifying and analyzing the most significant drivers that affected the sustainability of the Oil and Gas supply chain during the Covid pandemic.Fifteen drivers were identified based on an extensive literature review and a survey conducted with experts working in the Oil and Gas industry.Multi-criteria decision-making methodologies were used to analyze these drivers.The analysis from the fuzzy analytical hierarchy process found that the most important drivers for the sustainability of the Oil and gas supply chain during the pandemic were"Risk management capacity","Government regulation"and"Health and safety of employees".On the other hand,the driver"Community Pressure"was found to be of the least importance.Furthermore,the study integrated the results of the fuzzy analytical hierarchy process with the fuzzy technique for order of preference by similarity to ideal solution to calculate the supply chain sustainability index.A case example was demonstrated to rank the industries based on such calculations.This study can support the governmental institutions in benchmarking the Oil and Gas industry based on its sustainability index.Additionally,the outcomes of the study will help industrial decision makers prioritize the drivers the company should focus and devise strategies based on the priority to improve the sustainability of their supply chain during severe disruption.This will be crucial as the World health organization has cautioned that the world may encounter another pandemic in the near future.

S-fuzzy Version of Stone's Theorem for Distributive Lattices

In this paper,we initiate a study of S-fuzzy ideal(filter) of a lattice where S stands for a meet semilattice.A S-fuzzy prime ideal(filter) of a lattice is defined and it is proved that a S-fuzzy ideal(filter) of a lattice is S-fuzzy prime ideal(filter) if and only if any non-empty α-cut of it is a prime ideal(filter).Stone's theorem for a distributive lattice is extended by considering S-fuzzy ideals(filters).